WO2008116314A1 - Method and apparatus for determining differential group delay and polarization mode dispersion - Google Patents

Abstract

A method and apparatus for measuring at least one polarization-related characteristic of an optical path (FUT) uses a light input unit connected to the FUT at or adjacent a proximal end of the FUT and a light output unit connected to the FUT at or adjacent its proximal or distal end. The light input unit injects into the FUT at least partially polarized light having a controlled state of polarization (I-SOP). The output light unit extracts corresponding light from the FUT, analyzes and detects the extracted light corresponding to at least one transmission axis (A-SOP), and processes the corresponding electrical signal to obtain transmitted coherent optical power at each wavelength of light in each of at least two groups of wavelengths, wherein the lowermost (λ1) and uppermost (λu) said wavelengths in each said group of wavelengths are closely- spaced. A processing unit than computes at least one difference in a measured power parameter corresponding to each wavelength in a wavelength pair for each of the at least two groups, the measured power parameter being proportional to the power of the said analyzed and subsequently detected light, thereby defining a set of at least two measured power parameter differences; computes the mean-square value of said set of differences; and calculating the at least one polarization-related FUT characteristic as at least one predetermined function of said mean-square value, the predetermined function being dependent upon the small optical frequency difference between the wavelengths corresponding to the said each at least said two pairs of closely-spaced wavelengths.

Description

METHOD AND APPARATUS FOR DETERMINING DIFFERENTIAL GROUP DELAY AND POLARIZATION MODE DISPERSION

CROSS-REFERENCE TO RELATED DOCUMENTS

This application claims priority from United States Provisional patent application number 60/907,313 filed 28, March 2007 and United States Continuation-in-Part application number 11/727,759 filed 28 March 2007. The entire contents of each of these patent applications are incorporated herein by reference.

TECHNICAL FIELD

This invention relates to a method and apparatus for measuring polarization- dependent characteristics of optical paths and is especially applicable to the measurement of differential group delay (DGD) at a particular wavelength, or root-mean-square or mean DGD over a specified wavelength range, of an optical path which comprises mostly optical waveguide, such as an optical fiber link. When the specified wavelength range is sufficiently wide, the root-mean-square or mean DGD measurement closely approximates the polarization mode dispersion (PMD) behavior of the optical path.

BACKGROUND ART

Orthogonal polarization modes in optical fibers used for optical communications systems have different group delays; known as differential group delay (DGD). This causes the polarization mode dispersion (PMD) phenomenon, i.e., a spreading of the pulses propagating along the fibers. Where long optical fiber links are involved, an overall PMD may be sufficient to cause increased bit error rate, thus limiting the transmission rate or maximum transmission path length. This is particularly problematical at higher bit rates. Thus, it is desirable to be able to obtain the PMD value of the optical fiber. If one knows the actual PMD value of a communications link, one can accurately estimate the bit error rate or outage probability (probability that the communication will fail over a period of time), or the power penalty (how much more power must be launched to maintain the same bit error rate as if there were no PMD). As a variable or quantity characterizing the said PMD phenomenon, the PMD value of a device is defined as either the root-mean-square (rms) value or mean value of DGD, the DGD of a given device being a variable that can vary randomly over both wavelength and time. (For simplicity in the text that follows, "average DGD" will sometimes be used when either rms or mean DGD definitions may apply.)

Depending on the application, it is often desirable to measure the DGD at a given wavelength, average DGD over a narrow wavelength range, and average DGD over a wide wavelength range. However, in many cases, it is not possible to measure the DGD at a given wavelength or average DGD over a wide wavelength range, and hence it is not possible to obtain a reliable determination of the PMD from a measurement taken at a given moment.

This is the case, for example, when measuring "PMD" in a narrow bandpass channel of a fiber link, such as when the measurement can only be taken using an available DWDM channel, having a usable bandwidth of, for instance ~70GHz (corresponding to 100GHz DWDM channel spacing) or ~35GHz (corresponding to 50GHz channel spacing).

"In-band" DGD or average DGD measurements for a given small wavelength range within the channel are of particular importance for telecom network providers using DWDM networks. For instance, it may be desired to add one or more very high bit rate channels (e.g. 40Gbps) to a "dark" channel on an active telecommunications fiber link already carrying multiple lower bit rate channels (e.g. lOGbps). On account of the tighter PMD tolerances at the higher bitrates, it is often necessary to characterize the fiber link, or at least the dark channel that will actually be used, for its suitability to adequately transport such high bitrate traffic, and this characterization must not at the same time disrupt the active lower bitrate channels.

Ideally, the characterization of a single narrow channel should be repeated at intervals over a long time period since there is little or no latitude to undertake an average of the measured DGD over with respect to wavelength. If the goal is to measure the PMD of the fiber link itself, despite the fact that the DWDM multiplexers / demultiplexers are attached to it, it is desirable to perform the in-band measurement in as many dark channels as may be available. A number of approaches are known in the art for both the measurement of (end- to-end) PMD in a "broadband" (i.e. unfiltered) fiber link and the measurement of DGD in a narrow-band channel on a fiber.

The phase shift method, taught in Jones (US4,750,833 [4]), can be used for the measurement of PMD. As described by Williams et al. (Proceedings SOFM, Boulder CO, 1998, pp. 23-26[5]), it can also be used for measurement of DGD in a narrowband channel. However, the method as described is inherently slow, as it entails maximizing the measured phase-shift difference by adjustment of polarization controllers, and is hence not suitable for outside-plant applications where fibers may be subject to relatively rapid movement.

The "pulse-delay method" of PMD measurement can measure DGD at a given wavelength by launching short light pulses into the fast and slow polarization modes of the fiber and measuring the difference between arrival times of the light pulses emerging from the corresponding output principle states, but it requires the use of high-speed electronic circuitry. PMD may be measured or estimated using polarization-scrambled short light pulses based on detection of arrival time for the polarization-scrambled short light pulses, such as described by Noe et al (J. Lightwave Technology, Vol.20(2), 2002, pp. 229-235[6]). However, this technique not only requires a high-speed electronics detection system but also involves rapidly-modulated light for the measurement. Measurement apparatus for in-band monitoring using actual telecommunications live traffic, as described by Yao (US 2005/020175 Al [7]) or by Boroditsky et al (US7256876) and Wang et al (J. Lightwave Technology, Vol.24(l l), 2006, pp. 4120- 4126[8]), permit direct determination of the PMD penalty (i.e. the extra system margin required to compensate for PMD impairment for the particular live traffic). However, they do not permit determination of the in-band DGD or "PMD" value of the link. Indeed, these in-band monitoring methods have advantage for DOP or SOP monitoring in the presence of the high bit rate carrier signals. Waarts et al (US 7,203,428, April 10, 2007 [9]) describe estimation of PMD using heterodyne detection with a tunable laser source, where a signal from a local oscillator (i.e. tunable laser source) is combined with an optical signal from the link and the beat frequency amplitude and phase are then analyzed for two orthogonal polarization state simultaneously to obtain a SOP. Thus, "PMD" may be estimated from the averaging of a plurality of SOPs. However, again this measurement may only give DOP or SOP information. This method also needs high speed electronics as well as an additional high coherence light source for the detection.

The use of high-speed electronics may be avoided by using a nonlinear detection technique, as described by Wielandy et al (J. Lightwave Technology, Vol.22(3), 2004, pp. 784-793 [10]), but it will complicate the design of the instrument.

It should be noted that the above described DOP or SOP measurement technique may also be affected by amplified spontaneous emission (ASE), fiber nonlinearities, etc. (N. Kikuchi, Journal of Lightwave Technology, Vol. 19(4), 2001, pp. 480-486 [11])). Its sensitivity to the ASE etc. is an important issue because most long fiber links are likely to use optical amplifiers, either EDFAs (erbium-doped fiber amplifiers) or Raman optical amplifiers. Moreover, the DGD range measurable using the SOP or DOP analysis method is limited.

The fixed analyzer (or equivalently, wavelength scanning) method, as described by CD. Poole et al (J. Lightwave Technology, Vol. 12 (6), 1994, pp. 917-929 [I]), was one of the first methods applied for PMD measurement. It provides limited accuracy for small PMD values even when a large wavelength range is used or for measuring PMD using small wavelength range. Moreover, it may not provide wavelength-dependent DGD information. Consequently, it is also unsuitable for measurement of narrowband channels.

The generalized interferometric method, as described by Cyr J. Lightwave Technology, Vol. 22(3), 2004, pp. 794-805 and US7,227,645 [2,3], the latter commonly owned with the present invention, provides accurate PMD measurement (corresponding to the spectral width of the broadband source), but is also unable to provide the DGD as a function of wavelength, and is not well suited for use in a narrowband channel.

Thus, currently potentially-available DGD or PMD measurement techniques adapted to measure DGD or PMD in a narrow-band individual channel of a DWDM systems will be either inherently expensive, be unreliable, have a limited dynamic range, or may introduce instabilities in rapid gain equalizers that are often found with reconfigurable optical add-drop multiplexers (ROADMs) and optical amplifiers. Thus, their realization as a viable commercial instrument is difficult. Accordingly, there is a need for a new improved method for enabling reliable, modest cost, and high accuracy measurement and monitoring of an in-band DGD value.

Depending upon the application, embodiments of this method should be able to respond to the need for "moderate-speed" monitoring (update speed ~ls) or "high-speed" monitoring (update speed ~1 ms).

Moreover, for reasons of convenience and operational expenses when characterizing a fiber, it is sometimes desirable to be able to measure the overall PMD of optical fiber from one end only, but currently most developed methods for carrying out such measurements in the fields are "two-ended", i.e. a special polarized source must be used at one (proximal) end and the analysis equipment at the other (distal) end [1,3]. A reliable and practical "single-ended" measurement method would be advantageous in terms of technician traveling and logistics and because no specialized sources or other equipment would need to be placed at the distal end. It might/would also be desirable to able to use much the same technique or instrument to make either single-end or two-end measurements.

It is known to use a so-called single-end PMD measurement technique to measure total PMD for fibers by accessing only one end of a FUT [12-14,17]. Basically, the simplest single-end PMD measurement comprises a CW tunable laser [12,17] or pulse tunable laser [14] having a polarization controller (or polarization state generator) or polarizer between its output and the FUT and has an analyzer to analyze the corresponding backreflected light. Usually the CW light from the tunable CW laser or pulsed light pulse from the tunable pulse laser is sent into the FUT and the backreflected light from the localized reflection (such as Fresnel reflection) at the distal end of the FUT is analyzed to obtain the total PMD value of the FUT. Although single-end PMD measurement concepts and approaches have been put forward previously, their realization as a viable commercial instrument for single-end PMD measurement is difficult. This difficulty arises because test and measurement instruments based on such concepts will either be not very reliable, or be very expensive, or have a long acquisition time, or require the fiber to be very stable over long periods (i.e. not robust), or have a very limited dynamic range.

For example, for most single-end PMD measurement techniques [12-16], the fiber-under-test (FUT) should not move during the measurement. As is also the case with the conventional fixed-analyzer method [13,15], any fiber movement will affect the number of extrema (i.e. maxima and minima) so that it may wrongly estimate the PMD value. Any power variation in backreflected light from the FUT for the single-end version of the fixed-analyzer method may also result in wrong estimates of DGD (or PMD). Unfortunately, such stability of the FUT throughout the time period over which all of the data are measured cannot be assured, especially where the DGD/PMD of an installed fiber is being measured.

Also, a fixed analyzer method as described in references [13,15] not only entails a strict requirement to restrict fiber movement, but also has one major potential drawback with respect to measurement reliability because the method measures fiber absolute loss only (not a normalized light power or transmission) using only one detector without considering other potential factors, such as fiber spectral attenuation, spectral loss of related components used for an instrument, or wavelength dependent gain of the detector. For example, if spectral attenuation of fibers is not taken into account, error or uncertainty in the measurement results may be introduced, especially for fibers having significant spectral variation (versus wavelength) as is often observed with older fiber cables.

In addition, among those known techniques using a CW light source, whether a broadband source or a tunable laser [12,13,17], the measured results may not be reliable because the backreflected light may comprise a significant contribution from Rayleigh backscattering, as well as any spurious localized reflections from connectors, etc. not located at the distal end of the FUT. The Rayleigh contribution grows significantly with fiber length whereas the reflected light intensity from the localized reflection(s) (such as Fresnel reflection at the distal end of FUT) decreases with fiber length, thus rendering a CW-light-source method impractical for the multi-kilometer FUT lengths of interest in most telecommunications applications.

Hence, although presently-known techniques meeting the above-mentioned requirements may permit a reasonably successful measurement of DGD/PMD to be made, at present their scope of application and performance would be insufficient for a commercially- viable, stand-alone instrument. Thus, known techniques and instruments, as discussed, for example, in references

[12-17], cannot readily be adapted to develop a robust, reliable and cost effective commercial single-end PMD test and measurement instrument. To measure total or overall PMD accurately from only one end of a fiber link, currently available techniques and concepts reported in the literature have significant limitations as described above.

Furthermore, as also explained in commonly-owned US patent No. 6,724,469 (Leblanc) [18], in optical communication systems, an unacceptable overall polarization mode dispersion (PMD) level for a particular long optical fiber may be caused by one or more short sections of the optical fiber link. Where, for example, a network service provider wishes to increase the bit rate carried by an installed optical fiber link, say up to

40 Gb/s, it is important to be able to obtain a distributed measurement of PMD, i.e., obtain the PMD information against distance along the fiber, and locate the singularly bad fiber section(s) so that it/they can be replaced - rather than replace the whole cable.

Accordingly, Leblanc discloses a method of measuring distributed PMD which uses a polarization OTDR, to identify high or low PMD fiber sections, but does not provide a real quantitative PMD value for the FUT. Consequently, because of its inherently "qualitative" nature, Leblanc' s technique is not entirely suitable for development as a commercial single-end overall PMD testing instrument that may measure the total PMD value for the entire of fiber link. It is known to use a so-called polarization-sensitive optical time domain reflectometer (POTDR; also commonly referred to as a "Polarization optical time domain reflectometer") to try to locate such "bad" sections. Basically, a POTDR is an optical time domain reflectometer (OTDR) that is sensitive to the state of polarization (SOP) of the backreflected signal. Whereas conventional OTDRs measure only the intensity of backreflected light to determine variation of attenuation along the length of an optical path, e.g., an installed optical fiber, POTDRs utilize the fact that the backreflected light also exhibits polarization dependency in order to monitor polarization dependent characteristics of the transmission path. Thus, the simplest POTDR comprises an OTDR having a polarizer between its output and the fiber-under-test (FUT) and an analyzer in the return path, between its photodetector and the FUT. (It should be appreciated that, although a typical optical transmission path will comprise mostly optical fiber, there will often be other components, such as couplers, connectors, etc., in the path. For convenience of description, however, such other components will be ignored, it being understood, however, that the term "FUT" used herein will embrace both an optical fiber and the overall transmission path according to context.) Generally, such POTDRs can be grouped into two classes or types. Examples of the first type of POTDR are disclosed in the documents [19-24].

The first type of POTDR basically measures local birefringence (1 /beat-length) as a function of distance z along the fiber, or, in other words, distributed birefringence. Referring to the simple and well-known example of a retardation waveplate, birefringence is the retardation (phase difference) per unit length between the "slow" and "fast" axes, hi other words, the retardation is the birefringence times the thickness of the waveplate. This is not a PMD measurement, though that is a common misconception. First, in a simplified picture, DGD(z) is the derivative, as a function of optical frequency (wavelength), of the overall retardation of the fiber section extending from O to z. Second, a long optical fiber behaves as a concatenation of a large number of elementary "waveplates" for which the orientations of the fast and slow axes, as well as the retardation per unit length, vary randomly as a function of distance z.

Accordingly, DGD(z) is the result of a complicated integral over all that lies upstream that exhibits random birefringence and random orientation of the birefringence axis as a function of z, whereas birefringence is the retardation per unit length at some given location. Additionally, as mentioned above, the derivative, as a function of optical frequency, of such integral must be applied in order to obtain DGD as per its definition.

A general limitation of techniques of this first type, therefore, is that they do not provide a direct, reliable, valid in all cases and quantitative measurement of PMD with respect to distance along the optical fiber. Instead, they measure local birefringence (or beat-length) and/or one or more related parameters and infer the PMD from them based notably on assumptions about the fiber characteristics and specific models of the birefringence. For instance, they generally assume a relationship between PMD and local values of the birefringence and so-called coupling-length (or perturbation-length), which is not necessarily valid locally even when it is valid on average.

As an example, such techniques assume that fibers exhibit exclusively "linear" birefringence. If circular birefringence is indeed present, it is "missed" or not seen, because of the properties of a round trip through the fiber (OTDR technique). Notably, correct measurement of modern "spun fibers" already requires assumptions to be made about their behavior, and consequently is not acceptable for a commercial instrument. As a second example, the birefringence and other parameters must be measured accurately throughout the length, even in sections where the local characteristics of the fiber do not satisfy the assumed models and conditions; otherwise, the inferred PMD of such sections, which is an integral over some long length, can be largely misestimated, even qualitatively speaking. In practice, although they can measure birefringence quantitatively (c/ F. Corsa et al. [\9]supra), or statistically screen high birefringence sections (Chen et al. [23] supra),oτ obtain qualitative and relative estimates of the PMD of short sections provided that one accepts frequently-occurring exceptions (Leblanc [18], Huttner [22], supra), POTDR techniques of this first type cannot reliably and quantitatively measure PMD, particularly of unknown, mixed installed fibers in the field. Furthermore, they are incapable of inferring, even approximately, the overall PMD of a long length of fiber, such as for example 10 kilometers.

Fayolle et al. [24] (supra) claim to disclose a technique that is "genuinely quantitative, at least over a given range of polarization mode dispersion". However, this technique also suffers from the fundamental limitations associated with this type, as mentioned above. In fact, while their use of two SOPs (45° apart) with two trace variances might yield a modest improvement over the similar POTDRs of the first type (e.g., Chen et al.'s [23], whose VOS is essentially the same as Fayolle et α/.'s [24] trace variance), perhaps by a factor of 4Ϊ , it will not lead to a truly quantitative measurement of the PMD with respect to distance along the FUT with an acceptable degree of accuracy. It measures a parameter that is well-known to be related or correlated with beat-length (birefringence), but not representative of the PMD coefficient. Indeed, even the simulation results disclosed in Fayolle et al.'s specification indicate an uncertainty margin of 200 per cent.

It is desirable to be able to obtain direct, quantitative measurements of PMD, i.e., to measure the actual cumulative PMD at discrete positions along the optical fiber, as if the fiber were terminated at each of a series of positions along its length and a classical end-to-end PMD measurement made. This is desirable because the parameter that determines pulse-spreading is PMD, not birefringence. If one knows the actual PMD value of a communications link one can determine, accurately, the bit error rate or outage probability (probability that the communication will fail over a period of time), or the 5 power penalty (how much more power must be launched to maintain the same bit error rate as if there were no PMD).

(In this specification, the term "cumulative PMD" is used to distinguish from the overall PMD that is traditionally measured from end-to-end. Because PMD is not a localized quantity, PMD(z) is an integral from 0 to z, bearing resemblance to a o cumulative probability rather than the probability distribution. When distance z is equal to the overall length of the FUT, of course, the cumulative PMD is equal to the overall PMD.)

The second type of known POTDR is dedicated specifically to PMD measurement. This type does not suffer from the above-mentioned fundamental5 limitations of the first type of POTDR and so represents a significant improvement over them, at least in terms of PMD measurement. It uses the relationship between POTDR traces obtained at two or more closely-spaced wavelengths in order to measure PMD directly at a particular distance z, i.e., cumulative PMD, with no need for any assumption about the birefringence characteristics of the fibers, no need for an explicit or implicit o integral over length, no missed sections, no problem with spun fibers, and so on. Even the PMD of a circularly birefringent fiber or a section of polarization-maintaining fiber (PMF) is measured correctly. In contrast to implementations of the first type, there is no need to invoke assumptions and complicated models in order to infer PMD qualitatively. Thus, measurement of cumulative PMD as a function of distance z along the 5 fiber, and its corresponding slope (rate of change of PMD with distance), as allowed by a

POTDR of this second type, facilitates reliable identification and quantitative characterization of those singular, relatively-short "bad" sections described hereinbefore.

Most known POTDR techniques of this second type rely upon there being a deterministic relationship between the OTDR traces obtained with a small number of0 specific input-SOPs and output polarization analyzer axes, as disclosed, for example, in US patent No. 6,229,599 (Galtarossa) [16] and articles by H. Sunnerud et al [14,15]. This requires the FUT to be spatially stable throughout the time period over which all of the traces are measured. Unfortunately, such stability cannot be assured, especially where an installed fiber is being measured.

In addition, known techniques of the second type require the use of short pulses; 5 "short" meaning shorter than the beat length and coupling length of any section of the FUT. hi order for them to measure PMD in fibers properly, without being limited to fibers of short beat length, they must use OTDR optical pulse widths of typically less ~10 ns. Unfortunately, practical OTDRs do not have a useful dynamic range with such short pulses. On the other hand, if a long light pulse is used, only fibers having long beat o lengths can be measured, which limits these techniques, overall, to measurement of short distances and/or with long measurement times, or to fibers with large beat length (typically small PMD coefficient). Hence, although it might be possible, using known techniques and meeting the above-mentioned requirements, to make a reasonably successful measurement of PMD, at present their scope of application and performance5 would be insufficient for a commercially- viable, stand-alone instrument.

In addition, the use of short pulses exacerbates signal-to-noise ratio (SNR) problems due to so-called coherence noise that superimposes on OTDR traces and is large when short pulses are used. It is due to the fact that the power of the backreflected light is not exactly the sum of powers emanating from each element (dz) of the fiber. o With a coherent source such as a narrowband laser, as used in POTDR applications, there is interference between the different backscattering sources. This interference or coherence noise that is superimposed on the ideal trace (sum of powers) is inversely proportional to both the pulse width (or duration) and the laser linewidth. It can be decreased by increasing the equivalent laser linewidth, i.e., the intrinsic laser linewidth as5 such, or, possibly, by using "dithering" or averaging traces over wavelength, but this reduces the maximum measurable PMD and hence may also limit the maximum length that can be measured, since PMD increases with increasing length. Roughly speaking, the condition is PMD»Linewidth < 1 (where the linewidth is in optical frequency units); otherwise the useful POTDR signal is "washed out" by depolarization. 0 It would be desirable, therefore, for there to be a technique to quantitatively measure cumulative PMD using pulses whose length could be greater than the beat length of the FUT (for high dynamic range, while maintaining a satisfactory spatial resolution), without stringent requirements regarding the stability of the FUT or making assumptions about the fiber behavior (e.g. strong mode coupling). hi summary, there is a need for a new method for characterizing such polarization-dependent characteristics of optical paths that is inherently robust to fiber movement and perturbations found in field conditions, and does not require expensive and cumbersome polarization optics. Preferably, this basic method should underlie several different embodiments that are particularly well suited for either or both of single- ended and two-ended measurements of DGD within a narrow DWDM channel, DGD at multiple wavelengths, PMD and cumulative PMD as a function of distance along a fiber link.

SUMMARY OF THE INVENTION

The present invention seeks to eliminate, or at least mitigate, the disadvantages of the prior art discussed above, or at least provide an alternative.

According to a first aspect of the invention, there is provided a method of measuring at least one polarization-related characteristic of an optical path (FUT) using light input means connected to the optical path at or adjacent a proximal end thereof, and light output means connected to the optical path at or adjacent either the proximal end thereof or a distal end thereof, the light input means comprising light source means for supplying at least partially polarized light and means for controlling the state of polarization (I-SOP) of said at least partially polarized light and injecting said light into the FUT, and output light means comprising means for extracting corresponding light from the FUT, analyzing means for analyzing the extracted light and detection means for detecting the analyzed light corresponding to the at least one transmission axis of the analyzer means (A-SOP) to provide transmitted coherent optical power at each wavelength of light in each of at least two groups of wavelengths, wherein the lowermost (X₁) and uppermost (λu) said wavelengths in each said group of wavelengths are closely- spaced and wherein the following three conditions are not all concomitantly met: a. the source and detection means are at the same end of the FUT; b. only one detector in the analyzing and detecting means is used; c. the light from the light source comprises principally temporal pulses having a spatial extent more than ten times the beat length of the FUT; and wherein the said group comprises a wavelength pair, said pair in each group corresponding to a small optical-frequency difference and defining a midpoint 5 wavelength therebetween, and wherein the I-SOP and A-SOP are substantially constant for each said wavelength in each said group, and wherein at least one of the midpoint wavelength, I-SOP and A-SOP is different between the respective said groups, the method including the steps of: i. Computing the at least one difference in a measured power parameter o corresponding to each wavelength in said wavelength pair for each of the said at least two groups, said measured power parameter being proportional to the power of the said analyzed and subsequently detected light, thereby defining a set of at least two measured power parameter differences; ii. Computing the mean-square value of said set of differences; and 5 iii. Calculating the at least one polarization-related FUT characteristic as at least one predetermined function of said mean-square value, said predetermined function being dependent upon the said small optical frequency difference between the wavelengths corresponding to the said each at least said two pairs of closely-spaced wavelengths; and o iv. outputting the valve of said at least one polarization-related FUT characteristic.

For two-end measurement, the said output light means may be connected to the FUT at or adjacent the distal end of the FUT.

Preferably, for measurement of DGD at a specified wavelength, for example, for narrow DWDM channel measurement, each said group comprises wavelength pairs5 having substantially said prescribed midpoint wavelength, and the said at least one polarization-related FUT characteristic is the differential group delay (DGD) at the said midpoint wavelength.

The said measured power parameter may be the computed normalized power T(y) , and said predetermined function can be expressed, for small optical-frequency0 differences (δυ), according to the following differential formula:

9 where the constant a ^ = J— , and υ is the optical frequency corresponding to the said

midpoint wavelength.

According to a second aspect of the invention, there is provided measurement 5 instrumentation, for measuring at least one polarization-related characteristic of an optical path (FUT), comprising: input light means for connection to the optical path at or adjacent a proximal end thereof, and output light means for connection to the optical path at or adjacent either the l o proximal end thereof or a distal end thereof for extracting, analyzing and detecting light that has travelled at least part of the FUT and providing corresponding electrical signals, and processing means for processing the electrical signals from the output light means to determine said at least one polarization-related characteristic; 15 the input light means comprising: light source means for supplying at least partially polarized light at each wavelength in at least two groups of wavelengths, and SOP controller means for controlling the state of polarization (I-SOP) of said at least partially polarized light and injecting said light into the FUT, 20 wherein the lowermost (λi) and uppermost (λu) of said wavelengths in each said group of wavelengths are closely-spaced, the said group comprises a wavelength pair, said pair in each group corresponding to a small optical-frequency difference and defining a midpoint wavelength therebetween, and

25 the SOP of the injected light and A-SOP are substantially constant for each said wavelength in each said group, and wherein at least one of the midpoint wavelength, I-SOP and A-SOP is different between the respective said groups, and the output light means comprising: extraction and analysis means for extracting corresponding light from the FUT and analyzing the extracted light, and detection means for detecting the analyzed light corresponding to at least one transmission axis of the analyzer means (A-SOP) to provide transmitted coherent optical power at each wavelength of the analyzed light in each of said at least two groups of wavelengths, wherein the lowermost (X₁) and uppermost (λu) said wavelengths in each said group of wavelengths are closely-spaced and wherein the following three conditions are not all concomitantly met: d. the source and detection means are at the same end of the FUT; e. only one detector in the analyzing and detecting means is used; f. the light from the light source comprises principally temporal pulses having a spatial extent more than ten times the beat length of the FUT; the processing means being configured and operable for : v. computing the at least one difference in a measured power parameter corresponding to each wavelength in said wavelength pair for each of the said at least two groups, said measured power parameter being proportional to the power of the said analyzed and subsequently detected light, thereby defining a set of at least two measured power parameter differences; vi. computing the mean-square value of said set of differences; and vii. calculating the at least one polarization-related FUT characteristic as at least one predetermined function of said mean-square value, said predetermined function being dependent upon the said small optical frequency difference between the wavelengths corresponding to the said each at least said two pairs of closely- spaced wavelengths; and viii. outputting the value of said at least one polarization-related FUT characteristic for display, transmission or further processing.

According to a third aspect of the invention, there is provided light source apparatus for successively and repetitively generating coherent light at two or more closely spaced wavelengths, the apparatus comprising: an optical gain medium; at least two laser cavities, each cavity sharing a portion of their respective laser cavities, including the said optical gain medium; at least one output coupler permitting extraction of a fraction of the intra- cavity light corresponding to each said at least two laser cavities; a beam splitter for dividing the light into at least two spatially separated portions, each said at least two laser cavities corresponding to at least one of said at least two portions; a multichannel wavelength tunable bandpass filter means comprising at least two channels corresponding to different closely-spaced wavelengths, operable to accept light corresponding to each of the said at least two spatially separated portions into respective channels, and operable to wavelength tune the said channels in a synchronized manner; and a multichannel light blocking means, operable to permit the continuation of the optical path of not more than one said spatially separated light portions incident upon it and blocking all of the other light portions, the choice of light portion which is not blocked depending upon a parameter of the said multichannel light blocking means.

Effective for the United States of America designation, according to an aspect of the invention, there is provided a method of measuring at least one polarization-related characteristic of an optical path (FUT) using light input means connected to the optical path at or adjacent a proximal end thereof, and light output means connected to the optical path at or adjacent either the proximal end thereof or a distal end thereof, the light input means comprising light source means for supplying at least partially polarized light and means for controlling the state of polarization (I-SOP) of said at least partially polarized light and injecting said light into the FUT, and output light means comprising means for extracting corresponding light from the FUT, analyzing means for analyzing the extracted light and detection means for detecting the analyzed light corresponding to the at least one transmission axis of the analyzer means (A-SOP) to provide transmitted coherent optical power at each wavelength of light in each of at least two groups of wavelengths, wherein the lowermost (λ_\) and uppermost (λu) said wavelengths in each said group of wavelengths are closely-spaced; and wherein the said group comprises a wavelength pair, said pair in each group corresponding to a small optical-frequency difference and defining a midpoint wavelength therebetween, and wherein the I-SOP and A-SOP are substantially constant for each said wavelength in each said group, and wherein at least one of the midpoint 5 wavelength, I-SOP and A-SOP is different between the respective said groups, the method including the steps of: ix. computing the at least one difference in a measured power parameter corresponding to each wavelength in said wavelength pair for each of the said at least two groups, said measured power parameter being proportional to the o power of the said analyzed and subsequently detected light, thereby defining a set of at least two measured power parameter differences; x. computing the mean-square value of said set of differences; and xi. calculating the at least one polarization-related FUT characteristic as at least one predetermined function of said mean-square value, said predetermined function5 being dependent upon the said small optical frequency difference between the wavelengths corresponding to the said each at least said two pairs of closely- spaced wavelengths.

Also effective for the United States of America designation, according to another aspect of the invention there is provided measurement instrumentation, for measuring at o least one polarization-related characteristic of an optical path (FUT), comprising: input light means for connection to the optical path at or adjacent a proximal end thereof, and output light means for connection to the optical path at or adjacent either the proximal end thereof or a distal end thereof for extracting, analyzing and detecting light5 that has travelled at least part of the FUT and providing corresponding electrical signals, and processing means for processing the electrical signals from the output light means to determine said at least one polarization-related characteristic; the light input means comprising 0 light source means for supplying at least partially polarized light at each wavelength in at least two groups of wavelengths, and SOP controller means for controlling the state of polarization (I-SOP) of said at least partially polarized light and injecting said light into the FUT, wherein the lowermost (λi) and uppermost (λu) of said wavelengths in each said group of wavelengths are closely-spaced, the said group comprises a wavelength pair, said pair in each group corresponding to a small optical-frequency difference and defining a midpoint wavelength therebetween, and the SOP of the injected light and A-SOP are substantially constant for each said wavelength in each said group, and wherein at least one of the midpoint wavelength, I-SOP and A-SOP is different between the respective said groups, and the output light means comprising: extraction and analysis means for extracting corresponding light from the FUT and analyzing the extracted light, and g. detection means for detecting the analyzed light corresponding to at least one transmission axis of the analyzer means (A-SOP) to provide transmitted coherent optical power at each wavelength of the analyzed light in each of said at least two groups of wavelengths, wherein the lowermost (X₁) and uppermost (λu) said wavelengths in each said group of wavelengths are closely-spaced; the processing means being configured and operable for: xii. computing the at least one difference in a measured power parameter corresponding to each wavelength in said wavelength pair for each of the said at least two groups, said measured power parameter being proportional to the power of the said analyzed and subsequently detected light, thereby defining a set of at least two measured power parameter differences; xiii. computing the mean-square value of said set of differences; and xiv. calculating the at least one polarization-related FUT characteristic as at least one predetermined function of said mean-square value, said predetermined function being dependent upon the said small optical frequency difference between the wavelengths corresponding to the said each at least said two pairs of closely- spaced wavelengths; and xv. outputting the value of said at least one polarization-related FUT characteristic for display, transmission or further processing.

Preferred embodiments and species of the foregoing five aspects of the invention are set out in the dependent claims appended hereto.

The foregoing and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description, in conjunction with the accompanying drawing, of preferred embodiments of the invention which are described by way of example only.

BRIEF DESCRIPTION OF THE DRAWINGS Two-End PMD Measurement

Figure 1 is a simplified generalized schematic illustration of parts of a measuring instrument connected to opposite ends of a fiber-under-test (FUT) for performing two- ended measurements on the FUT to determine DGD and/or mean DGD and/or rms DGD;

Figure IB is a simplified schematic diagram similar to Figure 1 but of an instrument using a tunable laser light source, one input-SOP controller (scrambler), one output-SOP controller (scrambler), a polarizer/analyzer and one detector to measure analyzed light; Figure 1C is a simplified schematic diagram of an instrument similar to that shown in Figure IB but which uses a coupler, a polarizer and two detectors; one detector for measuring analyzed light after the polarizer and the other detector for measuring light that is proportional to a total output light power from FUT;

Figure ID is a simplified schematic diagram of an instrument similar to that illustrated in Figure IB but having two detectors connected to the coupler to measure two repeated powers in order to reduce uncorrelated noise contributions to the measurement;

Figure IE is a simplified schematic diagram of an instrument similar to that shown in Figure 1 C but having a single detector and an optical switch for connecting the detector alternatively to measure analyzed light from the polarizer and light from the coupler proportional to a total output light power from the FUT;

Figure IF is a simplified schematic diagram of an instrument similar to that shown in Figure IE but with the coupler and polarizer replaced by a polarization beam splitter (PBS), the optical switch connecting the single detector to alternatively to the output ports of the PBS;

Figure IG is a simplified schematic diagram of an instrument similar to that 5 shown in Figure IB but which uses a PBS and two detectors;

Figure IH is a simplified schematic diagram of an instrument similar to that shown in Figure 1 but which has a polarimeter for analyzing and detecting light from the FUT;

Figure II is a simplified schematic diagram of a broadband light source basedo two-end PMD measurement/test instrument which is similar to that shown in Figure IB but uses a broadband light source to provide the light and tunable filter (between polarizer and a detector) to enable detection of only light corresponding to a small spectral width centered about the passband wavelength of the filter;

Figure U is a simplified schematic diagram of a broadband light source based5 two-end PMD measurement/test instrument similar to that shown in Figure II but using a dispersion element (multi-channel filter) and a multi-channel detector array that measures analyzed light after the polarizer simultaneously or within a short time period; Single-End Overall PMD Measurement

Figure 2 corresponds to Figure 1 but is a simplified schematic diagram of o measurement test instrument for single-end measurement of overall PMD;

Figures 2B to 2G correspond to Figures IB to IG, respectively, and illustrate corresponding single-end measuring instruments in which both parts of the measuring instrument are at the same, proximal end of the FUT; Single-End Cumulative PMD Measurement 5 Figure 3 is a simplified schematic diagram of a polarization-sensitive optical time domain reflectometer (POTDR) embodying an aspect of the present invention;

Figure 3A is a simplified schematic diagram of a polarization-sensitive optical time domain reflectometer embodying an aspect of the present invention;

Figure 3B is a polarization-sensitive optical time domain reflectometer o embodying an aspect of the present invention;

Figure 3 C is a polarization-sensitive optical time domain reflectometer embodying an aspect of the present invention;

Figure 4A is a flowchart illustrating operation of light source and input SOP controller of the two-end PMD measurement instrument of Figures 1C and IG;

Figure 4B is a flowchart illustrating operation of an analyzer and detection unit of the two-end PMD measurement instrument of Figures 1C and IG;

Figure 4C is a flowchart illustrating a group of power (data) acquisition step of the flowchart of Figure 4B;

Figure 4D is a flowchart illustrating a power (data) acquisition step of the flowchart of Figure 4C; Figure 5 A illustrates sections of a flowchart illustrating operation of the single- end PMD measurement of Figures 2C and 2G;

Figure 5B is a flowchart illustrating a group of power (data) acquisition step of the flowchart of Figure 5 A;

Figure 5C is a flowchart illustrating a power (data) acquisition step of the flowchart of Figure 5B;

Figure 6A is a flowchart illustrating operation of the POTDR of Figure 3;

Figure 6B is a flowchart illustrating a trace acquisition step of the flowchart of Figure 6A;

Figure 7 is a schematic diagram illustrating a tunable modulated optical light source;

Figure 7A is an example of a schematic diagram illustrating a SOA-based tunable modulated optical light source;

Figure 8A is a schematic diagram illustrating a tunable pulsed light source with a delay that can be used for both single-end overall PMD measurement and single-end cumulative PMD measurement;

Figure 8B is a schematic diagram illustrating another alternative tunable pulsed light source without a delay that can be used for single-end overall PMD measurement;

Figure 8C illustrates schematically another yet another alternative tunable pulsed light source that can be used for both single-end overall PMD measurement and single- end cumulative PMD measurement;

Figure 9A is a simplified schematic diagram of a laser source that has been modified to ensure that the emitted light has a high degree of polarization (DOP);

Figures 1OA and 1OB are schematic representations of alternative tunable pulsed light sources that can be used for both single-end overall PMD measurement and single- end cumulative PMD measurement.

DESCRIPTION OF PREFERRED EMBODIMENTS hi the drawings, the same or similar components in the different Figures have the same reference numeral, where appropriate with a prime indicating a difference.

The various aspects of the present invention, and their respective implementations, are predicated upon the same underlying theory. Embodiments of these aspects can be advantageously used for two-ended measurement of PMD or wavelength- dependent DGD, for either a narrow optical channel or over a prescribed wide wavelength range, single-end overall PMD measurement, single-end cumulative PMD measurement, and other related variants. hi each of the preferred embodiments of this invention described hereinafter, there will usually be three main parts, namely (i) an input light controller, (ii) an analyzer and detection unit and (iii) an analogue and digital processing unit, together with one or more control units. In so-called two-ended cases, the input light controller will be located at a proximal end of the FUT while the analyzer and detection unit and, conveniently, the analogue and digital processing unit will be located at the distal end of the FUT. A first control unit at the proximal end of the FUT controls the input light controller and a second control unit at the distal end of the FUT controls the analyzer and detection unit and the analogue and digital signal processing unit, hi the so-called single-ended cases, where all of the components of the measuring instrument are at the proximal end of the FUT, the two control units may be combined into a single control unit.

Although each instrument embodying this invention will have the above- described three parts or sections, there will be many detailed differences in configuration according to the three different PMD measurements types, namely (i) two-ended overall PMD measurement, (ii) single-ended overall PMD measurement and (iii) single-ended cumulative PMD measurement.

Thus, the input light controller will comprise an at least partially polarized light source, for example a tunable laser or a broadband source, and an input SOP controller for controlling the SOP of light from the light source before it is injected into the FUT. The analyzer and detection unit may comprise, in addition to an output SOP controller, a polarizer and one detector, or a PBS and two detectors, or a coupler and a polarizer with 5 two detectors, and so on. Where the input light source is broadband, the analyzer and detection unit may also comprise a tunable filter for selecting the optical frequency. (Alternatively, but less advantageously, the input light source could comprise such a tunable filter.) The analogue and digital processing unit may comprise a data acquisition unit, a sampling and averaging unit and a data processor unit, analog-to-digital o conversion being carried out in the sampling and averaging unit.

Using the single-end measurement method, an overall PMD can be extracted by analyzing backreflected light from a strong localized reflection at the distal end of FUT (e.g. Fresnel reflection, a Bragg reflector, etc.), so a long pulse may advantageously be used, since virtually all of the backreflected light arises from the localized reflection and5 not from Rayleigh backscattering distributed along the pulse length. It may also be preferable to use two-closely spaced wavelengths for the measurement. To use the single-end measurement method to measure cumulative PMD, however, OTDR traces as a function of fiber length must be analyzed, so it may be preferable to use a short pulse in order to obtain clear POTDR traces that do not suffer undue spatial depolarization due to0 the PMD-induced evolution of the SOP of the "leading edge" of the pulse with respect to its "trailing edge".

In addition, typically, there may be an approximately "continuous" increase in the cumulative PMD "curve" as a function of fiber length required to be measured for one acquisition. Since, for a given closely-spaced wavelength separation, there is a maximum 5 PMD value (due to saturation) and a minimum PMD value (due to detection sensitivity) that can be measured, it may hence also be preferred to inject light pulses having two or more (e.g. three or four) closely spaced wavelengths, hi this way, measurements taken with different closely-spaced wavelength spacings can be "stitched" together in the processing, and hence the effective difference between the measurable minimum and o maximum PMD values can be significantly enhanced.

For a two-ended PMD measurement the laser must be able to set or modulate its optical frequency to produce two or more closely spaced wavelengths at different times.

Preferred embodiments of the main three PMD measurement methods and instrument configurations for two-end PMD measurement, single-end overall PMD measurement and single-end cumulative PMD measurement according to the invention,

5 and modifications, alternatives and substitutions thereto, will now be described with reference to Figures 1 to 3C.

Two-End PMD Measurement

In the following description for the two-end PMD measurement, the term i o "modulated optical pulse" is used to refer to propagating light, which, over a defined time interval, is differentiated from at least some other pulses by one or more of a characteristic wavelength, characteristic average power, characteristic pulse duration, characteristic superposed amplitude or phase modulation at a frequency much greater than the reciprocal of the pulse duration, characteristic extinction ratio following its

15 duration, characteristic duration of sampling of the said light in the acquisition process, or any other measurable distinguishing property. hi a first preferred embodiment of this present invention illustrated in Figure 1 , test/measurement apparatus for two-ended measurement of DGD/PMD comprises an input light controller means 42 situated at or adjacent the proximal end of FUT 18 and

20 connected thereto by a connector 16A and analyzer and detection means 44 situated at or adjacent the distal end of the FUT 18 and connected thereto by a connector 16B. The input light controller means 42 comprises a light source 12 and an input SOP controller means 14A (conveniently referred to as an I-SOP controller or scrambler means), which controls the SOP of light from the light source 12 before injecting it into the FUT 18 via

25 connector 16A.

In the event that the degree of polarization (DOP) of the light source 12 is not high, the DOP may be increased by inserting a polarizing element 19 (e.g. polarizer, polarization beam splitter, etc.) into the optical path downstream from the light source 12.

However, if polarization maintaining fiber (PMF) is not used between the light source 12

30 and the polarizing element 19, it may be necessary to add an additional polarization adjuster 13 (generally a "factory-set" polarization controller), as shown in Fig 9A, in order to approximately maximize the power transmitted through the polarizing element 19. It should also be noted that the polarizing element 19 may be the same as the polarizing element (20,2OA, 20C) for particular embodiments of one-sided measurement, as shown for instance in Figures 2B-G and 3A and 3B. A first (input) control unit 30A controls the wavelength of the tunable laser source

12A and the setting of the input I-SOP controller 14A, specifically to scramble the SOP of the light from light source 12 before it is injected into the FUT 18.

The analyzer and detection means 44 comprises an output SOP controller (A- SOP) 14B (conveniently referred to as an A-SOP controller or scrambler means), followed by a polarization discriminator 20, and detection means 22. If the detection means 22 is not able to measure high light power correctly, power controller means (not shown), for example an optical attenuator, may be interposed to attenuate the light extracted from the FUT 18 before it is applied to the detection means 22. The purpose of the optical attenuator is to ensure that the light level at the distal end is not so high as to potentially "saturate" or render non-linear the detection means 22. Such may be the case if, for instance, the measurement is carried out over a short optical fiber link, wherein the overall attenuation induced by the fiber is small. For long links, the optical attenuator will normally be set to induce minimum attenuation.

The analog and digital processing unit 40 comprises a sampling and averaging unit 32 and a data processor means 34, optionally with a display means 36 for displaying the results. The components of the analyzer and detection unit 44 (except for the polarization discriminator) and the analog and digital signal processing unit 40 are controlled by a second, output control unit 30B.

Under the coordination of control unit 3OB, the sampling and/or averaging circuitry 32, in known manner, uses an internal analog-to-digital converter to sample the corresponding electrical signals from the detectors 22B and 22C as a function of time, and the sampled signal is time-averaged over a portion of its duration to provide a corresponding digital level. This portion is chosen so as to avoid transient effects and/or bandwidth limiting effects in the detected power, polarization, and/or wavelength due to the light source means 12, the I-SOP controller 14 A, the analyzing means comprising the A-SOP controller means 14B and the polarization discriminator means 20, and/or any distortion in the (pulsed) signal arising from bandwidth limitations of the analog electronics.

The resulting averaged powers are used by data processor 34 to derive the DGD at a particular wavelength or PMD value over a prescribed wavelength range of the FUT 18, as will be described in more detail hereinafter according to the particular aspect of the invention.

Various different configurations of the two-ended instrument of Figure 1 are illustrated in Figures IB to U and will now be described briefly. The instrument configurations depicted in Figures 1 to IH have in common that they use a tunable laser source whereas those depicted in Figures II and U use a broadband light source and tunable filter.

Thus, in each of the "two end" instruments illustrated in Figures 1 to IH, the light source 12A comprises a tunable optical modulated laser source 12A whose output is coupled to either a polarization maintaining fiber (PMF) or single mode fiber (SMF), as appropriate, for injecting modulated optical pulses into the fiber-under-test (FUT) 18 via the (input) state of polarization (I-SOP) controller means 14A and input connector 16A. The output light extracted from the FUT 18 is analyzed by the polarization discriminator 20 and the analyzed light is measured during a time period during which light from the light source means 12 is detected, successively, at each of two different wavelengths, λ⁽ _L ^k) and λ*u ⁾ , that are closely-spaced relative to each other.

The main differences between the different configurations lie in the analyzer and detection means 44. Thus, in the analyzer and detection means 44 of the instrument shown in Figure IB, the polarization discriminator comprises a linear polarizer 20A and the detection means comprises a single detector 22A. Figure 1C shows an instrument similar to that shown in Figure IB but which differs in that it has two detectors 22B and 22C and a coupler 21 interposed between the A-SOP controller 14B and the polarization discriminator (polarizer) 2OA. Detector 22B is connected to the polarizer 2OA and measures analyzed light therefrom and detector 22C is connected directly to the coupler 21 and measures light that is proportional to a total power of the light extracted from the FUT 18. Thus, the SOP of the extracted light is transformed by the A-SOP controller or scrambler 14B, following which the light is split into two parts by coupler 21. The first detector 22B connected to one of the two outputs of the coupler 21 via the polarizer detects one of the polarization components and the second detector 22C connected to the other output of the coupler 21 measures a power that is proportional to a total output light power from FUT. The light may be approximately simultaneously detected by detectors 22B and 22C. It should be noted, however, such that truly simultaneous detection of the analyzed light with two detectors of 22B and 22C may not be always necessary; it may be detected instead at slightly different times.

The instrument illustrated in Figure ID is similar to that illustrated in Figure 1C but differs in that the polarizer 2OA and coupler 21 are transposed, the two detectors 22B and 22C being connected to respective outputs of the coupler 21 to measure two repeated powers.

The instrument shown in Figure IE is similar to that shown in Figure 1C in that it comprises a coupler 21 and a polarizer 2OA, but differs in that it has only one detector 22 A. An optical switch 23 controlled by control unit 30B connects the input of detector

22 A alternatively to the output of the coupler 21 and the output of polarizer 2OA to measure, respectively, the analyzed light and total output light power from the FUT 18.

The instrument shown in Figure IF is similar to that shown in Figure IE in that it uses a single detector 22A and an optical switch 23, but with a PBS 2OC instead of a linear polarizer. The control unit 30B causes the switch 23 to connect the detector 22 A alternatively to the respective output ports of the PBS 2OC to measure the analyzed light from each port.

Because the optical switch 23 is used to route the output light from two optical paths from the coupler 21 and polarizer 2OA (Fig. IE), or from the PBS 2OC (Fig. IF), into the same detector, the light from the two different optical paths may be detected at different times. This would allow the use of only one detector (and associated electronics) while maintaining many of the advantages associated with the use of two detectors. Of course, the cost reduction associated with the use of only one detector would be largely counteracted by the increased cost of introducing the optical switch, and there would also be a measurement time penalty.

The instrument shown in Figure IG is similar to that shown in Figure IF but differs in that the switch is omitted and the two detectors 22B and 22C are connected to respective output ports of the PBS 2OC each to measure analyzed light therefrom. The SOP of the light from the distal end of the FUT 18 is transformed by the A-SOP controller or scrambler 14B, following which the light is decomposed by the PBS 2OC 5 into two components having orthogonal SOPs, typically linear SOPs at O- and 90-degree relative orientations. The first detector 22B is connected to one of the two outputs of the PBS 2OC to receive one of these orthogonal components and the other output (with respect to light from the FUT 18) is connected to the second detector B 22C to receive the other orthogonal component. Once suitably calibrated to take into account theo relative detector efficiencies, wavelength dependence, etc., as will be described hereinafter, the sum of the detected powers from detectors 22B and 22C, respectively, is proportional to the total incident (i.e. non-analyzed) power (often referred to as the Stokes parameter So). The light may be approximately simultaneously detected by detectors 22B and 22C. 5 It should be appreciated that, where the polarization discriminator 20 comprises a polarizer 21 A and coupler 21 (Fig. 1C), the detector 22C connected to the coupler 21 receives light that is not polarization-dependent.

The instrument illustrated in Figure IH is similar to that shown in Figure IB but differs in that the analyzer and detection means 44 comprises a polarimeter 45 having its o input connected to the FUT 18 via connector 16B and its output connected to sampling and averaging unit 32. The polarimeter 45 is controlled by control unit 3OB to perform the analysis and detection of the light received from the FUT 18.

Preferred embodiments of the invention which use a broadband light source 12B instead of a tunable laser source 12A will now be described with reference to Figures II5 and IJ. The measurement/test apparatus illustrated in Figure II is similar to that described with reference to and as shown in Figure IB, but differs in that its input light controller means 42 comprises a polarized broadband light source 12B instead of a tunable laser source and its analyzer and detection means 44 differs from that shown in Figure IB because it has a tunable filter 27 interposed between the polarizer 2OA and the o detector 22A. The tunable filter 27 is controlled by the control unit 3OB.

It should be appreciated that the tunable filter 27 could alternatively be placed anywhere in the optical path between the output of the FUT 16B and the detector 22 A, while remaining in close proximity to control unit 3OB and is not limited to being placed between the polarizer 2OA and the detector 22B as shown in Figure II. Indeed, more generally the tunable filter 27 could be placed anywhere between the broadband source 12B and the detector 22 A. However, placing the filter in the input light controller 42 at the proximal end of the FUT 18 may lead to control and synchronization difficulties, as communication between the tunable filter 27 at the proximal end and the control unit 30B at the distal end of the FUT would be difficult. hi the embodiment of Figure II, if the inherent DOP of the broadband source is not very high, "well-polarized" broadband light may be obtained by adjusting incident SOP of light from a broadband light source 12B by passing the light through a polarizer before injecting it into the FUT 18. (See Fig. 9A). hi this case, an additional polarization adjuster (i.e. polarization controller) and a polarizer (See Figures 1OA, 1OB and 2D) would be inserted between broadband light source 12B and I-SOP controller 14A. The polarization controller would adjust the input SOP of light to obtain an approximately maximum output power of light from the polarizer.

The instrument illustrated in Figure U is similar to that shown in Figure II but differs in that the tunable filter 27 is replaced by a spectrometer means or multi-channel filter means, specifically a dispersion element 27A, for example a grating-based wavelength separator, to separate the different wavelengths of light as a function of angle. The single detector is replaced by detection means for detecting light powers at these wavelengths approximately simultaneously, for example, a multi-channel detector array 22D or similar means. Alternatively, a detector array may be replaced by several fiber pigtailed photodetectors that may be connected to a fiber array to detect light at different spatial positions, or simply to launch lights at different spatial positions having different optical wavelengths into different photodetectors. Although this design has a higher cost, it can measure DGD or PMD rapidly.

Preferably, in the "two-ended" measurement instruments shown in Figures 1 to IJ there is no "upstream" communication between the control unit 4OB at the distal end of the FUT 18 and the control unit 4OA at the proximal end. The control unit 30B comprises software or firmware that allows it to determine, from information encoded onto the optical signal by the input light controller 42, conveniently under the control of control unit 3OA, as to whether a particular detected modulated optical pulse extracted from the FUT 18 corresponds to an uppermost, lowermost, or, where applicable, intermediate closely-spaced wavelength. The preferred embodiment described hereinbefore is common to principal aspects of this invention. However, the details of the preferred embodiments, including details of their operation, corresponding to each of these principal aspects will be described in more detail in the next sub-sections.

In the description that follows, the term "modulated optical pulse" is used to refer to propagating light, which, over a defined time interval, is differentiated from at least some other pulses by one or more of a characteristic wavelength, characteristic average power, characteristic pulse duration, characteristic superposed amplitude or phase modulation at a frequency much greater than the reciprocal of the pulse duration, characteristic extinction ratio following its duration, characteristic duration of sampling of the said light in the acquisition process, or any other measurable distinguishing property. The meaning of "modulated optical pulse" will become clearer in the context of the following more detailed description.

Measurement of DGD at a particular wavelength In a narrow DWDM channel, it is frequently not practical to measure the DGD at more than one wavelength (λ_mi_d) within the channel, since the optical-frequency spacing of the closely-spaced wavelengths may be a significant fraction of the useable optical passband and, consequently, measurement at another midpoint wavelength may cause one of the two closely-spaced wavelengths to experience excessive attenuation, polarization-dependent loss, and other deleterious effects that may render the measurement unreliable or impractical. (As will be described in more detail hereinafter, the use of a very small optical-frequency spacing may not suffice to permit the measurement of a small DGD value.) In general, however, when the PMD of the FUT is relatively small, for example less than 0.2-0.5ps, the DGD within a small in-band wavelength range (such as 30 GHz), may exhibit a small variation, although it is often still desirable to obtain DGD at each wavelengths so as to obtain mean DGD or rms DGD in this small channel wavelength range.

It should also be noted that the measurement of DGD at a particular wavelength is not limited to "in-band" applications such as testing optical links through in DWDM channels. Note that, for DGD measurement in a "dedicated" DWDM channel, i.e. a measurement that is always to be undertaken at approximately the same particular wavelength, it is not necessary that the light source means 12 be widely tunable or very broadband, but only that it be capable of emitting coherent light at each of two different closely-spaced wavelengths centered about the aforesaid "particular wavelength". However, for most measurement applications, it is desirable that the light source means 12 be tunable or very broadband in order to perform measurements on any one of a number of other DWDM channel wavelengths, for instance in the telecommunications C and/or L bands. A more detailed description of the operation of preferred embodiment for this tunable light source or broadband light source means will be given in a later sub- section.

As described in the "Background" section hereinbefore, the DGD can vary with time and/or environmental conditions. For many measurement applications, the speed ("update rate") of the measurement is not critical. Consequently, it is advantageous for cost reasons to use inexpensive polarization scramblers for the Input-SOP controller 14A and the analyzing means. An example of a low-cost SOP scrambler that is suitable for both of the I-SOP and A-SOP controllers 14A and 14B is described in co-owned United States Provisional patent application number 60/996,578 filed 26 November 2007.

The actual SOP of light exiting the input I-SOP controller 14A is, in general, unknown, but undergoes "continuous scanning", i.e. is varied slightly between groups of closely-spaced wavelengths, such that over a sufficiently long time, normally corresponding to the minimum time for a reliable DGD measurement, the SOPs will cover the Poincare sphere approximately uniformly.

The output A-SOP controller 14B, located at the distal end of the FUT 18, also causes the SOP of the light exiting the FUT 18 to be varied slowly in a similar manner to the input I-SOP controller 14 A, although in general the respective rates of variation are not the same and the SOPs exiting either the I-SOP controller 14A or the A-SOP controller 14B are uncorrelated.

More specifically, for a particular measurement sequence k, the control unit 3OB causes the light signal, analyzed by the intervening polarization discriminator, such as a polarization beam splitter (PBS) or polarizer, to be measured during a portion of time during which light from the light source means 12/12 A is detected, successively, at each of two different wavelengths, λ^ and λ^ , that are closely-spaced relative to each other, during which portion of time the SOPs exiting the I-SOP controller 14A and A- SOP controller 14B, respectively, are approximately constant and form a k-th SOP couple / - SOP ^(k) , O - SOP (k) ). (Preferably, the aforementioned portion is less than 50% of the "physical" pulse length, for reasons that will be explained further below.) The midpoint wavelength of the pair of modulated light pulses is defined as the average of the actual wavelengths of the modulated light pulses, i.e., λ⁽^_id = (Λ[^A) + Λff) /2 . (The labels L and U refer, for convenience and ease of understanding, to "lowermost" and "uppermost" with respect to the midpoint wavelength λ^{*._d ). The measured analyzed light signal is converted to an electrical signal by the sampling and averaging means 32 and subsequently digitized before application to the data processor 34 for subsequent processing thereby.

During the transition from one closely-spaced wavelength to the other, the light from the light source means 12A is briefly extinguished, say for about 40μs, a period that is much shorter than the typical reaction period of DWDM channel equalizers found in many optical networks. The precise period of this extinction is used by the control unit

3OB to identify whether the subsequent pulse corresponds to an uppermost or lowermost wavelength.

The measurement sequence described above is repeated for K different groups, each group corresponding to a slightly different I-SOP and A-SOP. In practice, for the continuous SOP scanning approach, K should be greater than 1000, and ideally greater than 10,000, to obtain satisfactory results.

The time period corresponding to light emission at each closely-spaced wavelength is not particularly critical, but clearly a longer duration will lead to a longer overall measurement time for this method. A good compromise between measurement time and limitations on the optical source wavelength switching speeds has been found to be a period of about 1 ms.

If the expected DGD to be measured is not roughly known, it is possible that the optical frequency difference of the closely-spaced wavelength pairs is, for instance, too large to permit accurate measurement of high DGD values, or alternatively, too small to permit measurement of a low DGD values, hi such a case, it may be desirable to perform a preliminary rough DGD estimation using this method using only a limited number of K values. (It should be noted that, with the continuous SOP scanning approach, K necessarily must still be relatively large, e.g. >500, for a rough measurement, whereas if the alternative "macroscopic-step SOP selection" approach is used, as described hereinafter, K may be a much smaller value, e.g. approximately 10.) Then, depending on the result, the spacing of the closely-spaced wavelengths may be adjusted, while maintaining the midpoint wavelength at the same value. However, as mentioned above, in a narrow DWDM channel, which may, for instance, only have a useable passband width of approximately 35 GHz, it is not always possible to increase the wavelength spacing.

An alternate approach for "adapting" the optical frequency difference between the closely-spaced wavelengths is to use more than two closely-spaced wavelengths in each group, the wavelength spacing between pairs of wavelengths being unequal. If, as described above, the preliminary DGD estimation indicates that the wavelength spacing should be different, one need only slightly shift the midpoint wavelength corresponding to the "optimal" closely-spaced wavelength pair to the midpoint wavelength corresponding to the initial close-spaced wavelength pair. Such an approach is well adapted to the preferred light source means 12 whose embodiment will be described in more detail hereinafter.

Advantageously, in order to estimate, and partially compensate for, the contribution of noise in the measurements, "repeated measurements" are taken for each group at the same two closely-spaced wavelengths, these repeated measurements being in principle substantially identical to the "original" measurements, in the absence of noise. hi practice, such noise can arise from any combination of ASE noise (from intervening optical amplifiers in the fiber link), polarization noise, optical source power fluctuations, etc. The method by which this technique is used to improve the measurement sensitivity will be described in more detail hereinafter.

It should be noted, however, that it is convenient to not actually transmit distinct "physical" repeated pulses in the preferred embodiment, but rather to perform the 5 functional equivalent in the acquisition process by sampling the "physical pulse" (corresponding to the period during which the laser emits at a particular wavelength) during a different portion of time than the portion during which the "initial" measurement was taken. Consequently, in a preferred embodiment, each "physical pulse" comprises two "optical modulated pulses". o The computational method by which the data thus acquired can be converted into a reliable DGD measurement, including in the presence of significant ASE noise, will be described in more detail hereinafter.

RMS or Mean DGD measurement using repeated DGD(λ) measurements 5 By repeatedly applying the above-described method of measuring DGD at a particular wavelength of the invention over a prescribed wavelength range, it is possible to estimate the polarization mode dispersion (PMD) of a fiber link (according to either or both of the "rms" or "mean" PMD definitions) from the DGD as a function of wavelength. Preferably, the wavelengths should be approximately uniformly distributed o across a prescribed wavelength range.

For reasons of overall measurement time, it is advantageous to replace the continuous SOP scanning described in the Summary of Invention hereinbefore with "macroscopic-step SOP selection", i.e. where I-SOP controller 14A and A-SOP controller 14B set the different input and output SOPs in a pseudo-random manner, such5 that the points whereby such SOPs conventionally are represented on the Poincare sphere are uniformly-distributed over the surface of said sphere, whether the distribution is random or a uniform grid of points. An example of a suitable commercially-available controller for such an application is the General Photonics Model PolaMight™ (multifunction polarization controller) 0 As mentioned in the context of the above-described measurement of DGD at a particular wavelength, it is frequently the case that the optical frequency difference of the closely-spaced wavelength pairs is, for instance, too large to permit accurate measurement of high DGD values, or too small to permit measurement of low DGD values, hi such a case, it may be desirable to perform a preliminary rough DGD estimation using this method but with a limited number of K values (e.g. 10), and then, depending on the result, change the spacing of the closely-spaced wavelengths. Note that, in this case, where the rms or mean DGD is calculated over a prescribed wavelength range, it is usually not necessary to maintain exactly the same midpoint wavelength for this measurement with a different optical frequency difference. The final DGD averaging over the wavelengths can take into account this slightly different wavelength. A preferred method of implementing this approach with the preferred embodiments of the optical source means 12 will now be described. (For simplicity of the foregoing description, we assume that the "repeated pulse" method, described in the measurement of DGD at a particular wavelength above, is not applied. The "intermediate wavelength" method described here can be readily generalized to include the "repeated pulse" method.) First, the input light controller means 42 injects into the FUT 18, for each group of two optical pulses, a third additional optical pulse having a wavelength (λπ) intermediate and unequally spaced with respect to the uppermost and lowermost wavelengths (λw ,λn) respectively, of the group. The input-SOP 14A and the output- SOP 14B, respectively, are approximately constant for all three optical pulses. All three analyzed pulses are detected by the detection system means 22, and are identified by their respective "extinction periods", as described in the measurement of DGD at a particular wavelength above. The three aforementioned optical pulses correspond to three different combinations of optical frequency differences (in comparison with two different close- spaced wavelengths, which of course correspond to only one possible optical frequency difference), and hence only add about 50% to the overall measurement time. Using the computation method described in more detail hereinafter, noise- and/or sensitivity- optimized DGD measurements can be made at different approximately uniformly spaced (midpoint) wavelengths over the prescribed wavelength range.

It should be noted that, if a significantly uneven distribution of the same number of DGD(λ) were used, a PMD value could still be calculated by a straightforward modification of the method that would be obvious to someone of average skill in the art, but this PMD value would not be, in general, as reliable as a PMD value obtained with approximately uniformly distributed wavelengths.

In order to avoid having to use complicated communication between the input light controller means 42 and the analyzer and detection means 44, it is desirable that the choice of midpoint wavelengths defined by the closely-spaced wavelengths that are generated by the tunable laser source 12A (FIG. 1 (B-H) or by tunable filter 27 (FIG. II) be predetermined for the prescribed wavelength range (e.g. C band, from 1530 - 1565 nm). In this way, there is no need for the numerical values of the injected wavelengths to be explicitly communicated, as these values can be inferred by the control unit 3OB from simple coding information in the extinction times, as discussed earlier. It may, however, be desirable for an initial "ready" signal to be sent from the input light controller means 42 to begin the measurement sequence. Again, this signal could be encoded in the light injected into the FUT, via the extinction period or other simple pulse frequency modulation. Once a set of DGD(λ) values have been obtained as described above, it is straightforward to compute, using standard statistical definitions, either or both of the rms DGD and the mean DGD from the different value of DGD obtained within the prescribed wavelength range. Note that such a measurement is particularly useful, since most current commercial approaches do not permit the PMD to be directly measured using both rms and mean definitions.

RMS DGD measurement (without individual DGD(λ) measurements)

The underlying measurement approach can be applied for the direct measurement of the rms DGD (i.e. PMD according to the rms definition) across a prescribed wavelength range. If information concerning the DGD as a function of wavelength is not required, this aspect of the invention allows for a much more rapid PMD measurement (for the same overall level of accuracy) than the method of RMS measurement using repeated DGD(λ) measurements described above, hi addition, since the analyzing and detecting light controller means 44 does not need to "know" the actual value of the wavelength being transmitted (only whether the wavelength corresponds to the "uppermost", "lowermost" or one or more "intermediate" wavelengths), there is no need for the use of predetermined wavelengths or an explicit "start" signal for the measurement, thereby simplifying the measurement procedure.

The computational method by which the data thus acquired can be converted into a reliable DGD measurement, including in the presence of significant ASE noise, is much the same as in the above described measurement of DGD at a particular wavelength, except that individual measurements taken with each group of closely-spaced wavelengths are averaged over "center wavelengths" (see later for a definition of center wavelength) approximately uniformly distributed across the prescribed range, as well as over different input-SOPs and output-SOPs. Ideally, but not necessarily, the choice of mid-point wavelengths is quasi-random, or at least not sequential in ascending or descending wavelength. Computational details will be described hereinafter.

As with the above described rms or mean DGD measurement using repeated DGD(λ) measurements, it is advantageous to inject more than two different closely- spaced wavelengths in each group of wavelengths, in order that the optimal optical- frequency spacing can be used in the computational process.

Before the measurement procedure for these above aspects is described in more detail, and with a view to facilitating an understanding of such operation, the theoretical basis will be explained, it being noted that such theory is not to be limiting.

RMS DGD measurement using rapid wavelength sweeping

An alterative way approach to measuring the rms DGD over a prescribed wavelength range is to use a rapidly swept tunable laser (or polarized broadband source / tunable narrowpass filter combination), where either or both of I-SOP and A-SOP vary little or not at all during the sweep. If the detection electronics are sufficiently rapid, this "spectral acquisition step" will provide a quasi-continuum of detected polarization- analyzed transmitted coherent optical power data as a function of optical frequency. In the subsequent data analysis, any desired closely-spaced wavelength step could be selected, and the average DGD determined from different wavelength pairs so selected in a similar fashion to that described earlier. Of course, if I-SOP and A-SOP vary during the sweep, this would further improve the accuracy of the measurement, provided that neither I-SOP nor A-SOP varies significantly between any two closely-spaced wavelengths in the sweep. Furthermore, repeating this procedure with multiple sweeps will of course further improve its accuracy.

Various Modifications to the Two-end PMD Measurement Means The invention encompasses various modifications to the two-end PMD measurement embodiment shown in Figures 1-lH. For example, if the light from the light source means 12 is not well-polarized, i.e. different SOPs for different wavelengths are experienced, it may be passed through a polarization adjuster (i.e. polarization controller) 13 (see Figure 9A) connected by non-polarization-maintaining fiber to the tunable pulsed laser source 12 and a polarizer 19, respectively, to produce a maximum output from a polarizer by adjusting an incident SOP of light, so as to have maximum optical power passing through the I-SOP controllers 14 A.

Although these modifications may be applied separately, certain embodiments of the invention may include several such modifications. A person of ordinary skill in this art would be able, without undue experimentation, to adapt the procedure for calibrating the relative sensitivities of the two detectors 22B and 22C, including the losses induced by the intervening coupler, etc. described hereinbefore, with reference to the polarized light source based two-end PMD measurement for use with the embodiment of Fig. IG. That said, it should be appreciated that, in the embodiment of Fig. 1C, calibration of the mean relative gain is not required; the measured total power is independent of SOP, and there is no need for an "absolute" calibration to directly measure absolute transmission values; they can be obtained to within an unknown constant factor. The subsequent normalization over the mean powers averaged over SOPs, as described hereinbefore, eliminates the unknown factor. Where the detection means 22 comprises a single detector 22A (e.g., Fig. IB), normalized powers (or transmissions) can be obtained by computing an average of all of the powers in first and second groups of powers, and dividing each of the powers by the said average power to obtain first and second groups of normalized powers, as described in detail hereinbefore. Fig. IB illustrates a PMD measurement instrument suitable for obtaining the

DGD or PMD using normalized powers obtained in this way. The PMD measurement illustrated in Fig. IB is similar to that illustrated in Fig. 1C but with coupler 21 and detector B 22C omitted. The data processor 34 will simply use the different normalization equations.

Where a polarimeter 45 is used (see Fig. IH), several (typically three) different polarization components of light exiting from FUT 18 can be measured, either simultaneously or at different times dependent on the polarimeter design.

It should be noted that the single-end measurement instrument of Figures 2 could be adapted to use a polarimeter 45 in its analyzer and detection means 44.

In the polarized broadband light source based two-end PMD measurement shown in Fig. II, a tunable filter 27 is used to select light wavelength. This tunable filter can be located after polarizer 2OA (Fig. II) or before polarizer 2OA. It should be noted that the tunable filter must be a polarization insensitive filter and the tunable filter may select different wavelengths at different time. hi any of the above-described embodiments, the input SOP controller 14A and output SOP controller 14B operate in such a manner that, for a given SOP of the light (which can be any SOP on the Poincare Sphere) received at its input, the SOP of the light leaving its output (either the input SOP 14A and output SOP 14B) will be any other one of a number of substantially uniformly distributed SOPs on the Poincare Sphere, whether the distribution is of random or deterministic nature. Typically, the number of input and output states of polarization is about 100-100,000, but it could be any practical number allowing for a reasonable coverage of the Poincare sphere. However, it may also be possible to use one for both input and output SOP. It is noted that the distribution of the SOPs need not, and generally will not, be truly random; so "pseudo-random" might be a more appropriate term in the case where a random distribution is indeed used for convenience because it is easier and less expensive to implement than a uniform grid of SOPs (the latter being in any case very susceptible to movement of the FUT 18 during measurement).

The detection system means 22, whether a single detector, a pair of detectors, a filter plus detector, or a detector array, and the sampling or sampling and averaging circuitry unit 32, may be as used in standard commercial power meters that are known to a person skilled in this art.

The control unit 3OB may advantageously be a separate computer. However, it is noted that a single computer could perform the functions of the data processor 34 and the control unit 3OB.

5 Various other modifications to the above-described embodiments may be made within the scope of the present invention. For instance the tunable modulated optical source 12 and input SOP controller 14A and analyzer and detection means 14B, 20 and 22 could be replaced by some other means of providing the different polarization states of the modulated optical sources entering the FUT 18 and analyzing the resulting signal or i o power caused leaving the distal end of FUT 18.

The polarimeter used in the instrument shown in Fig. IH, (typically splitters with three or four analyzers and photodetectors in parallel), measures more than one polarization component of the signal or power approximately simultaneously, but other similar configurations are feasible. Alternatively, an I-SOP controller 14A may launch

15 three or more pre-defined input SOPs of light, for example having a Mueller set, which is well known in the art, and a polarimeter may be used as an analyzer and detection means as shown in Fig. IG.

It should be noted that each group is not limited to one pair of modulated optical pulses or one pair of series of modulated optical pulses. Indeed, it may use three or more

20 different closely-spaced wavelengths per group of powers, instead of the minimally- required two closely-spaced wavelengths λι_ and λu.

However, it should also be noted that more than one pair of modulated optical pulses and more than one pair of light pulses usually may not be required for two-end overall PMD measurement if one may know a rough PMD value of the FUT. Otherwise,

25 such as discussed previously for auto pre-scan, more than one pair of modulated optical pulses or more than one pair of series of light pulse may be used for the acquisition.

It should also be noted that a single DGD at one given midpoint wavelength may be obtained by averaging over a large number of randomly input and output SOPs for a given constant midpoint wavelength having two closely-spaced wavelengths. Therefore,

30 the DGD as function of wavelength in a given wavelength range may also be given by measuring many single DGDs at different midpoint wavelengths within the given wavelength range, thereby the mean DGD and RMS DGD may be further computed by averaging over all or most of single DGD at different wavelengths in the given wavelength range. Otherwise, a RMS DGD may also be computed from a mean-squared difference that is obtained by averaging over wavelength and/or SOP. It must also be appreciated that the midpoint wavelength is defined as the mean of the two closely-spaced wavelengths, and is particularly useful for facilitating description of the basic one wavelength pair implementation. It is not explicitly needed anywhere in the computations, and the actual laser wavelength is not "set" at the midpoint wavelength. Only the knowledge of the step is needed, i.e., the difference between any pair that is used in the computations of cumulative PMD, irrespective of the midpoint wavelength, even if it were to be random and unknown. (When more than one wavelength pair is used per group, as mentioned above, it is useful to introduce the concept of "center wavelength" as a wavelength "label" corresponding to the particular group. This will be discussed further hereinafter.) Although the above-described method of operation changes the midpoint wavelength for each SOP, this is not an essential feature of the present invention. While superior performance can be obtained by covering a large wavelength range in order to obtain the best possible average of DGD, as per the definition of PMD, a PMD measurement embodying the present invention will work with no bias and may provide acceptable measurements of PMD, with a constant center- wavelength or even both constant input and output SOPs and constant center-wavelength with one pre-defined wavelength step (or frequency difference).

SINGLE-END OVERALL PMD MEASUREMENT As mentioned hereinbefore, if DGD/PMD is to be measured from one end of the

FUT 18, the analyzer and detection unit 44 and the analog and digital signal processing unit 40 can be located with the input light controller 42 at the proximal end of the FUT 18, together with a single control unit 30 performing the control functions of the control units 3OA and 30B in the two-ended embodiments. Also, because the parts are co- located, certain parts may be combined, their components being modified as appropriate. Single-end measuring instrument configurations will now be described with reference to Figures 2 to 2G which correspond to Figures 1 to IG (the two-end measuring instrument configurations).

Thus, Figure 2 shows a tunable OTDR-based single-end overall PMD measurement apparatus similar to the two-end measurement instrument of Figure 1 but in which the input light controller means 42 and analyzer and detection means 44 are co- located at the proximal end of the FUT 18 and share a backreflection extractor 52 which connects the input I-SOP controller 14A and the output A-SOP controller 14B to the FUT 18 via connector 16. The backreflection extractor 52 is bidirectional in that it conveys the light from the I-SOP controller 14A to the FUT 18 and conveys the backreflected light from the FUT 18 to the A-SOP controller 14B. As was the case in Figure 1 the tunable pulsed light source 12 is connected to I-SOP controller 14A by a PMF 29A.

A fiber patch cord with either a PC (FC/PC or FC/UPC) connector or a fiber pigtailed mirror 50 is connected to the distal end of FUT 18 to produce a localized reflector at the distal end of the FUT. hi fact, any type of reflector may be used if it can reflect the light from the end of FUT 18 back into the measuring instrument.

The other change, as compared with Figure 1, is that the instrument shown in Figure 2 has a single control unit 30 which controls the tunable pulsed light source 12, the two SOP controllers 14A and 14B, the sampling and averaging unit 32 and the data processor 34. Otherwise, the components of the measuring unit shown in Figure 2 are similar or identical to those of the measuring instrument shown in Figure 1 and operate in a similar manner. The signal processing, however, must be adapted so as to allow for the fact that the extracted light comprises light from the light source 12 that travelled the FUT 18 for at least part of its length and then was backreflected and travelled the same path to the backreflection extractor. It should be noted that the term "tunable OTDR" mentioned hereinbefore in the context of this single-end overall PMD measurement is not limited to a fully functional, commercial-type OTDR, but rather refers to an apparatus that can provide optical pulses for injection into a fiber, and subsequently detect and perform time-gate averaging only on those pulses corresponding to reflections corresponding to a particular time delay (i.e. distance corresponding to the end of the fiber). Nonetheless, the use of an OTDR permits the FUT end to be identified and the FUT length measured, thereby enabling the time- gate window to be correctly selected.

It should be noted that the various modifications and alternatives described with reference to the two-ended measurement instrument of Figures 1 to IH could, for the most part, be applied to the single-end measurement instrument shown in Figure 2. Such modified configurations of the single-end measuring instrument will now be described briefly with reference to Figures 2B to 2G. hi the instrument shown in Figure 2B, the input light controller 42 and the analyzer and detection unit 44 share a polarization discriminator (polarizer) 2OA and a I/O-SOP controller 14 both of which are bidirectional in the sense that they convey input light towards the FUT 18 via the connector 16 and backreflected light returning from the FUT 18 in the opposite direction. The I/O-SOP controller 14 hence combines the functions of the separate I-SOP 14A and A-SOP 14B controllers, but where the scrambling is necessarily highly correlated for light traversing it in either direction. The backreflection extractor comprises a circulator/coupler 52A connected to the light source 12 by PMF 29A and to the input of the polarization discriminator (polarizer) 2OA by a second PMF 29B. The circulator/coupler 52A conveys the backreflected light to a detection system which, in Figure 2B, is shown as a single detector 22A. The output of the polarization discriminator (polarizer) 2OA is connected to the input of the bidirectional I/O-SOP controller by regular fiber. Other components are the same as in Figure 2.

The alignment of PMF 29A and 29B is fixed in the factory in such a manner that substantially all of the optical power from the tunable pulsed laser source 12 is maintained in one of the two axes of the fiber 29A and 29B (conventionally, the "slow" axis). Since the circulator/coupler 52A is polarization-maintaining, this alignment is to its point of attachment to PBS or polarizer. During attachment of each end of the PMFs 29A and 29B to the component concerned, the azimuthal orientation of the PMF is adjusted to ensure maximum transmission of the optical pulses towards the FUT 18. hi use, in the instrument shown in Figure 2G, the input light from light controller 42 is launched into FUT 18 via fiber connector 16 and backreflected light caused by any localized reflection (such as Fresnel reflection from the distal end 50 of FUT 18) returns back to analyzer and detection means 44 via fiber connector 16, entering the I/O-SOP controller 14 in the reverse direction. Its SOP is transformed by the SOP controller (or scrambler) 14, following which the light is decomposed by the polarization discriminator 20, specifically a PBS, into two components having orthogonal SOPs, typically linear SOPs at O- and 90-degree relative orientations. The first detector 22B is connected to one 5 of the two outputs of the PBS 20 to receive one of these orthogonal components and the backreflection extractor 52 (e.g. circulator/coupler) is connected to the other output (with respect to backreflected light from the FUT 18). The second detector 22C is in turn connected to that output port of the backreflection extractor 52 that transmits light from the PBS 20, so as to receive the other orthogonal component. Once suitably calibrated too take into account the relative detector efficiencies, wavelength dependence, circulator loss, etc., as will be described hereinafter, the sum of the detected powers from detectors 22B and 22C is proportional to the total backreflected power (S₀). The backreflected light may be detected approximately simultaneously by detectors 22B and 22C. hi the instrument shown in Figure 2C, the input light controller means 425 comprises tunable pulsed light source 12, and shares a backreflection extractor, a polarizer 2OA and I/O SOP controller means 14 with the analyzer and detection means 44. The backreflection extractor is shown as a circulator/coupler 52A. As before, the input light from the light controller means 42 is injected into FUT 18 via a fiber connector 16 and backreflected light reflected from any localized reflection (such as o Fresnel reflection) from the distal end 50 of FUT 18 returns back to the analyzing and detecting light controller means 44 and enters the I/O-SOP controller 14 in the reverse direction, following which the light returns back the polarizer 2OA. The detector 22A is connected to an output of circulator/coupler 52. hi the instrument shown in Figure 2D, the backreflected light reflected from any5 localized reflection from the distal end 50 of FUT 18 returns back to the I/O-SOP controller 14 in the reverse direction, following which the light returns back the polarizer 2OA and then is divided two parts by coupler 21. The detector 22B and 22C are connected to two outputs of coupler 21 to produce two repeated measured powers.

It should be noted that simultaneously detecting the backreflected light with two0 detectors of 22B and 22C may not be always necessary. It may also be detected at slightly different time. Also note that one detector with one optical switch 23 may also be used. In this case, two detectors of 22B and 22C may be replaced by one detector 22 A plus one optical switch 23 (Fig. 2E and 2F). The optical switch is used to route the backreflected light from different optical paths, either from circulator (or coupler) 52A or the PBS 2OC (Fig. 2F) or the coupler 21 (Fig. 2E), into same detector and thereby the backreflected light from different optical paths are detected at different time.

It should also be noted that in those configurations, such as polarizer 2OA based design in Fig. 2(B, C and D) and PBS 2OC based design in Fig. 2G, a polarized light from a tunable light source may also be obtained by adjusting incident SOP of lights from tunable light source before going through either polarizer or PBS. This is to say no any additional polarizer being required if a tunable (pulsed) light source may not be well polarized or experienced different light SOP at different wavelength, but an additional polarization controller is still required to insert position between tunable (pulsed) light source 12 and circulator/coupler 52A. For this case, 29A and 29B is preferred to be replaced by SMF.

Under the control of control unit 30, which also controls the tunable laser source 12, the sampling and averaging circuitry 32, in known manner, uses an internal analog-to- digital converter to sample the corresponding electrical signals from the detector 22 as a function of time to obtain the corresponding electrical response signals, and corresponding electrical response pulse signals then may be sampled and averaged to provide the mean response pulse for a particular series of light pulses, and the backreflected light power for that series obtained by averaging said mean response pulse over a substantial portion of its duration to provide a backreflected light power, the resulting plurality of powers of light backreflection. This averaging 'time' window (or "time-gate") may depend upon the pre-filtering of the sampling and averaging electronics. The resulting averaged powers are used by a data processor 34 to derive the DGD or PMD value, i.e., the differential group delay (DGD or polarization mode dispersion (PMD) of the FUT 18 from its distal end or any other connectors. It will be appreciated that the usual conversions will be applied to convert time delay to distance according to refractive index to obtain the length of fiber. hi addition to controlling the sampling and averaging circuit 32, the control unit 30 controls the wavelength of the tunable pulsed laser source 12 and the I/O-SOP selected by I/O-SOP controller 14. More specifically, for each setting k of the I/O-SOP controller 14, the control unit 30 causes the light backreflected power to be measured at least one pair of wavelengths λ⁽ _L ^k) and λ⁽^ ⁾ , respectively, that are closely-spaced relative

5 to each other. The midpoint wavelength of the pair of series of light pulses is defined as the average of the actual wavelengths of the series of light pulses, i.e., λ_k = (λ⁽ _L ^k) + λ⁽y⁾)/2. (The labels L and U refer, for convenience and ease of understanding, to "lower" and "upper" with respect to the midpoint wavelength λ_k ).

It should be appreciated that, where the group comprises one or more than one i o pair of series of light pulses, the midpoint wavelength as defined above in fact differs for each pair in the group.

The one, or more than one, pair of wavelengths in one group may also be used to measure the powers of the backreflections from the localized reflection at the distal end of FUT and then to extract PMD values for the FUT 18. However, it may not be

15 necessary to use more than one pair of wavelengths for the single-end PMD measurement unless for auto pre-scan acquisition (see more detailed discussion about auto pre-scan below). An optimal pair of wavelength may be satisfy the PMD_FUT ~ otiXπδv)^"1, where VL^(k) - vy^(k) = δv, and the VL^(1C) and vu^(k) corresponding to the pair of wavelengths λ_L ^(k) and λu^(k) under v = c/λ where c is light speed in vacuum.

20 It must also be appreciated that the center wavelength is only a conceptual definition, defined only for the purpose of facilitating description when a group comprises more than two wavelengths. In the limit where a group comprises only two wavelengths, it is of course equivalent to the "midpoint wavelength" defined hereinbefore. Center wavelength is not needed anywhere in the computations, and there

25 is no need for accurately "centering" the group on some target center wavelength since the latter is defined as the midpoint wavelength, and there is no need to set the laser wavelength at the center wavelength. Only the knowledge of the step(s) is needed, i.e., the difference between any pair that is used in the computations of cumulative PMD, irrespective of the center wavelength.

30 The I/O-SOP controller 14 sets the different I-SOPs and A-SOPs in a pseudo- random manner, such that the points conventionally representing SOPs on the Poincare sphere are uniformly-distributed over the surface of said sphere, whether the distribution is random or a uniform grid of points.

Before the tunable OTDR based single-end overall PMD measurement procedure is described in more detail, and with a view to facilitating an understanding of such operation, the theoretical basis will be explained, it being noted that such theory is not to be limiting.

Various Modifications to the Single-end PMD Measurement Means The invention encompasses various modifications to the single-end overall PMD measurement instrument shown in Figure 2. For example, in the tunable pulsed light source means 12, the PMF 29A may be replaced by a polarization adjuster 14 (see Figure 10A) connected by non-polarization-maintaining fiber to the tunable pulsed laser source 12 and to the input of backreflection extractor 52, respectively. If the optical path between the output of tunable pulsed light source means 12 and the input of the polarization discriminator 20 (e.g. PBS in Fig. 2) is polarization- maintaining, the polarization-maintaining circulator 52, e.g. in Figure 2 could be replaced by a polarization-maintaining coupler (e.g., a 50/50 coupler). The circulator is preferred, however, because it gives about 3 dB more dynamic range than a 50/50 coupler. It is also envisaged that the polarization discriminator 20 could be a polarizer and coupler, as shown in Figure 2B. hi that case, the detector B 22C would be connected to the coupler 21 to receive backreflected light that is not polarization-dependent.

If the optical path between the output of the tunable pulsed laser source 12 and the input of the polarization discriminator 20 is not polarization maintaining, the backreflection extractor, i.e., coupler or circulator 52 need not be polarization- maintaining.

A patchcord with either a FC/PC (or FC/UPC) connector or a fiber-pigtailed mirror may be used to connect at the distal end of FUT to create a localized reflection for measuring an overall PMD from the FUT. The light pulse length or duration from tunable OTDR may prefer to be long, for example of 1 to over 20 us, but a short pulse length or duration may also be applied. Although these modifications may be applied separately, the embodiment of the invention illustrated in Figures 2, 2(B-G) includes several such modifications. Specifically, the optical path between the tunable pulsed laser source 12 and the I/O-SOP controller 14 is not polarization maintaining, i.e., the PMFs 29A and 29B of Figure 2 are replaced by a polarization state adjuster connected by single-mode optical-fiber (e.g. a non-PMF fiber marketed as SMF-28 by Corning, Inc.) -based components (such as circulator and polarizing splitter 20), and then a polarization state adjuster maximizes the pulsed laser optical power passing through the I/O-SOP controller 14.

Instead of PBS 20 in Fig. 2G, the polarization discriminator 20 comprises a polarizer 2OA and coupler 21 combination (Fig. 2C), at the expense of approximately

3dB dynamic range for the case of a 50/50 coupler. The second detector B 22C (Fig. 2G) is connected to one of the arms of the coupler 21 so as to detect a fraction of the backreflected light for processing to deduce the total backreflected power of the pulses.

A person of ordinary skill in this art would be able, without undue experimentation, to adapt the procedure described hereinbefore for calibrating the relative sensitivities of the two detectors A and B (22B and 22C), including the losses induced by the intervening circulator or coupler, etc., for use with the single-end overall PMD measurement instrument of Figure 2G. It should be appreciated that, in the embodiment of Figure 2C, calibration of the mean relative gain is not required; the measured total power is independent of SOP, and there is no need for an "absolute" calibration to directly measure absolute transmission values; they can be obtained to within an unknown constant factor. The subsequent normalization over the mean traces averaged over SOPs, as described hereinbefore, eliminates the unknown factor.

It is envisaged that, where the detection means 22 comprises a single detector 22 A (Fig. 2B), normalized powers can be obtained by computing an average of all of the powers in first and second groups of powers, and dividing each of the powers by the said average power to obtain first and second groups of normalized powers, as described in detail hereinbefore.

Figure 2B illustrates a single-end PMD measurement suitable for obtaining the PMD using normalized powers obtained in this way. The single-end overall PMD measurement illustrated in Figure 2B is similar to that illustrated in Figure 2C but with coupler 21 and detector B 22C omitted. The data processor 34 will simply use the different normalization equations.

In any of the above-described embodiments, the operation of the I/O-SOP controller 14 is such that, for a given SOP of the light (which can be any SOP on the Poincare Sphere) received at its input, the SOP of the light leaving its output will be any one of a number of substantially uniformly distributed SOPs on the Poincare Sphere, whether the distribution is of random or deterministic nature. Typically, the number of output states of polarization is about 100-500, but it could be any practical number. However, it may also be possible to use one I/O-SOP controller (rather than two SOP controller for the two-end PMD measurement as shown in Fig. 1). It is noted that the distribution of the SOPs need not, and generally will not, be truly random; so "pseudorandom" might be a more appropriate term in the case where a random distribution is indeed used for convenience because it is easier and less expensive to implement than a uniform grid of SOPs. The detector means 22, whether a single detector or a pair of detectors, and the sampling and averaging circuitry unit 32, may be as used in standard commercial OTDRs that are known to a person skilled in this art.

Where the polarization discriminator 20 comprises a PBS 2OC or a polarizer 2OA and coupler 21 combination, there will be a penalty of approximately 3dB dynamic range for the case of a 50/50 coupler where the second detector 22C is connected to one of the arms of the coupler 21 so as to detect a fraction of the light for processing to deduce the total light power, however, such reduced power may not be critical for the measurement.

The control unit 30 may advantageously be a separate computer. However, it is noted that a single computer could perform the functions of the data processor 34 and the control unit 30.

SINGLE-END CUMULATIVE PMD MEASUREMENT

The polarization-sensitive optical time domain reflectometer (POTDR) illustrated in Figure 3 comprises tunable pulsed light source means 12, bidirectional polarization controller means 14 (conveniently referred to as an I/O SOP controller means), sampling and averaging unit 32 and data processor means 34, all controlled by a control unit 30, and detection means 22 comprising first and second detectors A and B, 22B and 22C, respectively. The tunable pulsed light source means 12 is coupled to a polarization maintaining fiber (PMF) 29A for producing light pulses for launching into a fiber-under- test (FUT) 18 from connector 16 via the I/O state of polarization (I/O-SOP) controller means 14, which, as explained later, also receives corresponding backrefiected light from the FUT 18 via connector 16.

The input light controller means 42 and analyzer and detection means 44 comprise a backrefiected light extractor, specifically a polarization-maintaining circulator 52 in Figure 3, a polarization discriminator (PD) means 20, specifically a polarization beam splitter (PBS) in Figure 3, and a input and output SOP controller (or scrambler) 14.

The circulator 52 is coupled to the input of PBS 20 by a second PMF 29B so that the optical path from the tunable laser source 12 to the PBS 20 is polarization-maintaining.

Preferably, a single-mode fiber is used to couple the PBS 20 to the I/O-SOP controller (or scrambler) 14. The alignment of PMF 29A and 29B is fixed in the factory in such a manner that substantially all of the optical power from the tunable pulsed laser source 12 is maintained in one of the two axes of the fiber 29A and 29B (conventionally, the "slow" axis). Since the circulator 52 is polarization-maintaining, this alignment is maintained until the distal end of PMF 29B, at its point of attachment to PBS 20. During attachment of each end of the PMFs 29A and 29B to the component concerned, the azimuthal orientation of the PMF 29A/B is adjusted to ensure maximum transmission of the optical pulses towards the FUT 18.

Backrefiected light caused by Rayleigh scattering and, in some cases, discrete (Fresnel) reflections, from the FUT 18 enters the I/O-SOP controller 14 in the reverse direction. Its SOP is transformed by the SOP scrambler 14, following which the light is decomposed by the PBS 20 into two components having orthogonal SOPs, typically linear SOPs at 0- and 90-degree relative orientations. The first detector 22C is connected to one of the two outputs of the PBS 20 to receive one of these orthogonal components and the circulator 52 is connected to the other output (with respect to backrefiected light from the FUT 18). The second detector 22B is in turn connected to that output port of the circulator 52 that transmits light from the PBS 20, so as to receive the other orthogonal component. Once suitably calibrated to take into account the relative detector efficiencies, wavelength dependence, circulator loss, etc., as will be described hereinafter, the sum of the detected powers from detectors 22B and 22C is proportional to the total backreflected power (S₀). Under the control of control unit 30, which also controls the tunable laser source

12, the sampling and averaging circuitry 32, in known manner, uses an internal analog-to- digital converter to sample the corresponding electrical signals from the detectors 22B and 22C as a function of time to obtain the corresponding electrical impulse response signals, then averages the impulse-response signals corresponding to a particular series of light pulses to produce an OTDR trace for that series. The resulting OTDR traces are used by a data processor 34 to derive the cumulative PMD curve PMD(z), i.e., the polarization mode dispersion (PMD) as a function of the distance z along the FUT 18 from its proximal end, that is the end which is coupled to the analyzer and detection means 44. It will be appreciated that the usual conversions will be applied to convert time delay to distance according to refractive index.

In addition to controlling the sampling and averaging circuit 32, the control unit 30 controls the wavelength of the tunable pulsed laser source 12 and the I-SOP and A- SOP couple selected by I/O-SOP controller 14. More specifically, for each setting k of the I/O-SOP controller 14, the control unit 30 causes the backreflected power to be measured at at least one pair of wavelengths λ⁽^ and λ⁽^ ⁾ , respectively, that are closely- spaced relative to each other. The midpoint wavelength of the pair of series of light pulses is defined as the average of the actual wavelengths of the series of light pulses, i.e., λ_k = (λ⁽ _L ^k) + λ⁽ _y ⁾) /2. (The labels L and U refer, for convenience and ease of understanding, to "lower" and "upper" with respect to the midpoint wavelength λ_k). It should be appreciated that, where the group comprises more than one pair of series of light pulses, the center wavelength as defined above in fact differs for each pair in the group. It must also be appreciated that the center wavelength is only a conceptual definition, and was defined only for the purpose of facilitating description of the basic one pair implementation. It is not needed anywhere in the computations, and there is no need for accurately "centering" the pair on some target center wavelength since the latter is defined as the mean of the actual pair. Nor is the laser wavelength set at the center wavelength. Only the knowledge of the step is needed, i.e., the difference between any pair that is used in the computations of cumulative PMD, irrespective of the center wavelength, even if it were to be random and unknown. The I/O-SOP controller 14 sets the different (I-SOP, A-SOP) couples in a pseudorandom manner, such that the points conventionally representing SOPs corresponding to each member of the couple are uniformly distributed over the surface of the Poincare sphere, whether the distribution is random or a uniform grid of points.

Before the operation of the POTDR is described in more detail, and with a view to facilitating an understanding of such operation, the theoretical basis will be explained, it being noted that such theory is not to be limiting.

Various Modifications to the Single-End Cumulative PMD Measurement Means

The invention encompasses various modifications to the embodiment shown in Figure 3. For example, in the tunable pulsed light source means 12, the PMF 29 A may be replaced by a polarization adjuster 14 (see Figure 1OA) connected by non-polarization- maintaining fiber to the tunable pulsed laser source 12 and to the input of backreflection extractor 52, respectively.

If the optical path between the output of tunable pulsed light source means 12 and the input of the polarization discriminator 20 is polarization-maintaining, the polarization-maintaining circulator 18 in Figure 3 could be replaced by a polarization- maintaining coupler (e.g., a 50/50 coupler). The circulator is preferred, however, because it gives about 3 dB more dynamic range than a 50/50 coupler.

If the optical path between the output of the tunable pulsed laser source 12 and the input of the polarization discriminator 20 is not polarization maintaining, the backreflection extractor, i.e., coupler or circulator 52 need not be polarization- maintaining.

Although these modifications may be applied separately, the embodiment of the invention illustrated in Figure 3 includes several such modifications. Specifically, the optical path between the tunable pulsed laser source 12 and the I/O-SOP controller 14 is not polarization maintaining, i.e., the PMFs 29A and 29B of Figure 3 are replaced by a polarization state adjuster 14 connected by single-mode optical-fiber (e.g. a non-PMF fiber marketed as SMF-28 by Corning, Inc.) -based components (such as circulator 52 and polarizing splitter 20), to maximize the pulsed laser optical power passing through the I/O-SOP controller 14 and launching into FUT 18. Instead of PBS 20, the polarization discriminator 20 may comprise a polarizer

2OA and coupler 21 combination, as shown in Figure 3B, at the expense of approximately 3-dB of dynamic range for the case of a 50/50 coupler. The first detector 26 A is connected to one of the arms of the coupler 2OA so as to detect a fraction of the backreflected light for processing to deduce the total backreflected power of the pulses. In the POTDR of Figure 3, an analogous procedure to that described above with respect to the embodiment of Figure 3 could then be carried out, although not required as stated above, to calibrate the relative sensitivities of the two detectors 22B and 22C, including the losses induced by the intervening circulator or coupler, etc.

A person of ordinary skill in this art would be able, without undue experimentation, to adapt the calibration procedure described hereinbefore with reference to the POTDR of Figure 3 for use with the embodiment of Figure 3. It should be appreciated that, in the embodiment of Figure 3B, calibration of the mean relative gain is not required; the measured total power is independent of SOP, and there is no need for an "absolute" calibration to directly measure absolute transmission values; they can be obtained to within an unknown constant factor. The subsequent normalization over the mean traces averaged over SOPs, as described hereinbefore, eliminates the unknown factor.

It is envisaged that the detection means 22 might comprise a single detector and normalized OTDR traces be obtained by computing an average of all of the OTDR traces in first and second groups of OTDR traces, and dividing each of the OTDR traces by the said average OTDR trace, point by point, to obtain first and second groups of normalized OTDR traces, as described in detail hereinbefore.

Figure 3 A illustrates a POTDR suitable for obtaining the PMD using normalized OTDR traces obtained in this way. The POTDR illustrated in Figure 3A is similar to that illustrated in Figure 3B but with coupler 21 and detector B 22C omitted. The data processor 34 will simply use the different normalization equations given in the Method of Operation provided hereinbefore.

In any of the above-described embodiments, the operation of the I/O-SOP controller 14 is such that, for a given SOP of the light (which can be any SOP on the Poincare Sphere) received at its input, the SOP of the light leaving its output will be any one of a number of substantially uniformly distributed SOPs on the Poincare Sphere, whether the distribution is of random or deterministic nature. Typically, the number of I- SOPs and A-SOPs is each about 100-200 for high quality results, but it could be any practical number. It is noted that the distribution of each of the I-SOPs and A-SOPs need not, and generally will not, be truly random; so "pseudo-random" might be a more appropriate term in the case where a random distribution is indeed used for convenience because it is easier and less expensive to implement than a uniform grid of I-SOPs and A- SOPs.

Although it is preferred to use two detectors to obtain two orthogonal polarization components simultaneously, it is envisaged that the two detectors in the embodiments of Figures 3 and 3B could be replaced by one detector plus one optical switch. The optical switch is used to route the two orthogonal polarization components (Fig. 3) or to route the one output from polarizer and another output directly from coupler (Fig. 3B) of the backreflected light to the same detector, for example alternately, so that two orthogonal polarization components or one output from polarizer and another output directly from coupler of the backreflected light can be detected sequentially by the same detector.

A normalized OTDR trace for that series of light pulses would be obtained by dividing at least one of the OTDR traces corresponding to the two detected different polarization components for that series by the sum of the OTDR traces corresponding to the two detected different polarization components for that series. This alternative may be used regardless of whether the analyzer and detector unit comprises a PBS or a coupler. Any modification to the normalization and processing is expected to be minor and within the common general knowledge of a person skilled in this art.

Alternatively, such an arrangement of one detector plus one optical switch could be used to detect one polarization component and the total optical power sequentially by the same detector. As before, the optical switch would route one polarization component and the total reference optical power to the same detector, and the normalized OTDR trace corresponding to that particular series of light pulses would be obtained by dividing the OTDR trace for that series by the OTDR trace for that series corresponding to total power. It is also worth noting that, while the use of one detector with one optical switch instead of two detectors disadvantageously at least doubles the total acquisition time in comparison with embodiments using two detectors,

It is also envisaged that a rotating polarization discriminator (PD), whether it is a polarizer or a PBS, may be used to sequentially acquire two orthogonal components for example via rotating the polarization discriminator by 90° to switch from detecting Px to detecting Py, or from detecting Py to detecting Px. The detector means 22, whether a single detector or a pair of detectors, and the sampling and averaging circuitry unit 232, may be as used in standard commercial OTDRs that are known to a person skilled in this art.

The control unit 30 may advantageously be a separate computer. However, it is noted that a single computer could perform the functions of the data processor 34 and the control unit 30.

Various other modifications to the above-described embodiments may be made within the scope of the present invention. For instance the tunable pulsed laser source 12 and I/O-SOP controller 14 could be replaced by some other means of providing the different polarization states of the pulses entering the FUT 18 and analyzing the resulting backreflected signal caused by Rayleigh scattering and/or discrete reflections leaving the FUT 18.

Thus, a polarimeter may be used (splitters with three or more analyzers and photodetectors in parallel), which measures more than one polarization component of the backreflected signal simultaneously, or some other configuration, so that the power that reaches the photodetectors is dependent on the state of polarization (SOP) of the backreflected light.

It should be noted that each group is not limited to one pair of series of light pulses. Indeed, it may be advantageous to use three or more different closely-spaced wavelengths per group of traces obtained with a common SOP, instead of the minimally- required two closely-spaced wavelengths λ|_ and λu (each group then comprises 2-Nχ OTDR traces instead of four, two sets of 2 -Nx traces in the case of the two-photodetector embodiments, where N^ is the number of wavelengths in a group of series of light pulses). For example, in the case where three closely-spaced wavelengths are used, one can choose the series of light pulses at the lowermost and intermediate wavelengths as one pair, and the series of light pulses at the intermediate and uppermost wavelengths as a second pair, such that the wavelength step between the light pulses in one pair is greater than the wavelength step between the light pulses in the other pair, perhaps a few times larger.

Since there are three combinations of wavelength steps corresponding to three wavelengths (i.e., N^(N^-l)/2), one can simultaneously obtain the data corresponding to two significantly different wavelength steps within a measurement time that is only 1.5 times greater than the time required to perform a one-step measurement. Thus, proceeding with three wavelengths (or more) per group proves highly advantageous because the cumulative PMD value can increase significantly along the length of the FUT 16 (from zero to the overall PMD of the FUT), and hence the use of two, three, or more different steps allows one to maintain a satisfactory relative precision (e.g. in %) at all positions along the fiber. It will be appreciated that one could also select the light series at the lowermost and uppermost wavelengths as a third pair, with a wavelength step greater than both of the others. The use of only one step gives one given absolute uncertainty, as for example ± 0.1 ps, which represents a small % uncertainty at a distance where the PMD has grown to a value of 10 ps, but is not good in % at short distances where the PMD is, for example, only 0.2 ps. To get a smaller uncertainty for smaller PMD values, a larger step must be selected. Hence the obvious advantage of implementing such an alternate embodiment where more than two wavelengths per group are used. It changes nothing to the setup, nor to the principle of the invention as described above, but saves time in the overall measurement process.

Although the above-described embodiment changes the center wavelength for each SOP, this is not an essential feature of the present invention. While superior performance can be obtained by covering a large wavelength range in order to obtain the best possible average of DGD, as per the definition of PMD, a POTDR embodying the present invention will work with no bias and may provide acceptable measurements of PMD(z), with a constant center-wavelength. UNDERLYING THEORY, DATA PROCESSING AND COMPUTATIONAL METHOD

Although the applicant does not wish to be constrained by theory, the following discussion of the underlying theory is provided so as to facilitate understanding of the various embodiments of the invention.

The computation of the DGD or rms DGD (i.e. PMD) based on PMD measurement principle of randomly input and output Sate of polarization Scrambling Analysis (SSA) method makes use of prior-art PMD-related measurement theory including Poincare Sphere Analysis (PSA) and Generalized Interferometric Method (GINTY) with appropriate adaptations resulting in the equations given below. The specific theory applied to the various aspects of this invention is closely related to the theory described in international patent application No. PCT/CA2006/001610 and the above-identified United States Continuation-in-Part application No. 11/727,759, the entire contents of each of which are incorporated herein by reference.

Throughout this specification, wavelength λ, where λ is the vacuum wavelength of the light, and optical frequency y are used, but they are of course related by the well known relationship λ = c/v. Although the use of optical frequency is more "natural" in this theory, in practice, for closely-spaced wavelengths, wavelengths can be used, it being understood that the appropriate conversion factors are applied to the equations presented herein.

It should be recalled that PMD is the statistical RMS value of differential group delay DGD(λ), estimated by averaging over a large wavelength range, or over a period of time, ideally both, so that the largest possible number of random occurrences of DGD are observed to obtain its RMS value.

FUNDAMENTAL THEORY

Randomly Input/Output SOP Scrambling Analysis for PMD Measurement

In the this section, we will describe the fundamental theory of 'Randomly Input and Output Sate of Polarization Scrambling Analysis (SSA) Method for Polarization Mode Dispersion Measurement' and its applications to measure a PMD by accessing either both ends or single end of FUT. The three main applications are: (1) 'Two-end PMD measurement method and apparatus for determining DGD and PMD of an optical link' (simply tilted as 'Two-end PMD measurement'), (2) 'Single-end overall PMD measurement using tunable OTDR and its method of determining PMD' (simply tilted as 'Single-end overall PMD measurement'), and (3) 'Polarization-sensitive optical time domain reflectometer (POTDR) and its method for determining cumulative PMD as function of fiber length' (simply tilted as 'Single-end cumulative PMD measurement'). The methods of operation, data processing and computational methods for these applications will be described in details in following sections.

If a tunable laser and polarization controller are used to launch and control the input light incident at an one end of FUT and a polarization state analyzer and a power meter are used to measure the power from the FUT, from either the same or different end of FUT, at two closely spaced optical frequencies, Vu and V|_, around a given midpoint frequency, V_1nJd, for a large number K of input / output state of polarizations, i.e., comprising a large number of "SOP couples" (I-SOP_k, A-SOP_k) each referring to both the input-SOP and the analyzer axis "seen" by the received light. Both the I-SOP and the A- SOP values should be chosen in a random manner, such that the points conventionally representing SOPs on the Poincare sphere are uniformly-distributed over the surface of said sphere, whether the distribution is random or a uniform grid of points. It has been found that, on average over a sufficiently large, uniformly distributed number K of said "SOP couples", the mean-square difference between normalized powers observed at vu and VL is related to the DGD at its midpoint frequency v_mj_d (v_mj_d = (vu+V|_)/2) by a simple relationship, valid in all cases for any type of practical FUT regardless of its degree of randomness or its polarization coupling ratio, including the extreme case of a PMF fiber, i.e.,

DGD(V) (1)

where < >_SOP represents the average over the K SOP couples, δv = (vu-vι_) is the "step", and a is a theoretical constant that is dependent on measurement set-up configuration, i.e. either two or one measurement configuration. ΔT(v) is a difference between the analyzed normalized powers (i.e. transmissions) observed at Vu and V|_, respectively, and its mean-square difference is,

where the normalized powers for a polarizer based one detector embodiment as shown in Figures IB, 2C and 3 A are, p(k) p(k)

^{L ~} U VPL) I SOP ^{U ~} ° ( VPU ) /SOP where the reference mean-value U₀ is a theoretical constant that is dependent on measurement set-up configuration, i.e. either two-end (Figure IB) or one-end (Figures 2C and 3A) measurement configuration, and the average power is defined,

Ip \ - J-V P'*⁾ I P \ - J_V P<*>

V i / SOP ^~ v Zw L ^• V V I SOP ^~ r Z-/ U

^Λ k ^ k

Furthermore, for a prescribed wavelength range, in preferred embodiments of the invention the averages indicated in equation (1) are preferably carried out over both many

SOP couples and midpoint wavelengths, both of which are changed from one group of two closely-spaced wavelengths to the next, thus obtaining the rms DGD (i.e. PMD) over the prescribed wavelength range, expressed as:

PMD = - — arcsinfα J UT(V)²) 1 (2) πδv V * V \ ^v ' f ∞PΛ J ^v '

where ( ) is averaged over both SOP and wavelength or wavelength across a prescribed wavelength range. hi the limit of a sufficiently small optical-frequency difference ("step") between the closely-spaced wavelengths, equations (1) and (2) simplify to yield the simpler differential formula that follows,

^DGDM

^(la)

The DGD or PMD value extracted from above equations (1) and (2) are valid for both two-end and single-end measurement configurations and they represent measured values between input and output ports. For a two-end measurement configuration, the theoretical constant a ds is

and, for a single-end measurement configuration, if a common (same) state of polarization controller (scrambler) is used as both input and output light SOPs' controlling, such as for figures 2, 2C-G, the theoretical constant a ^ is

The reference mean- value U₀ is also different for different measurement configurations. For a two-end measurement configuration, the reference mean-value U₀ is

«o = \ (5) and, for a single-end measurement configuration, if an incident state of polarization (I- SOP) of light is parallel to the analyzer axis, for example in Fig. 2C, the reference mean- value U₀ is

«o =f (6)

Note the relationship in equation (1) is hold for DGD-δv < ³A for two-end measurement configuration and DGD-δv < ¹A for single-end measurement configuration, thus clarifying the meaning of "closely-spaced wavelengths".

It should be noted that DGD(v) and PMD computed from equations (1) and (2), respectively, are exact measured DGD and PMD values between input connector (16A) and output connector (16B) of FUT, and they may not present the one-way (forward) DGD or PMD from the FUT, for example, for the single-end measurement configuration, the measured values of DGD and PMD are a roundtrip value for FUT, but, for the two- end measurement configuration, a measured DGD or PMD extracted from equations (1) and (2) are an one-way (forward) DGD or PMD of the FUT. For the single-end PMD measurement configuration, a roundtrip factor (a_rl = .j— ) is required to multiply on a

V 8 measured roundtrip PMD from equation (2) to provide one-way (forward) PMD of FUT.

The normalized power will in fact be obtained differently in each embodiment, i.e., by suitable programming of the data processor 34. This explanation of the theory is provided for the basic one-photodetector embodiment of Figures IB, 2C and 3 A, where normalization over the average power is both necessary and sufficient, assuming total power is stable when the (I-SOP, A-SOP) couple is changed, or as a function of time.

Note that the normalization procedure for the two-end measurement configuration (figure

IB) and single-end (figure 2C and 3A) are very similar, but reference mean- values (uo) (see equations (5) and (6)) are different. Also note, for the single-end cumulative PMD measurement, a normalized power trace (T(z)) as function of distance z is computed. A detailed description of this normalization procedure is provided hereinafter.

It should be note that equation (1) produces a DGD value at a given midpoint wavelength, defined as the average wavelength of the particular closely-spaced wavelengths used in the measurement and also it gives a DGD as function of optical wavelength/frequency. The equation (2) produces a PMD value for a prescribed wavelength range. The PMD is defined as the root-mean-square (rms) value of DGD by averaged over wavelength.

Two-End PMD Measurement

The two-end PMD measurement is often a case for most available PMD measurement techniques used in the field. The basic theory of randomly input and output SSA method described above can be applied for two-end PMD measurement, where the test link may involve either no optical amplifier or with optical amplifiers. When optical amplifiers are used in the test link, the ASE lights from amplifiers will be mixed launched polarized coherent lights and, consequently, both ASE and launched lights are measured by photodetector 22 A (Figure IB).

Below we describe how to apply our basic theory of SSA to two-end PMD measurement that can be applied for these both cases, without or with optical amplifiers, for the test link, by accessing two ends of FUT.

DGD Measurement without Amplifiers in the Test Link

If a tunable laser source, which can select its optical frequency by either step tuning, or frequency sweeping, or frequency modulation, or similar means, or if a polarized broadband light source is used, then tunable filter may be used to select the optical frequency (wavelength), and an input polarization controller are placed at a proximal of FUT and a polarization state analyzer, usually an output polarization controller, polarizer (or PBS) and a power meter (combined with tunable filter if polarized broadband light source is used instead of tunable laser source) are located at the opposing end of FUT for measuring the power from fibers at two closely spaced optical frequencies, vy and V|_, around a given midpoint frequency, v^a, for a large number K of input / output state of polarizations, i.e., comprising a large number of "SOP couples" (I-SOPk, A-SOPk) each referring to both the input-SOP and the analyzer axis "seen" by the received light. Both the I-SOP and the O-SOP values should be chosen in a pseudo-random manner, such that the points conventionally representing SOPs on the Poincare sphere are substantially uniformly-distributed over the surface of said sphere, whether the distribution is random or approximately a uniform grid of points. By average over a sufficiently large, uniformly distributed number K of said SOP couples, the forward DGD at its midpoint frequency v_m,_d (v_m,_d = (vu+V|_)/2) ca be calculated from equation (1) as,

DGD(v) = — — arcsinfα J (AT(V)²) ] (7) πδv \ * v \ ^v ' /SOP )

It should be note that equation (7) produces a one-way (forward) DGD value (i.e. DGD) at a given midpoint frequency (wavelength) for the FUT.

As already mentioned, the PMD is defined as the root-mean-square (rms) value of DGD by averaged over wavelength (note the DGD averaged over time may give to a rms DGD (not mean DGD)). An rms DGD (i.e. PMD) over the prescribed wavelength range now is computed by equation (2) as:

PMD = — arcsinfα ,/ (AT²) 1 (8) πδδvv V * V \ ISOPΛ ) 9

It should be appreciated to note again that, in equations (7) and (8), a = J—

must be used for the two-end PMD measurement configuration. The relationship holds for DGD-δv < 3/4, thus clarifying the meaning of "closely-spaced wavelengths".

In the limit of a sufficiently small optical-frequency difference ("step") between the closely-spaced wavelengths, equations (7) and (8) can simplify to yield the simpler differential formula that follows,

^DGD^'^ U^Any)%_F ^<7a)

™ -/KL <^8a>

Note that equations (7) and (8) can directly adapt basic theoretical equations in (1) and (2) to compute the forward DGD and PMD of FUT.

DGD Measurement with Amplifiers in the Test Link

In many field applications, optical amplifiers (typically erbium-doped optical amplifiers) have been inserted into the link. That is, the FUT 18 may comprise at least one, and possibly several, optical amplifiers at various spacings (e.g. 60km) within the FUT 18. When an optical amplifier is present, a power meter located at distal end of FUT 18 will likely also detect (substantially unpolarized) amplification spontaneous emission (ASE) light in addition to the signal emitted by the optical generator means. The presence of ASE in the detected signal can be taken into account by "scaling down" the mean-square differences <ΔT(v) )_SOP by a factor that can be computed independently from the same raw data. This factor, σ_r ²(v) , is a relative variance of the normalized powers defined as,

where the reference variance is and {T(v))_sop mean to

average over both normalized powers at Vu and V|_. (Note for the normalized powers T(v) averaged over a sufficient number of randomly scrambled SOPs, {T(v))_sop = — ).

Then a forward DGD (one-way) at a given midpoint wavelength is obtained by dividing the mean-square differences by the relative variance in equation (9) as,

DGD(v)

And, moreover, a forward rms PMD (one-way) for a prescribed wavelength range can be expressed by,

where average over SOP in equation (10) is now replaced by the average over both SOP and wavelength, and a relative variance of the normalized powers now is expressed as,

In the limit of a small step, equations (10) and (11) simplify to a differential formula as,

It should be noted that if two launched powers of "closely-spaced wavelengths" are equal and there is negligible spectral attenuation from FUT for these "closely-spaced wavelengths", the measured powers for "closely-spaced wavelengths" can directly be applied into equations (10) and (11), i.e. no need any normalization for measured powers (note in this case, (T(v))_sop may not be equal ¹A). This is because, under this condition, a normalization procedure described above may only produce a 'constant factor' that is multiplied on measured powers in order to obtain normalized power (between 0 and 1), but by using equations (10) and (11) to compute DGD or PMD, this constant 'factor' is eventually cancelled because there is an exactly the same 'factor' multiplied on both mean-square difference and relative variance if they are both directly computed from measured powers. In other words, if equations (10) and (11) are used, only relative powers that are proportional to normalized powers are required to be obtained to calculate the DGD or PMD.

It should be appreciated to note that equations (10) and (11) can apply for both cases with or without amplifiers 'noise' for the test link.

An alternative method of the invention, an estimate of the PMD (i.e. rms or mean DGD value over an optical frequency range) can be obtained by root-mean square or mean averaging all single DGD(v) values at different midpoint wavelengths indicated in equation (7) or (10) over an optical frequency range.

Single-End PMD Measurement The single-end PMD measurement is a very important measurement technique for the field application. The above basic theory of SSA described above can also be applied for single-end PMD measurement. The single-end PMD measurement described here is divided as two cases: the first case is to measure all overall PMD of a FUT by analyzing backreflected light from another distal end of FUT, and the second case is to measure cumulative PMD as function of FUT length. Both cases only access one end of FUT.

Single-End Overall PMD Measurement

For the single-end PMD measurement using backreflected light from the distal end of fiber, it may be often involving the test fiber without optical amplifiers. Below we describe our basic SSA theory being applied for the single-end overall PMD measurement by accessing only one end of FUT.

If a mirror (such as a fiber pigtailed mirror) is connected at the distal end of the FUT, and if one could neglect Rayleigh backscattering and any spurious discrete reflections (e.g. from any connectors or splices) along the FUT, the tunable OTDR could be replaced by a tunable CW laser (no pulses) and a power meter for measuring the power reflected from the mirror at the distal end of the FUT at two closely spaced optical frequencies, vy and V|_, around a given midpoint frequency, Vjmd, for a large number K of (I-SOP, A-SOP) couples, i.e., one such setting referring to both the input-SOP and the analyzer axis "seen" by the backrefiected light. (N.B. λ = c/v, where λ is the vacuum wavelength of the light. Although the use of optical frequency is more "natural" in this theory, in practice, for closely-spaced wavelengths, wavelengths can be used, it being understood that the appropriate conversion factors are applied to the equations presented herein.). It has been found from basic PMD measurement theory above that, on average over a sufficiently large, uniformly distributed number K of said (I-SOP, A-SOP) couples, the mean-square difference between normalized powers (i.e. transmission) observed at vu and V[_ is related to the roundtrip-DGD(v) at its midpoint frequency v_c (v_c = (vu+V|_)/2) by a simple relationship as Equation (1), valid in all cases for any type of practical FUT regardless of its degree of randomness or its polarization coupling ratio, including the extreme case of a PMF fiber, as,

DGD_RoundTnp(y) = ^arcsin(«_Λ / T₇Q (12)

where a theoretical constant value a = J — for the single-end roundtrip DGD

measurement, < >_SOP represents the average over the K (I-SOP, A-SOP) couples, δv = ( VU-VL ) is the "step", ΔT is the difference between the normalized powers observed at Vu and vι_, respectively.

The relationship holds for DGD_R0UndTπp-δv < 1/2, thus clarifying the meaning of "closely-spaced wavelengths".

The roundtrip DGD(v) derived by equation (12) is not double the forward

DGD(v). The roundtrip DGD_RMS extracted from rms of DGD(v) over a wavelength range is also not double. For the late case, however, when averaged over wavelength, or time, the PMD value (statistical average) (i.e. rms DGD) is related to the roundtrip-PMD

(i.e. rms DGD_R0UndT_πp) through a simple factor, the roundtrip factor α_rt = v3/8 , i.e., DGD_RMS = α_rt-DGD_Roundτ_πpRMs or PMD = V3?8 ^• PMD_RoundTπp, where PMD is defined as the root-mean-square (RMS) value of DGD.

It should be noted that a different roundtrip factor results if the alternative definition of PMD, i.e., the mean value of DGD, is used instead of the RMS-DGD definition. Typically, in order to measure an overall PMD reliable, a tunable OTDR should be used. The tunable OTDR launches relatively long pulses into the FUT, the at least one photodetector in the OTDR then detecting the backreflected power of the localized reflection at the distal end of FUT.

The roundtrip DGD of the FUT section comprised between the output of the instrument and the selected reflection is obtained as previously from equation (12), where the power observed for a given (I-SOP, A-SOP) couple is now obtained as, for example, the power of the pulse backreflected from the selected reflection averaged over a predetermined portion of the pulse duration.

It is noteworthy that the above defined backreflected power may be obtained by averaging each response pulse over a substantial portion of its duration, therefore it is preferable to apply a long OTDR pulse (e.g. 1 to 20 us) for this single-end PMD measurement technique.

Furthermore, in preferred embodiments of the invention if an overall total PMD is desirable to be measured, the averages indicated in equation (12), are preferably carried out over both I-SOP, A-SOP and midpoint-wavelengths, all three of which are changed from one group of two closely-spaced wavelengths to the next, thus obtaining the roundtrip PMD instead of only one particular DGD at one particular wavelength. A roundtrip rms DGD (i.e. roundtrip PMD) over the prescribed wavelength range is expressed as:

PMD_RomdTnp arcsin(α_ώ ^ {AT(vγ )^ ) (13)

Moreover, a forward PMD value can be obtained by multiplying an above specified round trip factor, α_rt = V3/8 , to equation (13) as following equation,

PMD = a_rt -PMD_RomdTrψ (14)

In the limit of a sufficiently small optical-frequency difference ("step") between the closely-spaced wavelengths, equations (12) and (13) simplify to yield the simpler differential formula that follows,

DGD_RmmdTrψiy)

(12a) πδv

PMD_RomdTnp = ^- ^■ J (AT(VY) _{sQp λ} (13a)

A PMD measured based on equation (13) has an advantage of short acquisition time. However, a rms DGDR_0UndTnp or mean DGDR_Oundτnp can also be obtained from measured DGD_ROundτ_πp(v) for many different midpoint wavelengths by root-mean square or mean DGDR_Oundτ_πp(v) from equations (12) or (12a) over a prescribed wavelength

range, e.g. rms DGD_RomdTnp = and

mean DGD_RomdTrψ = (,DGD_RoundTri\ . A forward rms DGD and mean DGD are then

obtained by simply multiplying a roundtrip factor of Λ/3/8 and 2/π on rms DGD_ROundTπp and mean DGDR_Oundτ_πp, respectively.

Single-End Cumulative PMD Measurement Above equations (12) and (13) described for the single-end overall PMD measurement can apply for measuring single-end cumulative PMD as a function of distance z by analyzing the Rayleigh backscattering lights for each location (z) along FUT length. Thus, it is necessary to use a short light pulse, for example from a tunable OTDR. Note that to use a too short light pulse would limit a measurable FUT length but a too long pulse may not be able to resolve beating length of fiber.

Indeed, if a very short light pulse is used, OTDR 'traces', or backreflected power as a function of distance z, are the same as if the above single-end overall PMD measurement were repeated an infinite number of times, with the end reflector shifted by a distance increment dz between measurements. Providing that the pulses are very short, and also ignoring the fact that the "coherence noise" always adds to an OTDR trace, the same result as in equation (12) is obtained, except that it is obtained as a function of distance z in one step. The different ΔT(v,z) values obtained with different (I-SOP, A- SOP) couples are now differences between whole OTDR traces as a function of z, instead of just one number, and give DGDR_Oun(πnp(v,z). Note T(v,z) is a normalized trace as function of fiber length z.

It is generally impractical to use very short pulses in the field, however, because attainment of a useful dynamic range would require an exceedingly long measurement time. Also, reduction of the high level of coherence noise resulting from using short pulses may require an unacceptably large equivalent laser linewidth, which results in a small maximum measurable PMD. The present invention takes account of the finding that, with large pulses, the mean-square differences <ΔT(V,Z)²>_SOP are simply 'scaled down' by a factor that can be computed independently from the same raw data. (Note that here the subscript SOP denotes an average over the (I-SOP, A-SOP) couples.) This factor, σ|: (z, v) , is the relative variance of the traces, a function of z depending on local characteristics of the fiber, defined as,

where the reference variance is σ*₀ = 4/45. The roundtrip DGD at a given midpoint wavelength then is obtained by dividing the mean-square differences in equation (12) by the relative variance in equation (14), i.e.

^DGDRoundTr_Ψ (*, ^V) =

Furthermore, in preferred embodiments of the invention the averages indicated in equations (14) and (15) are preferably carried out over both (I-SOP, A-SOP) couples and center wavelengths, both of which are changed from one group of two closely-spaced wavelengths to the next, thus obtaining the roundtrip PMD instead of only one particular

DGD at one particular wavelength.

PMD_RoundT (z)

Moreover, since the typical user will prefer the forward PMD value to be displayed instead of the roundtrip value, the result is multiplied by the above-specified roundtrip factor, α_rt = Λ/3 / 8 . Thus, the forward PMD is as,

PMD(z) = a_rl - PMD_RoundTnp(Z) (17) where the average over (I-SOP, A-SOP) couples in equation (14) is also replaced by the average over both (I-SOP, A-SOP) couples and wavelength, i.e.

It should be noted that a roundtrip rms DGD or a roundtrip mean DGD (i.e. roundtrip PMD) can also be obtained by root-mean square average or mean average roundtrip DGD at given midpoint wavelength over prescribed wavelength range as rms DGD_RomdTrψ(z) = ^DGD_RomdTrψ(z)²)_λ

and mean DGD_RoundTrψ (z) = (DGD_RoundTrψ(z))_λ .

A forward rms DGD(z) and mean DGD(z) are then obtained by simply multiplying a roundtrip factor of V3/8 and 2/π on rms DGDR_OundTπp and mean

DGDRoundTπp, respectively.

In the limit of a sufficiently small optical-frequency difference ("step") between the closely-spaced wavelengths, equations (15) and (16) simplify to yield the simpler differential formula that follows,

(15a)

PMD_RmιndTrψ(z) = ^-. (16a)

It should be note that, as yet another possible, although undesirable alternative, it is also envisaged that, in the above equations (8), (11), (13) and (16), the averages over (I-SOP, A-SOP) couples and wavelength could be replaced by averages over a large range of optical frequencies (i.e., wavelengths) only, where the (I-SOP, A-SOP) couple is kept constant. However, in this "constant-SOP" case, the method loses its applicability to all FUT types, i.e., if only the midpoint wavelength is scanned without scrambling of the (I-SOP, A-SOP) couples being applied, these relationships are no longer universally 5 valid, and may be significantly less reliable and/or accurate — even if still roughly valid. Generally, if no scrambling is performed, the methods are only valid if the FUT is "ideal" or "nearly ideal", i.e., it exhibits excellent random coupling and has an infinite or "near- infinite" polarization coupling ratio, and if one chooses a large value of the PMD • Δv product (typically >10), where Δv is the width of the optical frequency range. As a l o consequence, small PMD values cannot be measured with any reasonable uncertainty in practice, hi addition, one frequently wishes to perform measurement on older installed fibers, which are generally much less "ideal" than fibers produced since about 2001.

It should be noted that the equations for computed DGD or PMD described above as well as below sections as the simple differential formula are fundamental equations for

15 the limit of a sufficiently small optical-frequency difference ("step") between the closely- spaced wavelengths and large "step" arcsin formula are obtained from the simple differential formula in order to achieve a best performance for the instrument.

It should also be note that any equations for computed DGD or PMD described above as well as below sections that use relative variance may be applied for both

20 normalized power (including normalized OTDR trace) and relative power (including relative OTDR trace). And also note that a relative power (or relative OTDR trace) is proportional to a normalized power (or normalized OTDR trace).

METHOD OF OPERATION, DATA PROCESSING AND COMPUTATION

25 Two-end PMD measurement, single-end overall PMD measurement and single- end cumulative PMD measurement have their common basic fundamentals of the 'randomly input and output sate of polarization scrambling analysis (SSA) for PMD measurement', but their detailed operations for designed instruments are not the same. For example, the two-end measurement must place the input light controller means at one

30 end of FUT and analyzer and detection means at another end of FUT. The applied light source may also be different, for example, two-end PMD measurement may use either a continuous wave (CW) or pulsed light source if it can select or modulate optical frequency of light to produce two or three closely spaced wavelengths for the measurement, but for the single-end PMD measurement, it is necessary to use a pulsed light source (usually a tunable OTDR) to resolve the reflecting from the distal end of 5 FUT. Even for the single-end PMD measurements of overall PMD and cumulative PMD measurements, they still have slightly different operations regarding pulse length, number of closely spaced wavelengths, acquired data and data processing.

Therefore, below we will describe the method of operation, data processing and computation in three different sections for Two-End PMD Measurement, Single-Endo Overall PMD Measurement and Single-End Cumulative PMD Measurement.

METHOD OF OPERATION

Method of Operation for Two-End PMD Measurement

The method of operation for the two-end PMD measurement instrument shown in5 Figure 1 for measuring DGD and/or PMD will now be described in more detail with reference to the flowcharts shown in Figures 4A, 4B, 4C and 4D. In steps 4.1 and 4.2, the user first installs the application and inserts the test modules in the platforms, then starts testing software to cause the system to initialize the test modules, specifically initializing the wavelength polarized light source 12 (either tunable laser source 12A or broadband0 light source 12B), the Input SOP controller 14A, the analyzing means 14B and 20 and the detection 22 and processing section 34. Then the one end of fiber under test (FUT) 18 would be connected to coherent source module after Input SOP controller 14A and the distal end of FUT 18 would be connected to analyzer module, and patch cords with either a PC or an APC connector (such as FC/PC or FC/ APC) are used to connect the modules5 with the FUT. The most instrument parameters usually are set at factory according to costumer requirements, but the user may manually select parameters for both light source and analyzer by steps 4.1c and 4.3, respectively. Assuming that the user selects manual parameter setting, the program proceeds to the manual parameter setting steps 4.1c and 4.4 and prompts the user as follows: o (a) To set a center wavelength for the tunable laser source 12 A or tunable filter 27. (b) To set a wavelength range [λmin, λmax] for the group center wavelengths that will be encompassed by the light source 12 providing that is correspond to an accessible wavelength range of the FUT 18.

(c) If available (i.e. not fixed at factory), to set the step or difference δv (or δλ) between 5 the pairs closely-spaced optical frequencies Vu and V_L (or wavelengths). Alternately, the user may enter the anticipated PMD value for the FUT and leave the processor to compute and then select the wavelength (i.e. optical frequency) step. As an example, the step can be conveniently set as δv = α_δv - PMD^"1 where α_δv ~ 0.15 to 0.2 and, thus, δλ can be extracted from δλ « (c/v_c ²) ^• δv where v_c = (V_U+V_L)/2. (Note: there is an optimal l o step for a given PMD value, as large as possible so as to maximize signal-to-noise ratio, but small enough to satisfy the above condition, i.e., PMD-δv < 0.15 to 0.2. It is also noted that closely-spaced optical frequencies (or wavelengths) may also be more than two and this may be especially interesting for testing and monitoring where DGD or PMD from FUT may be varied versus time.)

15 (d) To set the number K of center- wavelengths and/or states of polarization selected by the I-SOP scrambler 14A and A-SOP scrambler 14B, i.e., the number (K) of groups of data to be acquired. For example, K may be set as 1000 to 100,000. Or, optionally, for the continuously scanning input and output SOP mode, only to set the number K of center- wavelengths and then to set a scanning time for both input SOP controller 14A and

20 analyzing means 14B and 20. Or, optionally, if only one center- wavelengths is selected, to set the number K of states of polarization selected by the I-SOP scrambler 14A and A- SOP scrambler 14B or a scanning time for the continuously scanning both I-SOP scrambler 14A and A-SOP scrambler 14B .

(f) Optionally, set the number of durations of pulses to be averaged to obtain each 25 individual power (for example 2 or >100) if series of modulated optical pulses are set into the FUT. No any setting required if only one modulated optical pulses being launched into the FUT.

(g) Set an overall total acquisition time for each individual PMD measurement and number of PMD measurement as well as its waiting time between any two measurements. (h) Select the modulated optical pulse duration Tp. Typically, a long pulse length is selected for the measurement because it has leads to a high dynamic range, and a high signal-to-noise ratio although a short pulse may still be used. (Typically, the modulated optical pulse length is chosen to be between 100 μs to 1 s, although pulse lengths outside of this range are also feasible.

(i) Optionally, set an input power of the tunable optical source means.

(j) Optionally, adjusting the power entering the analyzer module from the FUT by means of an optical attenuator in the optical path, for example, at a location just after the input of the analyzer module. But it is usually automatically set by the instrument. (k) Optionally, enter the cable or fiber name and /or its relevant information.

(1) Save all measurement parameters to a data file that will be retrieved for data processing by the data processor 34.

If, in decision step 4.3, the user selects automatic parameter setting, the program starts the auto parameter setting procedure in step 4.5 and carries out the following steps: (a) Select pre-defined certain default measurement parameters, namely

(1) The center wavelength range [λmin, λmax] that will be covered by the light source 12,

(2) Number K of SOPs and/or center wavelengths by the I-SOP scrambler 14A and A-SOP scrambler 14B (for example, 1000-10,000) for one PMD data acquisition, or, alternatively, a scanning time of I-SOP scrambler 14A and A-SOP scrambler

14B,

(3) Time for each individual acquisition (measurement), waiting time between any two individual acquisitions, and number of repeated acquisitions,

(4) Frequency pulse duration Tp (or length) for tunable coherent source, and (5) Launched light power and received power.

(b) The test module may also be designed to have a pre-scan acquisition using a reduced number of groups, such as K = 50-100, to obtain estimations of optimal wavelength step frequency difference δv (or δλ) between the two closely-spaced optical frequencies Vu and V_L (or wavelengths λu and X_L). Pre-scan data acquisition is performed to find the appropriate step or difference δv (frequency) or δλ (wavelength) between the two closely- spaced optical frequencies vu and V_L (or λu and X_L). For example, such data acquisition may be carried out by using, for each group, four different laser wavelengths to obtain a total combination of six different frequency or wavelength steps. In this case, a properly communications between two ends of the FUT may be required.

(c) Auto mode may also be designed to automatically produce cable or fiber name and / or with relevant information;

Once the measurement parameters have been entered, whether manually or automatically, the program proceeds to step 4.6 and computes wavelength step δλ (or frequency difference δv) if the anticipated total PMD of the FUT has been specified or estimated via the aforementioned auto-setting procedure, and the appropriate sequence of wavelengths λs based on the parameter settings. It is preferred to use three or four (or even more) different laser wavelengths to produce three or six (or even more) different wavelength step to cover wide measurable PMD range.

Finally, all the measurement parameters, whether directly specified or computed as described above, are stored in the header of the data file or instrument (Step 4.7).

It should be noted that a linewidth of the tunable coherent source will usually be set, in the factory or by design, at a relatively small level (e.g. of <1 to 2 GHz) in order to ensure the ability to measure a high PMD (e.g. >50ps) from the FUT.

It should be noted that, conveniently, at each SOP and/or center wavelength, the frequency difference δv (or wavelength step δλ) between the two closely-spaced optical frequencies vu and V|_ (wavelengths λu and λ_L) may remain the same or similar. Each SOP and/or wavelength may only be set in a short time period. Figure 4(C) shows in more detail of the data acquisition step 4.10 to acquire a Ath group of powers. The pre-defined wavelength step of δλ can be used to compute a sequence of wavelengths λs as already discussed in step 4.6. The frequencies V_L ^(1C) and vu^(k are calculated with satisfaction of V_L ^(1C) - v^^k) = δv where δv is the frequency difference (or when the wavelength difference δλ is used, it satisfies λu^(k) - λL^(k) = δλ). The maximum measurable PMD, PMD_1113x corresponding to a given step δv, can be estimated as PMD_nJ3x ~ a_n(πδv)^'1 and δλ can be extracted from δλ = (λø /c) - δv where λ₀ = (X₁^_n + λ^ ) 12. The control unit 30 control (b) of the test module to obtain the Mi group of powers as follows:

• Set SOPk by the I-SOP scrambler 14A and A-SOP scrambler 14B (Step of 4.3.1 of Figure 4(C)) if macroscopic SOP step selection is used for either or both of the scramblers (14A,14B), or, if continuous SOP scanning is used for either or both of the scramblers (14A,14B), set a scan time for input and output SOP scramblers (14A,14B) where the input and output SOPs may be slowly continuously randomly scanned to uniformly cover Poincare sphere. • Control the light source 12 or tunable filter 27 to set the lower wavelength to λ_L ^(k) (Step of 4.3.2 of Figure 4C). Detection and processing unit 34 will acquire data of powers as P_XL and P_yL (Step of 4.3.3 of Figure 4C). More details of this data acquisition are shown in Figure 4D will be described below. The same data acquisition process is repeated to obtain duplicate or repeated powers of P_XL" and P_yL ¹' (Step of 4.3.4 of Figure 4C).

• Repeat the same data acquisition for the upper wavelength λu^(k) (where the λu^(k) is also set by the light source 12 or tunable filter 27 while keeping the approximately same input and output SOPs controlled for both I-SOP scrambler 14A and A-SOP scrambler 14B. The detection and processing unit 36 then acquiring data of powers P_xu and P_yu and duplicates P_xu" and P_yu" (Steps of 4.3.5, 4.3.6 and 4.3.7 of Figure

4C), or alternatively, the data may be acquired from one short period time but to split it as two data that present at different time.

Figure 4D gives more detail of the data acquisition of step 4.3.3 shown in Figure 4C for acquiring of P_yL and P_xL in the Mi group of powers. The launched modulated optical pulses from the light source 12 are sent into FUT 18 and the output modulated optical pulses are exited from the distal end of FUT 18. The exited modulated optical pulses are then sent into the test analyzer module of instrument to be split into two routes - y and x - by either a PBS 20 or 2OC or a coupler 21, for example a 3-dB coupler, with one of two output arms being connected with a linear polarizer 2OA. The split light optical pulses entering into routes y and x are detected by two photodetectors, for example, two APDs such as 22B and 22C (or 20) (Steps of 4.4.1 and 4.4.2 of Figure 4D). Alternatively, the exited modulated optical pulses incident into the test analyzer module are directly sent to a linear polarizer. The light pulses are either directly detected by one photodetector, for example, one APD such as 22 A (Figure IB) or split into two routes - y 5 and x - by a coupler 21, for example a 3-dB coupler, entering into routes y and x are detected by two photodetectors, for example, two APDs such as 22B and 22C (Figure IH). The 'durations' of the response signals of modulated optical pulses from the distal end of FUT are sampled or sampled and averaged to obtain 'response pulse signals, such as Py(t) and P_x(t) (Steps of 4.4.3 and 4.4.4 of Figure 4D). The final sampled or sampled l o and averaged power of P_yL or P_xL are then obtained by averaging said previously acquired response pulse signals over its substantial portion of its duration around centre of the pulse of impulse response signals, Py(t) or Px(t), (Steps of 4.4.5 and 4.4.6 of Figure 4D). The length of pulse duration to be averaged usually depends on pre-filtering of electronics.

15 Once the Ath group of powers has been acquired as described above, in Step 4.10

(see Figure 4B), the data of group k is saved into the data file in Step 4.11. Step 4.12 then increments the group number register.

The data acquisition step 4.10 and group storing step 4.11 will be repeated for different center-wavelengths and/or input and output SOP selected by the I-SOP

20 scrambler 14A and A-SOP scrambler 14B in accordance with the manual parameter setting step of 4.4 or from auto parameter setting of step 4.5 or default parameter setting until K groups of powers have been acquired and stored in the data file.

The step 4.9 will decide whether or not this individual acquisition is completed. If decision step 4.9 gives a positive result and, in step 4.11, the program saves data in step

25 4.11. If not completed, acquisition will process the steps 4.10 and 4.11 again.

The step 4.8 will decide whether or not stat a new individual acquisition. If the entire measurement acquisition is finished, the step 4.15 will save all individual data for the overall entire acquisition. If not, the processor will reset k =0 to start a new individual acquisition for steps of 4-9, 4.10, 4.11 and 4.12. Step 4.16 will decide whether or not to

30 start another acquisition.

At this stage, the measurement parameters and all groups of powers have been saved in the proper files.

The decision step 4.17 may launch data processor, step 4.18 may load currently available acquired data from data file, step 4.19 may process them to estimate the DGD value at given center wavelength or mean DGD or RMS DGD (i.e. PMD) value over a wavelength range for the FUT and step 4.21 may display it. Optionally step 20 may allow the user to save the processed result, such as DGD or mean DGD or RMS DGD values versus time.

Optional decision from step 4.16 then may give the user an opportunity to initiate another acquisition process for the same FUT. If the user decides to do so, the program returns to the parameter setting step 4.3. If not, decision step 4.17 gives the user the option of exiting acquisition, in which case the data stored in the data file will be retained for later processing, or to initiate processing of already acquired and stored data of powers.

If processing is initiated, step 4.18 allows the user to select the date file to be processed in a conventional "open file" dialog box and the data processor 34 accesses the previously saved acquisition data comprising detected powers and associated measurement parameters from the data file, and uses the data to compute DGD or mean

DGD or RMS DGD of the FUT.

It should note the above steps may obtain rms DGD (i.e. PMD) as well as to obtain DGD at given midpoint wavelength or DGD as function of wavelength, and a rms DGD or mean DGD may be computed as the method described in below sections that may also be included in data processing step 4.19.

Note that, for the case of K = 1, i.e. the powers of light may be obtained in a similar manner for only one group having both the same input and output SOPs and same center-wavelength, one may also be able to roughly evaluate the PMD although this simple case may not be able to provide a sufficiently accurate and meaningful result, as there may be a significant uncertainty on the measured result.

Method of Operation for Single-End Overall PMD Measurement The method of operation of the tunable OTDR based single-end PMD measurement illustrated in Figures 2G and 2C will now be described with reference to the flowcharts shown in Figures 5 A, 5B and 5C. In step 5.1, the user first installs the application and inserts the test module in the platform, then starts testing software to cause the system to initialize the test module, specifically initializing the tunable pulsed light source 12, the I/O-SOP controller 14 and the OTDR detection and processing section 34. Then the fiber under test (FUT) 18 would be connected to test module (i.e. instrument) and a patch cord with either a PC connector (such as FC/PC or FC/UPC) or a fiber-pigtailed mirror 50 is connected to the distal end of the FUT. This would create a localized reflection at the end of FUT that is used for the PMD measurement. Decision step 5.2 prompts the user to select either manual parameter setting or automatic parameter setting. Assuming that the user selects manual parameter setting, the program proceeds to the manual parameter setting step 5.3 and prompts the user as follows:

(a) To set a wavelength range [λmin, λmax] for the group center wavelengths that will be encompassed by the tunable pulsed laser source 12.

(b) To set the step or difference δv (or δλ) between the pairs closely-spaced optical frequencies Vu and V_L (or wavelengths). Alternately, the user may enter the anticipated PMD value for the FUT and leave the processor 34 to select the wavelength step. As an example, the step can be conveniently set as δv = α_δv PMD^"1 where α_δv~ 0.1 to 0.15 and, thus, δλ can be extracted from δλ « (c/v_c ²) ^• δv where v_c = (V_U+V_L)/2. (Note: there is an optimal step for a given PMD value, as large as possible so as to maximize signal-to- noise ratio, but small enough to satisfy the above condition, i.e., PMD-δv < 0.1 to 0.15.)

(c) To set the number K of center-wavelengths and/or states of polarization selected by the I/O-SOP controller 14, i.e., the number (K) of groups of data to be acquired. For example, K may be set as 200.

(d) To set the averaging time Δt of each individual power (for example, Δt = 0.05 or 0.10 second), or set the number of durations of pulses reflected from the distal end of the FUT to be averaged to obtain each individual power (for example 50 or 100). Note that after setting the averaging time Δt and the number K of center-wavelengths and/or states of polarization a total acquisition time for PMD measurement may also be obtained.

(e) To select the pulse duration Tp (such as = 275, 1000, 2500, 5000, 10000, 20000 ns) or pulse length for OTDR. In order for the pulse reflected from the selected reflection not to be superposed in time with some portion of a pulse reflected from another reflection, the

5 pulse length, Lp, shall be selected such that Lp < Δz, where Δz is the distance along the FUT between the selected reflection and the nearest of anyone or all other reflections.. Typically, a long pulse length is selected for the single-end PMD measurement because it has advantages of leading to high dynamic range, and / or a high signal to noise ratio, and / or a short averaging time (thereby a short overall acquisition time) although a short o pulse may still be used.

(f) To set the FUT length, normally the full effective optical length of the FUT.

(g) Optionally to select a high dynamic range or a low dynamic range according to the optical fiber length. Typically, in a normal operation the test module prompts the user to select a high dynamic range, but it may also allow the user to test a very short fiber by5 choosing a low dynamic range for acquisition. With the low dynamic range mode, the output peak power of the launched OTDR pulses is reduced, either by inserting an optical attenuator in the optical path, for example, at a location just before the output of the test module, or electrically, for example, by decreasing the bias current of the gain medium of the tunable pulsed laser. o (h) Optionally to enter the cable or fiber name and /or its relevant information.

(i) Save all measurement parameters to a data file that will be retrieved for data processing by the data processor 34.

If, in decision step 5.2, the user selects automatic parameter setting, the program starts the auto parameter setting procedure in step 5.4 and carries out the following steps:5 (a) Select pre-defined certain default measurement parameters, namely

(6) The center wavelength range [λmin, λmax] that will be covered by the tunable pulsed laser source 12,

(7) Number K of (I-SOP, A-SOP) couples and/or center wavelengths to be set by the I/O-SOP controller 14 (for example, 200) for a real single-end PMD data acquisition,

(8) Averaging time Δt (for example, Δt = 0.05 or 0.1 second) or the number of duration of pulse reflected from the distal end of the FUT to be averaged (for example 50 or 100) for each individual power, and

5 (9) Pulse duration Tp (or length) for OTDR.

It is noted that these default parameters set in (1), (3) and (4) will also be used for pre- scan acquisition.

(b) The test module will conduct a pre-scan acquisition using a reduced number of groups, such as K = 50, to obtain estimations of the FUT length, of total loss from FUT i o and of optimal wavelength step frequency difference δv (or δλ) between the two closely- spaced optical frequencies vu and v_L (or wavelengths λu and X^). The OTDR will launch a standard OTDR pulse (e. g, 1 or 10 μs) to detect the end of the fiber (or a user defined localized reflection) so that the FUT length can be obtained and the pulse repetition period (Tr) can also be deduced according to the round-trip time through the length of the

15 fiber. From this OTDR acquisition, a loss of FUT may also be estimated, otherwise, a saturation situation on photodetectors may be observed if there is any. Then a decision can automatically be made on whether or not to reduce the output peak power for the OTDR light pulses. Pre-scan data acquisition is performed to find the appropriate step or difference δv (frequency) or δλ (wavelength) between the two closely-spaced optical

20 frequencies Vu and V_L (or or λu and λ^. For example, such data acquisition may be carried out by using, for each group, four different laser wavelengths to obtain a total combination of six different frequency or wavelength steps. The optimally appropriate wavelength step to be used in the actual single-end PMD measurement data acquisition may be found by processing of these pre-scan acquisition data of powers. To save all

25 automatically-selected measurement parameters to the header of the data file that will be retrieved for data processing by the data processor 34.

(c) Auto mode may also be designed to automatically produce cable or fiber name and / or with relevant information;

Once the measurement parameters have been entered, whether manually or automatically, the program proceeds to step 5.5 and computes wavelength step δλ (or frequency difference δv) if the anticipated total PMD of the FUT has been specified or estimated via the aforementioned auto-setting procedure, the repetition period T_r according to the round-trip time through the length of the fiber, and the appropriate 5 sequence of wavelengths λs based on the parameter settings.

Finally, all the measurement parameters, whether directly specified or computed as described above, are stored in the header of the data file (Step 5.6).

It should be noted that a linewidth of the tunable pulsed light source will usually be set, in the factory, at a relatively small level (e.g. of 1-2 GHz or less) in order to ensure i o the ability to measure a high PMD from the FUT.

With the group number register initialized to k = 0, decision step 5.7 determines whether the total number of groups of powers have been acquired. If not, the program proceeds to step 5.8 to acquire the Mi group of powers.

It should be noted that, conveniently, at each SOP and/or center wavelength, the 15 frequency difference δv (or wavelength step δλ) between the two closely-spaced optical frequencies vu and vι_ (wavelengths λu and XL) may remain the same or similar. Each

SOP and/or wavelength may only be set in a short time period.

Figure 5B shows in more detail of the data acquisition step 5.8 to acquire a Mi group of powers. The pre-defined wavelength step of δλ can be used to compute a 20 sequence of wavelengths λs as already discussed in step 4.5. The frequencies VL^(1C) and vu^(k are calculated with satisfaction of V_L ^(1C) - Vu^(k) = δv where δv is the frequency difference (or when the wavelength difference δλ is used, it satisfies λu^(k) - λ_L ^(k) = δλ).

The maximum measurable PMD, PMD_m3x corresponding to a given step δv, can be estimated as PMD _max ~ α_rt(π δv)^~1 and δλ can be extracted from δλ = (λg / c) • δv 25 where λ₀ = (λ_πάn + X_103X ) Z L The control unit 30 controls the test module to obtain the Mi group of powers as follows:

• Set SOP_k by the I/O-SOP controller (Step of 5.3.1 of Figure 5B).

• Control the tunable pulsed laser 12 to set the lower wavelength to λ_L ^(k) (Step of 5.3.2 of Figure 5B). Detection and processing unit 36 will acquire data of powers as PxL and PyL (Step of 5.3.3 of Figure 5B). More details of this data acquisition are shown in Figure 4C will be described below. The same data acquisition process is repeated to obtain duplicate or repeated powers of P_xL" and P_yL" (Step of 5.3.4 of Figure 5B).

• Repeat the same data acquisition for the upper wavelength λu^(k) (where the λu^(k) is also set by the tunable pulsed laser 12) while keeping the same (I-SOP, A-SOP) couple. The detection and processing unit 36 then acquiring data of powers P_xU and Pyu and duplicates P_xU" and P_yU" (Steps of 5.3.5, 5.3.6 and 5.3.7 of Figure 5B).

Figure 5C gives more detail of the data acquisition of step 5.3.3 shown in Figure 5B for acquiring of P_yL and P_xL in the Mi group of powers. The launched light pulses from the OTDR are sent into FUT and a small fraction (or most) of pulse lights are reflected from the localized reflector such as using either a PC connector of the patchcord or a fiber pigtailed mirror connected at the end of FUT. The reflected light pulses are then returned into the test module or instrument to be split into two routes - y and x - by either a PBS or a coupler, for example a 3-dB coupler, with one of two output arms being connected with a linear polarizer. The split light pulses entering into routes y and x are detected by two photodetectors, for example, two APDs such as 22'B and 22'C (Steps of 5.4.1 and 5.4.2 of Figure 5C). The 'durations' of the response signals from the reflected light pulses by the distal end of FUT or any other locations along fiber are sampled and averaged to obtain 'averaged' mean response pulse signals, such as P_y(t) and P_x(t) (Steps of 5.4.3 and 5.4.4 of Figure 5C). The final averaged power of P_yL or P_xL are then obtained by averaging said previously sampled and averaged mean response pulse signals over its substantial portion of its duration around centre of the pulse of impulse response signals, Py(t) or Px(t), (Steps of 5.4.5 and 5.4.6 of Figure 5C). The length of pulse duration to be averaged usually depends on pre-filtering of electronics.

Once the Ath group of powers has been acquired as described above, in Step 5.9 (see Figure 5A), the data of group k is saved into the data file. Step 5.10 then increments the group number register.

The data acquisition step 5.8 and group storing step 5.9 will be repeated for different center-wavelengths and/or (I-SOP, A-SOP) couples selected by the I/O-SOP controller 14 in accordance with the manual parameter setting step of 5.3 or from auto parameter setting of step 5.4 until K groups of powers have been acquired and stored in the data file.

At this stage, the measurement parameters and all groups of powers have been saved in the same data file associated with the header information of measurement parameters.

During the data acquisition the step 5.20 (optionally) may load any currently available acquired data from data file and process them to estimate the RMS DGD (i.e. PMD) value for the FUT 18 and step 5.21 may display it as well as elapsed time of the acquisition, length and loss of the FUT. Note the estimated PMD value may frequently be varied until the end of the data acquisition. Optionally step 5.22 may allow the user to save the processed result.

Also at this stage, decision step 5.7 gives a positive result and, in step 5.11, the program saves and closes the data file in step 5.11.

Optional decision from step 5.12 then may give the user an opportunity to initiate the acquisition of another K groups of powers for the same FUT. If the user decides to do so, the program returns to the parameter setting step 5.2. If not, decision step 5.13 gives the user the option of exiting acquisition, in which case the data stored in the data file will be retained for later processing, or to initiate processing of already acquired and stored data of powers. If processing is initiated, step 5.14 allows the user to select the date file to be processed in a conventional "open file" dialog box, whereupon, in step 5.16, the data processor 34 accesses the pre-saved acquisition data of powers and associated measurement parameters from the data file, and uses the data to compute total RMS DGD (i.e., PMD) of the FUT. On the other hand, box 5.15, which is not a "step" as such, indicates that the user may launch the data processing software independently at any time, allows the user may launch the data processing software independently at any time to process any previously acquired data file. In step 5.17, the data processor 34 saves the result of computed PMD value and measurement parameters in a file and in step 5.18 displays or otherwise outputs the measured PMD value with possible other results such as length and loss of the FUT.

Note that, for the case of K = 1, i.e. the powers of light backreflection may be obtained in a similar manner for only one group having both the same (I-SOP, A-SOP) couple and same center-wavelength, one may also be able to roughly evaluate the PMD although this simple case may not be able to provide a sufficiently accurate result, as there may be a significant uncertainty on the measured result. The manner in which the data processing step 5.16 processes the stored data will be described in the sections below.

It should note the above step may obtain rms DGD (i.e. PMD), but it can also obtain DGD as function of wavelength and then rms DGD or mean DGD may be computed as the method described in below sections that may also be included in data processing step 5.16.

Method of Operation for Single-End Cumulative PMD Measurement

The method of operation of the POTDR illustrated in Figure 3 for measuring cumulative PMD as function of FUT length will now be described with reference to the flowchart shown in Figures 6A and 6B. hi step 6.1, the user causes the system to initialize the POTDR, specifically initializing the tunable pulsed light source 12, the VO- SOP controller 14 and the OTDR detection and processing section. Decision step 6.2 prompts the user to select either manual parameter setting or automatic parameter setting. Assuming that the user selects manual parameter setting, the program proceeds to the manual parameter setting step 6.3 and prompts the user as follows:

(a) To set the wavelength range [λmin, λmax] of the group center wavelengths that will be covered by the tunable pulsed laser source 12.

(b) To set the step or difference δv (or δλ) between the pairs of closely-spaced optical frequencies Vu and V_L (or wavelengths). Alternately, the user may enter the anticipated total PMD value of the FUT and leave the processor to select the wavelength step. As an example, the step can be conveniently set as δv = α_δv - PMD^"1 where α_gv~ 0.1 to 0.15.

It should be noted that the POTDR may be configured to allow the user to select a number M of steps larger than one; the control program will then select M steps based on the anticipated total PMD of the FUT, with appropriate ratios between the steps (note: there is an optimal step for a given PMD value, as large as possible so as to maximize signal-to-noise ratio, but small enough to satisfy the above condition, i.e., PMD δv < 0.1 to 0.15. But the apparatus here described must perform the challenging task of measuring simultaneously a large range of cumulative PMD values as a function of z, from PMD = 0, at z = 0, to PMD = Total PMD of the FUT, at z = FUT length. This is the reason why a few measurements with different steps in order to measure all different "sections" of the FUT with similar relative (e.g. in %) accuracy is desirable, or alternatively as mentioned here and above, use more than two closely-spaced wavelengths per group, a number N^ of wavelengths per group leading to a theoretical number of M = N_λ • (N _λ - 1) / 2 pairs with different steps in each scan, so as to save time).

(c) To set the number (K) of center-wavelengths and/or (I-SOP, A-SOP) couples selected by the I/O-SOP controller 14, i.e., the number (K) of groups of traces to be acquired.

(d) To set the averaging time Δt of each individual trace (for example, Δt = 1 or 2 seconds), or set the number electrical impulse response signals to be averaged to obtain each individual trace (for example 1250 or 2500).

(e) To set the pulse duration (as Tp =50, 100, 200, 300 ns), or length.

(f) To specify the FUT length, normally the full effective optical length of the FUT.

If, in decision step 6.2, the user selects automatic parameter setting, the program proceeds to step 6.4 and carries out the following steps:

• Selects certain default measurement parameters, namely

(1) center wavelength range [λmin, λmax] that will be covered by the tunable pulsed laser source 12, typically the whole wavelength range that the actual tunable laser can access. (2) number K of (I-SOP, A-SOP) couples and/or center wavelengths to be set by the

I/O-SOP controller 14, for example, 100 or 200, for final POTDR data acquisition,

(3) averaging time Δt (for example, Δt = 1 or 2 seconds) or number of electrical impulse response signals to be averaged (for example 1250 or 2500) for each individual OTDR trace,

(4) pulse duration (e.g., Tp = 50, 100, 200, 300 ns) or pulse length, and

(5) linewidth of tunable pulsed laser (optional).

It is noted that these default parameters set in (1), (3), (4) and (5) will also be used for pre-scan acquisition.

• The POTDR conducts a pre-scan using a reduced number of groups, such as K = 20, to obtain rough estimates of the FUT length and the optimal wavelength step δλ (or frequency difference δv) between the two closely-spaced optical frequencies vy and v_L (or λu and λ_L). Thus, the OTDR will launch a standard OTDR pulse (e.g. lμs) to detect the end of the fiber so that the FUT length can be obtained and the pulse repetition period deduced according to the round-trip time through the length of the fiber. Acquisition of OTDR traces then will be performed to find the best suited step or difference δv (or δλ) between the two closely-spaced optical frequencies vu and V_L (or λu and λ^ via a fast estimate of the overall PMD of the FUT. For example, such acquisition may be carried out by using, for each group, four different laser wavelengths (Nj₁ = 4) to obtain a total combination of six different wavelength steps (M = 6). The best suited wavelength step to be used in the actual POTDR data acquisition may be found by processing of these pre-scan data.

Once the measurement parameters have been entered, whether manually or automatically, the program proceeds to step 6.5 and computes wavelength step δλ (or frequency difference δv) if the anticipated total PMD of the FUT has been specified or estimated via the aforementioned auto-setting procedure, the repetition period T_r according to the round-trip time through the length of the fiber, and the appropriate sequence of wavelengths based on the parameter settings. Finally, all the measurement parameters, whether directly specified or computed as described above, are stored in the header of the data file (Step 6.6).

Figure 6A shows an optional step (following step 6.5) for setting the laser linewidth, if allowed by the laser light source 12, according to the previously-entered parameters. For example, a small (large) linewidth may be chosen to measure large (small) total PMD. In the case where the total PMD is not specified and no auto-setting procedure has been carried out, the specified wavelength step (δλ) may be used to estimate the total PMD and then the laser linewidth may also be selected accordingly.

With the group number register initialized to k = 0, decision step 6.7 determines whether the total number of groups of traces have been acquired; if not, the program proceeds to step 6.8 to acquire the group k of OTDR traces.

Figure 6B shows in more detail the trace acquisition step 6.8 to acquire a Ath group of OTDR traces. As described previously, there is at least one pre-defined frequency difference δv (or wavelength step δλ) between the two closely-spaced optical frequencies Vu and V_L (or wavelengths), and hence the number of total selected laser wavelengths must be at least two. If a plurality of different wavelength steps δλ are used, then these wavelength steps may be selected to optimally measure different ranges of PMD values. For example, one may choose to have two wavelength steps, δλj and δλ₂, which requires Nj₁ = 3 different wavelengths per group. Furthermore, a judicious choice of the ratio of said two steps may be, for example, δλ!/δλ₂ = 5. The maximum measurable PMD, PMD_max corresponding to a given step δv can be estimated as

PMD_1113x ~ α_rt(πδv)^~1 , and δλ can be extracted from δλ = (λ² ₀ /c) - δv , where ^λo = (^λ _mi_n + ^λ _maχ)^{/ 2} • T^ control unit 30 controls the POTDR to obtain the Ath group of traces as follows: o Set couple (I-SOP_k, A-SOP_k) by means of the I/O-SOP controller 14 (step 6.8.1 of Figure 6B). o Control the tunable pulsed laser 12 to set wavelength to λ_L ^(k) (step 6.8.2 of Figure

6B) and then launch OTDR light pulses. Detection and processing unit 36 acquires OTDR traces Px_L and Py_L (step 6.8.3 of Figure 6B). The same data acquisition process is repeated to obtain duplicate or repeated traces PX_L" and

Py_L" (step 6.8.4 of Fig. 6B). o Repeat the same data acquisition for the upper wavelength λu^(k) while keeping the same (I-SOP_k, A-SOP_k). The detection and processing unit 36 then acquires OTDR traces Pxu, Pyu and duplicates Pxu", Pyu" (steps 6.8.9 and 6.8.10 of Figure 6B). o Where the group comprises more than one pair of series of light pulses, to set the wavelength to at least one additional wavelength λ/^k) intermediate the lower and upper wavelengths (step 6.8.5 of Figure 6B). The detection and processing unit 36 acquires OTDR traces Pxi and Pyi (step 6.8.6 of Figure 6B). The same data acquisition procedure is repeated to obtain the repeated traces Pxi" and Py₁" (step 6.8.7 of Figure 6B).

Once the kth group of OTDR traces have been acquired as described above, in step 6.9 (see Figure 6A) the group is saved into the data file. Step 6.10 then increments the group number register.

The data acquisition step 6.8 and group storing step 6.9 will be repeated for different center-wavelengths and/or (I-SOP_k, A-SOP_k) selected by the I/O-SOP controller 14 in accordance with the parameter setting step 6.2 or 6.3 until K groups of traces have been acquired and stored in the data file. At this stage, the measurement parameters and all groups of OTDR traces have been saved in the same data file.

Also at this stage, decision step 6.7 gives a positive result and, in step 6.11, the program closes the data file. Optional decision step 6.12 then gives the user an opportunity to initiate the acquisition of another K groups of traces for the same FUT. If the user decides to do so, the program returns to the parameter setting step 6.2. If not, decision step 6.13 gives the user the option of exiting, in which case the data stored in the data file will be retained for later processing, or initiating processing of already acquired and stored data.

If processing is initiated, step 6.14 allows the user to select the data file to be processed in a conventional "open file" dialog box, whereupon, in step 6.16, the data processor 32 accesses the pre-saved acquisition data and associated measurement parameters from the data file, and uses the data to compute cumulative PMD as a function of distance (z) along the FUT. On the other hand, box 6.15, which is not a "step" as such, indicates that the user may launch the data processing software independently at any time, even if no acquisition was just completed, to process any previously acquired data file. In step 6.17, the data processor 32 saves the results (e.g. the cumulative PMD curve as a function of z and measurement parameters in a file retrievable by a spreadsheet software) and in step 6.18 displays or otherwise outputs the resulting cumulative PMD curve in a tangible form.

The manner in which the data processing step 6.16 processes the stored data will be described in the sections below.

It should note the above steps may obtain rms DGD (i.e. PMD), but it can also obtain DGD as function of wavelength and then rms DGD or mean DGD may be computed as the method described in below sections that may also be included in data processing step 6.16.

DATA PROCESSING AND COMPUTATION

Data Processing and Computation for Two-End PMD Measurement The manner in which the data processing step 6.19 processes the stored data will now be described.

1. The Data Structure

Each light power from the FUT, obtained with one given setting of the wavelength and of the input and output SOPs as described in the Method of Operation for the two-end PMD measurement, constitutes an elementary data cell, i.e. one datum consists of one power value. The next data unit is one group of four powers (i.e. four data cells), two sets of four powers for the embodiments of Fig. 1C and Fig. IG where two powers are obtained simultaneously from photodetectors 22B and 22C, all obtained with given input and output SOPs as set by I-SOP scrambler 14A and A-SOP scrambler 14B. The two sets of four powers forming group k preferably have been obtained in the following sequence (time flowing from left to right) or other similar means, such as of two repeated powers being measured at the same time but with different detectors (such as simultaneously measuring the same power by two detectors and a coupler), as:

I-SOP_k ¹, A-SOP_k° and/or λ_k: λ = λ⁽ _L ^k) λ = λ (k)

where the labels x and y refer to the power obtained simultaneously or at slightly different time from photodetectors 22B and 22C, respectively, λ^ - λ⁽ _L ^k) is equal to the step δλ, the midpoint wavelength is defined as λ_k = (λ^ + λ⁽ _L ^k))/2 , and the double prime indicates the repeated powers.

Finally, the overall data stored in the data file after acquisition is depicted as a matrix in Eq. (18) below, to which we will refer in all that follows. The matrix comprises K groups each of four powers of light (two sets of four when two photodetectors are used):

λ = Q, ( k )

A = 2 ( * ) Λ Li

Data = (17)

It should be noted that the input and output SOPs can each be selected randomly ("macroscopic SOP step") from one to another or undergo slow continuous SOP scanning, in both cases in such a way that, over time, each substantially uniformly covers the Poincare sphere.

2. Auto Calibration of the Relative Gain

For the embodiment of Figure ID, it is necessary to perform the below described calibration procedure of the relative gain of the two detectors 22B and 22C before proceeding with any further computation. The same procedure is not performed for the other embodiments, e.g. if there is only one detector.

The calibration principle is predicated upon the fact that, when input and output

SOP scramblers are used to generate a sufficiently large number of SOPs so as to substantially cover the Poincare Sphere, the average power of the light from the FUT 18 will exit from the two ports of the PBS with a 1 : 1 ratio (equal). Hence, any observed deviation from this 1 : 1 ratio for the observed detector powers can be quantified and taken into account, as follows.

After data acquisition is completed, K groups of four light powers obtained from both photodetectors have been stored, i.e., a total number of J = 4-K powers (data) from detector 22B and also J = 4-K powers from detector 22C, as depicted in matrix (18). The j^th powers (j = 0, l..( J-I)) from 22B and 22C are referred to below as Px_j and Py,, respectively. If the overall losses in the two arms of the PBS were identical and the gains of both photodectors and associated electronics were also equal, the ratio of the powers Py and Px after averaging both populations over all J occurrences would be

In practice, the ratio obtained from the average of the measured powers does not equal 1 because of different losses in the arms of the PBS and different "effective" gains of the photodetectors, which includes the photodiode responsivity as well as the overall gains of the following electronics, amplifiers and sampling circuitry. (Note that it is not necessary to determine the individual gains separately.) Therefore, before proceeding with the rest of the computations, all the J powers obtained from photodetector 22C, i.e. all the Py,, are multiplied as follows:

y j ⁼ S Forward ' J ] where

g^Fomard

This calibration may need to be carried out at every wavelengths, but in practice, for center wavelengths that are relatively closely-spaced (e.g. <20 run), the relative wavelength dependence of the components, detectors, etc. may be negligible and this calibration process need only be carried out once per PMD measurement sequence.

As a result of the calibration, i.e. after all Py powers (data) have been multiplied by the measured relative gain as described above, the data processor 34 can compute the normalized light powers. More precisely, the normalized powers in the case of the embodiment of Figure ID are obtained by dividing the sampled and averaged signal Px from detector 22B, or the signal Py from detector 22C, or (and preferably) the weighted difference (Px-Py)/2 or (Py-Px)/2, as will be described in more detail in the next section, or any weighted difference (1+ W)^(Px-W-Py), where w is a weighting factor, by the sum (Px+Py) of the sampled and averaged signals from both of the detectors 22B and 22C, which sum represents the total power impinging on the PBS, i.e., without selection of a particular polarization component. It should be noted that other calibration may also be possible. For example, a potential alternative calibration technique is to use an internal reference with fiber couplers (splitters) or internal reflector to send a predefined amount (percentage) of light power from launched OTDR light to two different detectors. The preferred computations giving the normalized powers of all preferred embodiments will now be described in detail.

3. Computation

The powers are processed to obtain the PMD value as will now be described. It should be note that, in all that follows, the symbols refer to the matrix "Data" in equation (17). The labels x and y refer to the backreflected light powers obtained from photodetectors 22B and 22C, respectively.

3.1 The Normalized Powers

The normalized powers, labelled hereinafter as T, are computed differently according to the embodiment. (i) For the embodiment of Figure ID (two photodetectors with a PBS), the transmissions (normalized power) is computed as follows either

iX .('*) ψn(k) __ Px'γ

Pxl^k) + PyI (*) /*"[^*'+ Py¹X

or wt,

^L

where it should be appreciated that the different Py powers have been pre-multiplied by the measured relative gain, g_For_wai_d, as indicated in the description of the auto calibration procedure, before they are used in equations (18a) and (18b).

(ii) For the embodiment of Figure 1C (two photodetectors with a coupler), the ratio of trace Px over trace Py is first computed as,

and then the above ratio is normalized with respect to its average over the K groups as,

where the reference mean- value is U₀ = 1/2 and the average ratio R is defined as,

or, when the coupler ratio changing against wavelength is negligible within a prescribed wavelength range, then (R_L}_SOP and (Ru)_50P can be replaced by:

(^R)_soP, =-^∑{K^k) +RT+W +RT) ⁽ⁱ⁸f⁾ Here, the auto calibration procedure is not required, i.e. above mentioned pre- multiplication of the powers Py by the measured relative gain may be skipped, (iii) For the embodiment of Figure IB (single photodetector), the only available powers are the Px powers (obtained here from photodetector 22A). The normalized power is obtained as in (19d) but without computing the ratio of power x over power y first, i.e. p_v(*) p_vtι(*) τ⁽*> - _u -TCL 7»<*⁾ _ _u ^rx L

^{L "} " ( VPL \ I SOP ^{l "} " ( VPL \ I SOP

where the average power is defined as,

(PL)_SOP = ^∑H^k) + M*0 {PV)SOP = ^Σ^ ⁺ ^) ⁽¹⁸ⁱ)'

Here assuming the launching power is stable during period for measuring powers. (iv) For the embodiment of Figure IH with two photodetectors combined with a coupler after analyzer, two powers of the Px and Px" powers are obtained from photodetectors 22B and 22C, respectively. The normalized powers are now obtained as,

P_yW p_v«(*)

where the average power is defined as,

= ^~ j Tfζ ∑ ÷-JP^χT

Here the auto calibration procedure is also not required. Note this the embodiment has an advantage of only requiring a half acquisition time in comparison of other embodiments.

Note for the above (iii) and (iv) normalization, the power during measurement must be stable. Also, if power is constant for all wavelengths within a prescribed wavelength range, ( )_sop can be averaged over either SOP or wavelength, both SOP and wavelength.

Fundamentally all of these relationships are valid in all cases if sufficiently random input and output SOP scrambling is applied, giving the correct value of the DGD at one particular midpoint wavelength, and then it is possible to obtain DGD against midpoint wavelength. Therefore, one can also compute a mean DGD or RMS DGD value for a given wavelength range.

In other case, scanning the midpoint wavelength serves the purpose of averaging DGD over wavelength as per the definition of the statistical PMD value so as to obtain a RMS DGD value (not a mean DGD). On the contrary, as discussed earlier, averaging only over wavelength while keeping the input and output SOPs unchanged requires that assumptions about the FUT be met, and also requires a large value of the product PMD-Δv. The same remarks apply for the equations presented hereinafter.

3.2 Noise Variance The second motivation for sampling repeated traces, which are substantially identical in the absence of noise for each setting of SOP and midpoint wavelength λπud, is the ability to obtain an accurate estimate of the variance noise from variations of light polarization and/or laser frequency and/or power (intensity). If this noise variance is known, it may be subtracted. Thanks to the repeated traces, the variance from polarization noise and/or laser frequency and/or power noise and/or any other noises etc. can be estimated independently as follows:

_\2

2 noise = {—) {(T_L -T\)(T_u -T^» _u))_sopλ (19)

V ^σ2o y

where σ₂₀ = l/12 .

It should be noted that this 'noise' variance could come from a randomly varied input and output SOP, and/or an instability of laser frequency and intensity, or any other noise sources. In order to obtain a reliable measurement result, the variance noise, e.g. from polarization variation and similar other effects, such as instability of laser frequency and intensity, should be less than few percent (e.g. of <2%) compared to the mean-square difference (see below Sub-section 3.4).

It should be note that above average may be averaged over SOP or averaged over both SOP and wavelength.

3.3 Relative Variance

The relative variance, for example mainly due to un-polarized ASE light from optical amplifiers in the test link (or any other depolarizing effects), as used in equations (10) and (11), is computed here as the average of the four available estimates, i.e.,

where σ^ = 1/12 , and the function "δ" is defined as,

Alternatively, the relative variance can also be computed via polarization component s_p, for example,

where σ_s ² _Q = 1/3, and s_p as,

5^ = 27^ - 1 ^ = 2^ - 1

But note that a relative variance computed from equation (20b) cannot be applied to any above or below mentioned 'relative power' related computation for extracting DGD or PMD, i.e. the measured power must be normalized properly.

It should be noted that above equation is valid under the condition of uniformly distributed I-SOPs and A-SOPs on Poincare sphere from either or both input and output polarization controllers. It can be only averaged over SOP or average over both SOP and wavelength.

The noise variance (equation 19) is then subtracted from the first estimation of the relative variance (equation 20a) in the computation, and a final relative variance is as follows,

3.4 Mean-Square Differences

The calculation here differs from the simple mean-square found in equations (10) and (11) which, for greater clarity, did not take into account the noise. Instead, the product of the repeated differences between normalized power at λu and λ_L is averaged as follows,

) .f VT"⁽ υ*⁾-T ¹ "I⁽ⁱ⁾ ϊ⁾ ( VΥ-±T)\

In conventional mathematical terms, equation (22) may be referred to as the second-order joint moment of the repeated differences. Doing so, the noise averages to zero instead of being "rectified", because the noise superimposed on a given trace is not correlated with the noise superimposed on the corresponding repeated power. That is the first motivation for acquiring repeated data.

Note that < >_SOPΛ ^m above equations can refer to averaging over either the SOP, or the midpoint wavelength, or over both, i.e., changing both SOP and wavelength from one group of powers to other.

3.5 Computation of the DGD or PMD Value

The DGD or rms DGD (i.e. PMD) then is computed according to the arcsine formula as, (23)

where ( >_SOP refers to only averaging over the SOP only.

where < )sop,λ refers to averaging over both the SOP and wavelength, and a theoretical

constant a = [9^" ds , ^ — 2 •

It should be appreciated that the arcsine formula, in equations (23) and (24), is not the only possible one. The purpose of using this formula is to obtain a result that is unbiased even if using a relatively large step, such that PMD-δv ~ 0.2, without introducing a significant error; this in order to maximize the signal-to-noise ratio and therefore the dynamic range of the instrument. Although applicable to any step size, if one were not concerned with maximizing the dynamic range, one could select a small step, in which case the following simpler differential formula is valid:

a (ΔTW^

DGD(v) = ds (23a) πδv

This is not to infer that these formula are better or particularly advantageous, but merely that it may conveniently be used if the step is much smaller, i.e., satisfying the condition PMD-δv < 0.01.

It should be noted that in an ideal situation where there is no ASE from optical amplifiers, 'depolarization' effect and other 'noises' of light polarization, frequency and intensity etc., then σ) = 1 , the above equations (23) and (24) are simplified as,

and their simpler differential formula are,

DGD(y) = -J (AT(V)²) (25a)

5 It should be noted that, in the equations above, ( ) can refer to averaging over either the wavelength, or over both the SOP and the wavelength, i.e., changing both SOP and wavelength from one group of powers to the next.

Note that a mean DGD or rms DGD may be computed from averaging DGD(v) from many different midpoint wavelengths over a prescribed wavelength range, such as

mean DGD = [DGD) _λ (28)

As shown in the equations (23) and (24), if the DGD(v) and PMD calculation involves to use the relative variance, σ² (v) , of the normalized power (T), then the normalized power may not be necessary to have to be computed to be normalized

15 between 0 and 1. In other words, some steps of above normalization procedure for obtaining normalized powers may be skipped.

For example, for the embodiment of Figure 1C (two photodetectors with a coupler), the relative power (P_R) can simply be obtained from the ratio of trace Px over trace Py as,

p_v(*) p_v»⁽t) p{k) _ ^rxU pn(k) _ ^rx U /₇QΛ

^RU ~ Pυ<*> ^RU ~ /V'^{W K }}

For the embodiments in Figure ID (two photodetectors with a PBS) and in Figure 1C (two photodetectors with a coupler), any reference constants and averaging for over SOP and / or wavelength in order to obtain a normalized power may be ignored (skipped) for the procedure to obtain a relative power (P_R).Then DGD and PMD may be computed to use following arcsine formula as,

DGD(v) =

where { >_SOP refers to only averaging over the SOP only.

PMD =

where < >_SO_P,X refers to averaging over both the SOP and wavelength. Here mean- square (ΔP_R )

' I SOP,λ can be found as follows, = ^ -O-Λ^n?^{) (32a)}

and the relative variance,

, is computed here as the average of the four available estimates, i.e.,

where - 1 / 12 , and the function "δ" is defined as,

Note that ( >sop_,λ can refer to averaging over either the SOP, or the wavelength, or over both, i.e., changing both SOP and wavelength from one group of powers to the next.

If one selected a small step, the arcsine formula, in equations (30) and (31) may be written as simpler differential formula as,

a ( APAv)²)

DGD(v) = ds \ ^{R y} ' I SOP (30a) πδv a

PMD= _*_ \ ^R I sSoOpP-.;λ

(31a) πδv

For the case where the tunable light source has a relatively big linewidth and a high PMD fiber is under test, a further linewidth 'correction factor' may be applied in equations where to extract a DGD or PMD value of the FUT having a greater accuracy.

It should be appreciated noted that above computed forward DGD or PMD for two-end PMD measurement is a DGD or PMD of FUT.

Data Processing and Computation for Single-End Overall PMD Measurement 1. The Data Structure

Each backreflected light power from the localized reflection (such as Fresnel reflection) at the distal end of FUT, obtained with one given setting of the wavelength and of the (I- SOP, A-SOP) couples, as described in the Method of Operation for the single-end overall PMD measurement, constitutes the elementary data cell, i.e. one data consists of one power value. The next data unit is one group of four powers (i.e. four data cells), two sets of four backreflected powers for the embodiments of Fig. 2C and Fig. 2G where two backreflected powers are obtained simultaneously from photodetectors 22B and 22C, all obtained with a given (I-SOP_k, A-SOP_k) as set by LO-SOP controller 14. The two sets of four powers forming group k preferably are obtained in the following sequence (time flowing from left to right):

λ = λ⁽ _L ^k) λ = λ⁽ _O ^{k )}

(I-SOP_k,A-SOP_k, λ_k)

where the labels x and y refer to the power obtained simultaneously (or at slightly different time) from photodetectors 22B and 22C, respectively, λ^ - λ⁽ _L ^k) is equal to the step δλ, the midpoint wavelength is defined as λ_k = (λ^ + λ⁽ _L ^k))/2 , and the double prime indicates the repeated powers.

Finally, the overall data stored in the data file after acquisition is depicted as a matrix in Equation (31) below, to which we will refer in all that follows. The matrix comprises K groups each of four powers of light backreflections (two sets of four when two photodetectors are used:

λ - = λ 1 ( ^k > λ = 2 < * ⁾

Data ^: (33)

2. Auto Calibration of the Relative Gain

For the preferred embodiment of Fig. 2 using a polarization beam splitter (PBS), it is necessary to perform the below described calibration procedure of the relative gain of the two detectors 22B and 22C before proceeding with any further computation. The same procedure is not performed for the other embodiments. The calibration principle is predicated upon the fact that, when an I/O-SOP scrambler 14 is used to generate a sufficiently large number of SOPs so as to substantially cover the Poincare Sphere, the average power of the backreflected light from the distal end (or other positions) of the FUT 18 will exit from the two ports of the PBS with a 2:1 ratio, the higher power corresponding to the port to which detector 22B is connected and the lower power corresponding to the port to which detector 22C is connected. Hence, any observed deviation from this 2:1 ratio for the observed detector powers can be quantified and taken into account, as follows.

After data acquisition is completed, K groups of four backreflected light powers

5 obtained from both photodetectors have been stored, i.e., a total number of J = 4-K powers (data) from detector 22B and also J = 4-K traces from detector 22C, as depicted in matrix (31). The j^Λ powers (j = 0, l..( J-I)) from 22B and 22C are referred to below as

Px_j and Py₁, respectively. If the overall losses in the two arms of the PBS were identical and the gains of both photodectors and associated electronics were also equal, the ratio of i o the powers Py and Px after averaging both populations over all J occurrences would be

j

In practice, the ratio obtained from the average of the measured powers does not equal 2 because of different losses in the arms of the PBS and different "effective" gains of the photodetectors, which includes the photodiode responsivity as well as the overall 15 gains of the following electronics, amplifiers and sampling circuitry. (Note that it is not necessary to determine the individual gains separately.) Therefore, before proceeding with the rest of the computations, all the J powers obtained from photodetector 22C, i.e. all the Py₁, are multiplied as follows:

* y ' j ~ &RoundTrφ ^' * S ' J

20 where

₌ ι < pχ > _^ Σy^PXJ' g^{RomdTrlp ~} 2 < Py > ^~ Y_JPy_j j

In practice, for center wavelengths that are relatively closely-spaced (e.g. <20 ran), the relative wavelength dependence of the components, detectors, etc. may be negligible and this calibration process need only be carried out once per single-end PMD

25 measurement sequence. Otherwise, this calibration may need to be carried out at every center wavelength, thereby increasing the overall measurement time of the measurement sequence.

As a result of the calibration, i.e. after all Py powers (data) have been multiplied by the measured relative gain as described above, the data processor 34 can compute the normalized backreflected light powers. More precisely, the normalized powers in the case of the embodiment of Figure 2 using a PBS are obtained by dividing the sampled and averaged signal Px from detector 22B, or the signal Py from detector 22C, or (and preferably) the difference (Px-Py)/2 or (Py-Px)/2, as will be described in more detail in the next section, or any weighted difference (1+ W)^(Px-W-Py), where w is a weighting factor, by the sum (Px+Py) of the sampled and averaged signals from both of the detectors 22B and 22C, which sum represents the total power impinging on the PBS, i.e., without selection of a particular polarization component.

It should be noted that other calibration may also be possible. For example, a potential alternative calibration technique is to use an internal reference with fiber couplers (splitters) or internal reflector to send a predefined amount (percentage) of light power from launched OTDR light to two different detectors.

The preferred computations giving the normalized powers of all preferred embodiments will now be described in detail.

3. Computation The powers are processed to obtain the PMD value as will now be described. It should be note that, in all that follows, the symbols refer to the matrix "Data" in Equation (33). The labels x and y refer to the backreflected light powers obtained from photodetectors 22B and 22C, respectively.

3.1 The Normalized Powers The normalized powers (i.e. transmissions), labelled hereinafter as T, are computed differently according to the embodiment.

(i) For the embodiment of Figure 2 (two photodetectors with a PBS), the normalized power is computed exactly the same as a normalization procedure for the embodiment of Figure ID (two photodetectors with a PBS) for the two-end PMD measurement as already in the previous related section. But note that the different Py powers must have been pre-multiplied by the measured relative gain, g_Ro_undTφ, from single-end measurement, as indicated in the description of the auto calibration procedure, before they are used in this normalization procedure.

(ii) For the embodiment of Figure 2D (two photodetectors with a coupler), the

5 normalized power is computed also exactly the same as a normalization procedure for the embodiment of Figure 1C (two photodetectors with a coupler) for the two-end PMD measurement as already in the previous related section. But note that a different reference mean- value U₀ = 2/3 for single-end measurement is used in this normalization procedure.

Here, the auto calibration procedure is not required, i.e. the above mentioned pre- o multiplication of the powers Py by the measured relative gain may be skipped.

(iii) For the embodiment of Figure 2C (single photodetector), again the normalized power is computed the same as a normalization procedure for the embodiment of Figure IB (two photodetectors with a coupler) for the two-end PMD measurement as already in the previous related section and a reference mean-value of U₀ = 2/3 for single-end 5 measurement must also be used in this normalization procedure.

Here we assume that light powers being launched into FUT at Pi^ and /![*' is nearly the same.

It should be noted that, in the equations above, { )sop_;λ can refer to averaging over either the I-SOPs, the A-SOPs, or the midpoint wavelength, ideally over all three, i.e., o changing both the (1-SOP₅A-SOP) couple and wavelength from one group of powers to the next. All of these relationships are fundamentally valid in all cases even if only polarization scrambling is applied, giving the correct value of the DGD at one particular midpoint wavelength. Then, scanning the midpoint wavelength only serves the purpose of averaging DGD over wavelength as per the definition of the statistical PMD value. On5 the contrary, as discussed earlier, averaging only over wavelength while keeping the (I- SOP, A-SOP) couple unchanged requires that assumptions about the FUT be met, and also requires a large value of the product PMD-Δv. The same remarks apply for the equations presented hereinafter. 3.2 Mean-Square Differences

The calculation here differs from the simple mean-square found in Eq. (1) (2) (12) and (13) which, for greater clarity, did not take into account the noise. Instead, the product of the repeated differences between normalized traces at λu and λ_t is averaged as follows,

Note the equation (22') is the same as equation (22). In conventional mathematical terms, equation (22') may be referred to as the second-order joint moment of the repeated differences. Doing so, the noise averages to zero instead of being "rectified", because the noise superimposed on a given trace is not correlated with the noise superimposed on the corresponding repeated trace. That is the first motivation for sampling repeated traces.

3.3 Computation of the PMD Value

The PMD then is directly computed according to the arcsine formula as,

where a roundtrip factor a_rt = J- . A theoretical constant α_ώ = J — is valid for the

cases where a common (same) state of polarization controller (scrambler) is used to control both input and output light SOPs, such as for Figures 2, 2C-G.

It should be appreciated that the arcsine formula, in Eq. (34), is not the only possible one. The purpose of using this formula is to obtain a result that is unbiased even if using a relatively large step, such that PMD-δv - 0.15, without introducing a significant error; this in order to maximize the signal-to-noise ratio and therefore the dynamic range of the instrument. If one were not concerned with maximizing the dynamic range, or keeping the overall measurement time reasonable, one might select a much smaller step, and use the simpler differential formula that follows,

PMD = a_rl -^-.J (AT(vγ)_{sop λ} (34a) This is not to infer that this formula is better or particularly advantageous, but merely that it may conveniently be used if the step is much smaller, i.e., satisfying the condition PMD δv < 0.01.

It should be noted that a forward PMD calculated from equations (34) and (34a) is a PMD or rms DGD of FUT.

It should also be noted that roundtrip rms DGD or roundtrip mean DGD can also obtained from a root-mean-square for DGD_RoundTnp(v) or mean for DGD_RomdTnp(v) at many different wavelengths for a given wavelength range and DGD_RomdTnp(y) at each given wavelength can be computed the arcsine formula as either,

DGD_Romdrnp (V) = ~ ;arcsin(«_Λ / TQ • (35)

or use the simpler differential formula that follows,

DGD_RomdTnp (V) = ^- • j {W(yf)_sop . (35a)

where normalized power (T) is obtained from each give wavelength.

A rms DGD and mean DGD (forward) can also be obtained by simply multiplying a roundtrip factor of V3/8 and 2/π on rms DGDR_0UndTnp and mean DGDR_OundTπ_P, respectively, where a rms DGDR_Oundτ_np or mean DGDR_0UIMiTnp can be obtained from measured DGD_ROundTπp(v) for many different midpoint wavelengths by root-mean square or mean DGDR_OundT_πp(v) from equations (35) or (35a) over a prescribed wavelength

range, e.g. rms DGD_RomdTnp and

mean DGD _RomdTnp = (DGD_RomdTrψ)_λ .

It should also noted that above computation equations for extracting DGD and PMD using normalized power (usually a normalized power is ranged between 0 to 1) may be replaced by other method. For example, only a relative power may be computed from measured powers, then a 'normalization factor' may be used in the equations (34) and (35) to cancel this factor that is multiplied on mean-square difference so as to obtain correct a DGD or PMD value.

It should be noted that the above equations for calculating the DGD or PMD have a theoretical constant a = J — . This theoretical constant value is valid for the cases ώ V 4 where the same common state of polarization controller (scrambler) is used as both input and output light SOP controlling, such as for figures 2, 2C-G. However, when two separated independent input and output state of polarization controllers (scramblers) are

5 used with a polarizer or PBS being located just before the detector, for example as shown

[g in figure 2G, a different theoretical constant i.e. a ^ = J— , must be used, (note this

theoretical constant is the same as for two-end PMD measurement equations as already described related above section).

For the case where the tunable pulsed light source has a relatively big linewidtho and a high PMD fiber is under test, a linewidth 'correction factor' may need to be applied in Eq. (8-11) in order to extract an accurate PMD value from the FUT.

Data Processing and Computation for Single-End Cumulative PMD Measurement 1. The Data Structure 5 Each OTDR trace, obtained with one given setting of the wavelength and of the

(I-SOP, A-SOP) couple, as described in the Method of Operation for the single-end cumulative PMD measurement (also called as single-end POTDR based cumulative PMD measurement), constitutes the elementary data cell. One trace consists of N power values corresponding to N values Z_n of the distance z, with n = 0...(N-I). o The next larger data unit is one group of four traces, two sets of four traces for the embodiments of Fig. 3 and Fig. 3 B where two traces are obtained simultaneously from photodetectors 22B and 22C (or sequentially in the case where an optical switch is used with one detector), all obtained with a given (I-SOP, A-SOP) couple as set by I/O-SOP controller 14. The two sets of four traces forming group k preferably have been obtained5 in the following sequence (time flowing from left to right), where the labels x and y refer to the traces obtained simultaneously from photodetectors 22B and 22C, respectively, λ⁽^ - λ⁽^ is equal to the step δλ, the midpoint wavelength is defined as λ_k - = J +. λ10⁽ _L0 ' ) / 2 , and the double prime indicates the repeated traces:

λ = λ⁽ _L ^k) λ = ^

Finally, the overall data stored in the data file after acquisition is depicted as a matrix in Eq. (36) below, to which we will refer in all that follows. The matrix comprises K groups each of four OTDR traces (two sets of four when two photodetectors are used), each trace consisting of N points corresponding to N values of distance Z_n, where n = 0 ... (N-I):

λ = λ ( k ) λ = ; ( * )

The data structure of equation (36) is the similar as that of equation (33), but data in equation (36) is OTDR traces as function of distance z instead of powers in equation (33) reflected from the distal end of FUT.

2. Auto Calibration of the Relative gain

For the preferred embodiment of Fig. 3, it is necessary to perform the below described calibration procedure of the relative gain of the two detectors 22B and 22C before proceeding with any further computation. The same procedure is not performed for the other embodiments. The calibration principle is predicated upon the fact that, when an I/O-SOP scrambler 14 is used to generate a sufficiently large number of SOPs so as to substantially cover the Poincare Sphere, the average power of the backreflected light over any segment along the FUT 16 will exit from the two ports of the PBS with a 2:1 ratio, the higher power corresponding to the port to which detector 22B is connected and the lower power corresponding to the port to which detector 22C is connected. Hence, any observed deviation from this 2: 1 ratio for the observed detector powers can be quantified and taken into account, as follows.

After data acquisition is completed, K groups of four OTDR traces obtained from both photodetectors have been stored, i.e., a total number of J = 4-K traces from detector 26A and also J = 4-K traces from detector 22B, as depicted in matrix (36). The j^Λ traces (j = 0, 1..(.J-I)) from 22C and 22B are referred to below as Px(z), and Py(z)_J? respectively. If the overall losses in the two arms of the PBS were identical and the gains of both photodetectors and associated electronics were also equal, the ratio of the traces Py and Px after averaging both populations over all J occurrences and over all the N values of z would be

hi practice, the ratio obtained from the average of the measured traces does not equal 2 because of different losses in the arms of the PBS and different "effective" gains of the photodetectors, which includes the photodiode responsivity as well as the overall gains of the following electronics, amplifiers and sampling circuitry. (Note that it is not necessary to determine the individual gains separately.) Therefore, before proceeding with the rest of the computations, all the J traces obtained from photodetector 22C, i.e. all the Py(z)_j, are multiplied as follows:

where

S_RθmdTr_ΨC

J n

In practice, for midpoint wavelengths that are relatively closely-spaced (e.g. <20nm), the relative wavelength dependence of the components, detectors, etc. may be negligible and this calibration process need only be carried out once per POTDR measurement sequence. Otherwise, this calibration may need to be carried out at every midpoint wavelength, thereby increasing the overall measurement time of the measurement sequence. As a result of the calibration, i.e. after all Py traces have been multiplied by the measured relative gain as described above, the data processor 34 can compute the normalized OTDR traces. More precisely, the normalized traces in the case of the embodiment of Figure 1 are obtained by dividing either the sampled signal Px from detector 22B, or signal Py from detector 22C, preferably the difference between the sampled signals from detectors 22B and 22C, (Px-Py)/2 or (Py-Px)/2, as will be described in more details in the next section, or any weighted difference (1+ w)^{" 1(}Px-w-Py), by the sum (Px+Py) of the sampled signals from both of the detectors 22B and 22C which represents the total backreflected power impinging on the PBS, i.e., without selection of a particular polarization component. The preferred computations giving the normalized OTDR traces for all preferred embodiments will now be described in detail. 3. The Point-by-Point Computation

The OTDR traces are processed to obtain the cumulative PMD as will now be described. It should be noted that the computation of PMD_n at each point z_n along the

FUT 18 is performed independently of any other point n. Each is deduced from averages

5 over the (I-SOP, A-SOP) couples and/or wavelength only. Thus, in the computations described below it is inappropriate to use the index n; it must simply be understood that the calculation is repeated in the same way for each point n, or, in other words, effectively at each distance Z_n. In all that follows, the symbols refer to the matrix "Data" in Eq. (36). It should also be emphasized that the labels x and y refer to the traces io obtained from photodetectors 22B and 22C, respectively.

3.1 The Normalized Traces

The normalized traces, labelled hereinafter as T(z), are computed differently according to the embodiment.

(i) For the embodiment of Fig. 3 (two photodetectors with a PBS), the normalized 15 OTDR trace is computed as follows, either

<k) _ Px£ .(*) f 7-fniW(k) __ Px .'«γ<*)

PxF + P^yF Px"[^K>+ Py !■(*)

L

p

y.,,™**)

or rp(k) 1 PxF - PyF 1 p_γ»⁽*⁾ _ Pv»⁽*>

2 Px_L ^(k) + PyF ^L 2 Px"l^k)+ Py"F

where it should be appreciated that the different Py traces have been pre-multiplied by the measured relative gain, g_RoundTripC , as indicated in the description of the auto calibration procedure, before they are used in Eq. (37a). (ii) For the embodiment of Fig. 3 B (two photodetectors with a coupler), the ratio of trace Px over trace Py is first computed as, p ,.,_, .

and then the above ratio is normalized with respect to its average over the K groups as,

p⁽*) DH(t)

\^KISOPΛ \^K)sop,λ where the reference mean-value is U₀ = 2/3 by assuming measured power for an input sate of polarization of light parallel to an axis analyzer, and the average ratio R is defined as,

(^R)SOPΛ ^{+ R}-L^{k) + R(}U^{k) + R}"u^k))' (^37d)

Here, the auto calibration procedure is not required, i.e. the above-mentioned pre- l o multiplication of the traces Py by the measured relative gain may be skipped.

(iii) For the embodiment of Figure 3 A (single photodetector), the only available traces are the Px traces (obtained here from photodetector 22). The normalized trace is obtained as in (5c) but without computing the ratio of trace x over trace y first, i.e.

p_γ{k) p_vιι(*)

1 S T^(k) - u ^u T^m - u ^u (We\

\ I SOP.λ \ I SOP,λ where the average trace is defined as,

It should be noted that, in the equations above, { >sop,λ can refer to averaging over either I-SOP_k, A-SOP_k, or the midpoint wavelength, ideally over all three, i.e., changing

20 I-SOP, A-SOP and wavelength from one group of traces to the next. AU of these relationships are fundamentally valid in all cases even if only I/O-SOP scrambling is applied, giving the correct value of the DGD at one particular midpoint wavelength. Then, scanning the midpoint wavelength only serves the purpose of averaging DGD over wavelength as per the definition of the statistical PMD value. On the contrary, as discussed earlier, averaging only over wavelength while keeping the I/O-SOP unchanged requires that assumptions about the FUT be met, and also requires a large value of the 5 product PMD-Δv. The same remarks apply for the equations presented hereinafter.

3.2 Relative Variance

The relative variance, as in equation (37b), is computed here as the average of the four available estimates, i.e.,

o where the reference variance is σ₁₀ = 4/45 , and the function "var" is defined as,

"^W=[^L-^W*] ^var(r"u)= [<^r'ul}~- -<^r«>i«]-

3.3 Mean-square Differences

The calculation here differs from the simple mean-square found in Eq. (3a)5 which, for greater clarity, did not take into account the noise. Instead, the product of the repeated differences between normalized traces at λu and λ^ is averaged as follows,

(^Δr2L_v <^ -7L)-σ"u-n ⁾>_5O,,_Λ =

⁽3⁹⁾ hi conventional mathematical terms, Eq. (39) may be referred to as the second- order joint moment of the repeated differences. Doing so, the noise averages to zero o instead of being "rectified", because the noise superimposed on a given trace is not correlated with the noise superimposed on the corresponding repeated trace. That is the first motivation for sampling repeated traces.

3.4 Noise variance

The second motivation for sampling repeated traces, which are substantially5 identical in the absence of noise, for each setting of center wavelength λ and SOP, is the ability to obtain an accurate estimate of the noise variance. That is because the relative variance, as computed in Eq. (38), includes both the variance of the hypothetical noiseless trace and the variance of the noise. However, if the noise variance is known, it can be subtracted since the variance of the sum of two independent random variables is equal to the sum of the variances. But thanks to the repeated traces, the noise variance can be estimated independently as follows:

°L. = P-I {σi - τ\ ) (T_Ϊ, - r_u ))_{SOP λ} (40)

The noise variance (Eq. 40) is then subtracted from the first estimate of the relative variance (Eq. 38) in the computation of the final relative variance as follows, σ² _τ = σ'² _r - σ² _noise (41)

3.5 Computation of the Cumulative PMD

The cumulative PMD then is computed according to the arcsine formula as,

PMD(z) = a_rl

where a roundtrip factor αr_rt = J- . A theoretical constant a_ds = J — is valid for the

cases where a common (same) state of polarization controller (scrambler) is used as both input and output light SOPs' controlling, such as for figures 3, 3A and 3B.

It should be appreciated that the arcsine formula, (42), is not the only possible one. The purpose of using this formula is to obtain a result that is unbiased even if using a relatively large step, such that PMD-δv ~ 0.15, without introducing a significant error; this in order to maximize the signal-to-noise ratio and therefore the dynamic range of the instrument. If one were not concerned with maximizing the dynamic range, or keeping the overall measurement time reasonable, one might select a much smaller step, and use the simpler differential formula that follows,

This is not to infer that this formula is better or particularly advantageous, but merely that it may conveniently be used if the step is much smaller, i.e., satisfying the condition PMD δv < 0.01. The cumulative PMD curve as a function of z is obtained by repeating the computation above, from equations (37) to equation (42), at each point n corresponding to distance Z_n.

It should be noted that above equations for calculating PMD have a theoretical

constant a _* = J y — 4 . This theoretical constant value is valid for the cases where one

common same state of polarization controller (scrambler) is used as both input and output light SOP controlling, such as for figures 3, 3 A and 3B. However, when two separated independent input and output state of polarization controllers (scramblers) are used with a polarizer or PBS being located just before the detector, for example as shown in figure

Ig 3C, then a different theoretical constant must be used, i.e. a = . — (note this theoretical

constant is the same as for two-end PMD measurement equations as already described related above section).

It should also be noted that the above computation equations (42) and (43) for extracting cumulative PMD using a normalized OTDR trace may be replaced by using a relative OTDR trace that is proportional to a normalized OTDR trace.

It should be noted that a forward PMD calculated from equations (42) and (43) is a PMD or rms DGD of FUT.

3.6 Optional Application of a Linewidth Correction Factor

If the effective spectral linewidth of the pulsed laser source is large, it may be desirable to perform an additional, although optional, data "post-processing" step to take into account the dependence of the measured cumulative PMD on the linewidth of the laser. Thus, one may multiply the N above-measured cumulative PMD values at z_n, PMD_n, by an appropriate linewidth-dependent correction factor. One expression of such a correction factor, suitable when the laser lineshape is approximately Gaussian, is:

where PMD_sat is the saturation cumulative PMD value, i.e., the limiting value towards which the measured cumulative PMD tends as the actual cumulative PMD grows toward infinity, if no linewidth correction factor is applied. It is given by:

PMD_sat = -^- - — (44)

4π σ_vL where σ_VL is the rms-width of the laser spectrum. (Note: for a Gaussian lineshape, the full- width at half-maximum is related to the rms-width by Δv_L = ^jS • ln(2) σ _vL .)

The last, optional, step comprises the computation of the N values of the correction factor according to Equation (44), and then the obtaining of the corrected PMD o values, PMD'_n, via multiplication of the PMD values measured before correction by the correction factor, i.e.

PMD'_n = α_LWn - PMD_n (45)

For example, if no correction factor is applied, Eqs. (44) and (45) indicate that the maximum cumulative PMD value corresponding to a bias of, say, -10%, is PMDmax =5 0.0817AV_L ^"'. AS a numerical example for this case, a full-width at half-maximum ΔV_L = 2 GHz gives PMD_sat ~ 93.7 ps and PMD_max ~ 40.8 ps. If the measured value happens to be equal to this pre-determined maximum value of 40.8 ps corresponding to a bias of - 10%, then the actual PMD is in fact 45.4 ps, i.e., the measured value suffers a bias of - 10%, as stated. Such a residual bias level may be acceptable in many field applications. 0 However, under these same physical circumstances, if the correction factor OI_LW =

1.11 is applied according to Eq. (45), one obtains the actual cumulative PMD¹ of 45.4 ps.

In practice, the uncertainty on the correction factor itself will grow if the correction factor becomes very large, i.e., when the directly measured (i.e., uncorrected) cumulative PMD is too close to PMD_sat, since any small error in the directly-measured5 PMD value or in the laser linewidth (or uncertainties as to the effective laser lineshape) can make the correction factor very unreliable, as can be appreciated from Equation (44).

However, the uncertainty remains small if the maximum allowable value of the correction factor is limited to a predetermined value, which then determines the maximum PMD that can be measured when the correction factor is applied. Doing so, not only is PMD_m3x larger than it would be without the correction, but more importantly, in contrast with the case where no correction is applied, there is no systematic bias when the actual PMD is equal to PMD_m3x, but rather only a small additional, zero-mean uncertainty. Using the previous example,, and setting the correction factor to a reasonable maximum value of 1.25, i.e., still close to unity, the maximum value of the actual PMD that can be measured, without bias, is PMD_m3x ~ 70 ps, compared to 40.8 ps with a bias of -10% if no linewidth correction factor is used. It is noted that, whenever the product PMD • Δv_Lis much smaller than unity, the application of such a correction factor in the post-processing serves no purpose since the factor is very nearly equal to unity anyway. The purpose of applying the correction factor is to increase the maximum PMD value that can be measured with no bias given the real linewidth of the laser. It should be appreciated that Equation (44) applies for the case of a nearly

Gaussian-shaped laser spectrum, and is given by way of example. Other formulas or relationships can be computed either analytically or numerically for any particular laser lineshape that deviates substantially from a Gaussian lineshape. The Gaussian lineshape is a special, though practically relevant, case for which the correction factor can be expressed as a simple analytical formula, whereas such simple analytical formulas cannot be found for arbitrary laser lineshapes.

TUNABLE LASER SOURCE FOR TWO-END PMD MEASUREMENT

As mentioned hereinbefore, it is desirable to have a tunable coherent source that can be tuned to many midpoint wavelengths combined with many input and output SOPs in order to either measure the DGD in any DWDM channel (as such in any spare DWDM channel with frequency spacing of about 35 GHz or 70 GHz) in either C or L band or to obtain accurately rms or mean DGD values (i.e. PMD) value where a sufficient wavelength range is available for the measurement. Consequently, it is desirable for the tunable coherent source to be tunable over a large range of wavelengths. Suitable tunable coherent sources, that are tunable over a range of several hundred nanometers, are known to those skilled in this art and so are not described in detail herein.

The tunable optical source of Figure 7 comprises a fiber optical amplifier, such as an SOA, based fiber ring laser design where a common gain medium 102 used for each of at least two different cavities (1,2,...,N) corresponding to at least two respective different wavelengths (1,2,...,N). An optical switch 106B acts to switch on and off the lights in the at least two different cavities at different time periods where the at least two different wavelengths are selected by the at least two different TBFs from a synchronized multi-channel tunable filter 104. In Figure 7, at least two polarization adjusters (1,2,...,N) are to adjust cavity SOPs of light if cavities are based on SMF fiber cavity. A beam splitter 106A is used to combine N cavities together and coupler 107 provides an output of light from laser cavities. The control unit 30' is used to adjust the tunable filer 104 center wavelength, control optical switch to turn 'ON' different laser cavities to emit different wavelengths as well as to control the gain medium, e.g. to supply the current for SOA if a SOA is used as a gain medium. Figure 7 A shows schematically an example of a preferred embodiment of such a tunable modulated optical source (used in 12A in Figure 1(B-H)), designed to emit three closely-spaced wavelength, in rapid sequence, where an optical chopper 130 acts as the optical switch, hi a preferred embodiment, the functions of the TBFs 104 can be realized using a single bulk diffraction grating, wherein the light paths of each of the three laser cavities is incident upon the said grating at slightly different angles in the diffraction plane, these slightly different angles having been selected to correspond to desired closely-spaced wavelengths about the nominal "center wavelength" of the laser. The TBFs may tune the "center- wavelength" (as defined hereinbefore) in one or more of the S, C and L or O and E bands, the particular accessible wavelength region depending upon the choice of the SOA 102' and the tunable filter 104 excess loss and wavelength- dependent loss. Preferably the SOA 102' is "polarization dependent", that is it optimally amplifies input light of a particular incident linear polarization and does not significantly amplify the corresponding orthogonally polarized. An example of such an SOA is the Model BOA 1004 manufactured by Covega Corporation. Thus, tunable modulated optical source 12A of Figure 7 A comprises a SOA 102', tunable optical bandpass filters (TBFs) 104, beamsplitting couplers 106A, 106B and 106C, an optical chopper 130 and three-port circulators 108 A and 108B connected in three ring cavity topology by polarization-maintaining fibers (PMF). The coupler 106D combines light outputs from couplers 106B and 106C.

A control unit 30 is coupled to the SOA 102', chopper 122 and the TBFs 104 by lines 120, 122 and 124, respectively, whereby it supplies control signals to selectively turn the lights on and off in different cavities at different time, as will be described in more detail later, and to adjust the wavelength by the TBFs.

The continuously tunable TBFs are typically grating based bandpass filters with bandwidth of 20 to 40pm (FWHM), which are used to tune the laser wavelength accurately and also to confine the light (photons) in this small TBF bandwidths so as to give an accurate laser wavelength with a narrow linewidth. If a PMF cavity is used, no any additional component is required. But if the cavity is based on SMF-28 fiber, for instance, one or two polarization controllers are still required to adjust state-of- polarization (SOP) in the laser cavity. The spectral linewidth of the tunable modulated optical coherent sources in the various above-described embodiments might range from less than 1 GHz to about 4 GHz.

It may be advantageous for this linewidth to be known, at least approximately, in order to facilitate application of the linewidth correction factor as described hereinbefore.

It should be appreciated that other kinds of tunable modulatable optical source could be used instead of that described hereinbefore. For example, it is envisaged that an external phase modulator could be used to generate optical sidebands on the output of an external cavity laser (ECL), distributed Bragg reflector laser (DBR), or distributed feedback laser (DFB).

A person skilled in this art will be aware of other alternatives for this tunable modulatable coherent source.

TUNABLE OTDR FOR SINGLE-END PMD MEASUREMENTS

As mentioned hereinbefore, it is desirable to use many midpoint wavelengths λmjd as well as many I-SOPs and A-SOPs. Consequently, it is desirable for the tunable OTDR to be tunable over a large range of wavelengths. Suitable tunable OTDRs, that are tunable over a range of several hundred nanometers, are known to those skilled in this art and so are not described in detail herein.

Figure 8A shows schematically an example of such a tunable pulsed laser source 12 which is disclosed in commonly-owned United States Provisional patent application serial number 60/831,448 filed July 18, 2006, the contents of which are incorporated 5 herein by reference. The tunable OTDR is based on a ring fiber laser design where a semiconductor optical amplifier (SOA) acts both as (i) a laser gain medium, and (ii) an external modulator that also amplifies the optical pulses when "on". (The SOA can amplify the input light pulses from 3-6dBm (input) to 17-2OdBm (output)).

Thus, tunable pulsed laser source 12 of Figure 8 A comprises a SOA 202, ao tunable optical bandpass filter (TBF) 204, a beamsplitting coupler 206 and a four-port circulator 208 connected in a ring topology by polarization-maintaining fibers (PMF). The coupler 206 has a first port connected to the SOA 202 by way of the TBF 104, a second port connected via a PMF loop 214 to the circulator 208 and a third port connected to one end of a delay line 210, the opposite end of which is terminated by a5 reflector 212. Thus, the ring comprises a first, amplification path extending between the circulator 208 and the coupler 206 and containing the SOA 202 and a second, feedback path between coupler 206 and circulator 208 provided by PMF 214.

The coupler 206 extracts a portion, typically 25-50%, of the light in the cavity and launches it into the delay line 210. Following reflection by the reflector 212, the light o portion returns to the coupler 206 and re-enters the cavity after a delay Δt equivalent to the round trip propagation time of the delay line 210. Conveniently, the delay line 210 comprises a fiber pigtail of polarization-maintaining fiber and the reflector 212 comprises a mirror with a reflectivity of about 95% at the end of the fiber pigtail. Of course, other suitable known forms of delay line and of reflector could be used. 5 A control unit 30 is coupled to the SOA 202 and the TBF 204 by lines 220 and

222, respectively, whereby it supplies control signals to selectively turn the SOA 202 on and off, as will be described in more detail later, and to adjust the wavelength of the TBF 204.

It should be noted that instead of producing short and high power light pulses0 from design in Figure 5(A), it can also generate long pulses by turning on the current of SOA for a much longer time than the delay time from the delay line 210. Such a tunable pulsed laser source 12' may provide a high output power at a low cost. For further details of this tunable pulsed laser source 12 and its operation, the reader is directed to US Provisional patent application No. 60/831,448 for reference.

It should be appreciated that other kinds of tunable pulsed light source could be

5 used instead of that described hereinbefore. For example, Figure 8B is an alternative design of Figure 8A where no delay line is used. The design in Figure 8B can effectively generate a long pulse from 275ns to 20us with a low cost, however, it may not suitable to produce OTDR pulse of less than 275ns.

Tunable pulsed laser source 12 of Figure 8B comprises a SOA 202, a TBF 204 l o and a beamsplitting coupler 207 connected in a ring topology by PMF to form a fiber ring laser cavity. The coupler 207 extracts a portion, typically 25-50%, of the light from the cavity as an output. A control unit 30 is coupled to the SOA 202 and the TBF 204 by lines 220 and 222, respectively, whereby it supplies the bias current on the SOA 202 and adjusts the wavelength of the TBF 104. The control unit 30 controls the SOA 202 by way

15 of line 220, turning its bias current on and off to cause it to generate light pulses.

Also for example, a suitable tunable pulsed light source where an acousto-optic modulator is used to pulse the light from a continuous-wave tunable laser is disclosed by Rossaro et al. (J. Select. Topics Quantum Electronics, Vol. 7, pp 475-483 (2001)), specifically in Figure 3 thereof.

20 Figure 8C illustrates schematically another suitable alternative tunable pulsed light source comprising a continuous wave (CW) widely-tunable linewidth-controllable light source 212" in combination with an independent SOA 230" which serves only as an amplifying modulator. The CW light source comprises a broadband semiconductor optical gain medium 232", typically an optical semiconductor optical amplifier (SOA),

25 and a tunable banpass filter (TBF) 234", controlled by the control unit 30 (Figure 2). The minimum small optical signal gain of >3-5dB can be close to 200nm (e.g. from 1250- 1440nm or 1440-1640nm). This minimum small signal gain is required to compensate the cavity loss so as to achieve a laser oscillation.

The continuously tunable TBF is typically a grating based bandpass filter with a

30 bandwidth of 30 to 80pm (FWHM), which is used to tune the laser wavelength accurately and also to confine the light (photons) in this small TBF bandwidth so as to give an accurately laser wavelength with a narrow linewidth. The "other components" identified in Figure 8C by reference number 136" will include an output coupler (typically 25/75 coupler and 25% is output port, but it can also be 50/50 coupler in order to get a more output power) and an optical isolator (can be integrated into optical gain medium, such as in the input of SOA).

If a PMF cavity is used, no any additional component is required. But if the cavity is based on SMF-28 fiber, for instance, one or two polarization controllers are still required to adjust state-of-polarization (SOP) in the laser cavity.

Use of the SOA 230" as an external modulator yields several advantages: one is a high light extinction (ON/OFF) ratio of about 50-60 dB, and a second is to amplify the input light to 10-2OdBm with a relative input power (of 0-6dBm) (note that an output power intensity is dependent on an operation wavelength). It is also worth noting that the device of Figure 8C will not produce a very narrow linewidth laser. The laser linewidth strongly depends on the TBF bandpass width. Typically, the tunable pulsed light source of Figure 6 can be designed to have a wavelength accessible range close to 200nm (for example, from 1250-1440nm or 1440-1640nm) by choosing properly SOAs (such as SOAs centered at 1350 nm and 1530 nm, respectively with a 3-dB gain bandwidth extends >70 nm and the maximum gain >22 dB).

It should also be noted that the device of Figure 8C will not produce a very narrow linewidth laser. The laser linewidth strongly depends on the TBF bandpass width. Typically, laser linewidth is about 4 to 15 GHz (for TBF bandwidth of 30-80pm). However, a wide laser linewidth (bandwidth) is advantageous for any OTDR application (including POTDR) for reducing coherence noise on the OTDR traces.

The spectral linewidth of the tunable pulsed laser sources in the various above- described embodiments might range from less than 1 GHz to more than 15 GHz. hi practice, it will usually be determined at the lower end by the need to minimize the coherence noise of the Rayleigh backscattering and at the upper end by the ability to measure moderately high PMD values. It may be advantageous for this linewidth to be known, at least approximately, in order to facilitate application of the linewidth correction factor as described hereinbefore. It may also be very advantageous for the laser linewidth to be adjustable in a known controlled manner, at least over some range, so as to circumvent or significantly mitigate the above mentioned limitation regarding maximum measurable PMD. If such ability to adjust the laser linewidth is available, one may select a larger linewidth where a small PMD value is to be measured, and select a smaller linewidth where a large PMD value is to be measured. Optimally, the laser linewidth would always be set as equal to approximately one half of the selected step δv.

A person skilled in this art will be aware of other alternatives to these tunable light sources.

Scrambling The term "pseudo-random-scrambling" as used herein is to emphasize that no deterministic relationship between one SOP and the next is needed or assumed by the computation. That is not to say, however, that the physical SOP controller 24 must be truly random as such. It may also follow, for example, that the SOPs define a uniform grid of points on the Poincare-sphere, with equal angles between the Stokes vectors.

Uniformly-Distributed

A "pseudo-random" SOP means that each of the three components (si, s2, s3) of the Stokes vector that represents that SOP on the Poincare sphere is a random variable uniformly distributed between -1 and 1, and that any one of the three components is uncorrelated with the two others (average of the product = 0). Nonetheless, whether the SOPs are on a grid or form a random set, the points on the sphere must be uniformly- distributed.

However, if a grid is used instead of a random set, the calculation or processing must not assume a deterministic relationship between one SOP and the next. Otherwise, if the FUT 16 moves, as may occur in real telecommunications links, such deterministic relationships between traces obtained with a deterministic grid will be lost.

Advantages of Embodiments of the Present Invention

(1) Two-End PMD Measurement a. The FUT 18 stability requirements are relaxed with the pseudo-random- scrambling approach because no deterministic relationships have to be assumed between powers obtained with different SOPs and/or wavelengths. This relaxing FUT stability requirement can be as small as 10 ms or even smaller, depending upon the particular embodiment. The measurement result is reliable for any type of optical fibers,

5 b. Permits the measurement of DGD at one given wavelength, and, when repeated at different wavelengths, permits the determination of DGD as function of wavelength then to further obtain mean DGD or rms DGD. c. Certain embodiments estimation of DGD at one given wavelength within a very short time (~lms), 0 d. Permits the measurement of very high DGD or overall PMD values (e.g. about 50 to 100 ps) from the FUT if a relatively narrow linewidth (e.g. of 1-2 GHz or less) of tunable coherent source is used, while also be capable to measure a small PMD (e.g. less than 0.1 ps) in high accuracy due to randomly scrambling, e. The dynamic range may range from 30 dB to over 60 dB for overall acquisition5 times ranging from less than tens to few minutes. An estimation of DGD value may also be possible obtained for a measurement time of less than one or hundredth second, f. Permits measurement of a FUT comprising in-line optical amplifiers, for example erbium doped fiber amplifiers (EDFAs) or Raman fiber amplifiers, and reliable o measurements can be taken even in the presence of significant ASE light from the optical amplifiers; and g. It is possible to design to have no two-way communications between two ends of FUT.

5 (2) Single-End Overall PMD Measurement a. They relax the FUT 18 stability requirement via the pseudo-random-scrambling approach because no deterministic relationships have to be assumed between powers obtained with different SOPs and/or wavelengths. The method can relax the FUT stability requirement for a very short time period, for example of 0.2 to o 0.4 s. The measurement result is reliable for any type of optical fibers, b. They permit all measurement equipment to be located at only one end of the FUT, c. They permit the use of very long pulses e.g. about 1 to 20 us or more as long as the OTDR can distinguish the localized refection at the distal end from other reflections, leading to a significantly high dynamic range, an overall short acquisition time, and a reduction of interference or coherence noise. For example, it may range from 25 dB to over 35 dB for overall acquisition times ranging from less than 2 minutes to over 5 minutes d. Permit the measurement of very high overall PMD values (e.g. about 50 ps or over) from the FUT if a relatively narrow linewidth (e.g. of 1-2 GHz or less) of tunable pulsed laser is used, but it still can measure a small PMD (e.g. less than 0.1 ps) in high accuracy due to randomly scrambling, and e. In contrast to the case where a CW laser may be used, the OTDR technique used in this single-end overall PMD measurement method can distinguish the Rayleigh backscattering and the localized reflection at the distal end of fiber, so that one no longer need to take into account the Rayleigh backscattering or other reflections such as from connectors between fiber sections, i.e. to provide a very reliable measurement results of PMD.

It should also be noted that the single-end PMD measurement method disclosed here may measure a PMD from a test instrument to the any localized reflection along fiber, for example from any connector or splicer of along FUT, if its backreflected light power may be high enough to be able to be measured properly.

(3) Single-End Cumulative PMD Measurement a. Relaxes the FUT 18 stability requirement via the pseudo-random-scrambling approach because no deterministic relationships have to be assumed between traces obtained with different SOPs and/or wavelengths. Moreover, this advantageous relaxing of the FUT 18 stability requirement is obtained whether it is actually performed via I/O-SOP scrambling (the preferred method), or, in the case of an "ideal" FUT (as defined previously), by relying only on the "natural" scrambling of the FUT's PSPs (principal states of polarization) which occur randomly and uniformly as a function of wavelength and fiber length; b. They permit the use of long pulses, in contrast to other POTDRs of the second type, leading to;

(i) significantly increased dynamic range, for example from 10 dB to over 20 dB for overall acquisition times ranging from less than 10 minutes to over 30 minutes for s typical pulse length of 100 or 200 ns. (ii) reduction of OTDR coherence noise that is superimposed on the traces,

(iii) increased maximum measurable PMD for a given laser spectral linewidth, c. They measure cumulative PMD directly, in contrast to previously-known POTDRs of the first type discussed herein, so no assumed specific birefringence model is needed, in particular, they are especially suitable for measuring cumulative PMD of spun fibers, d. They produce results that are genuinely quantitative, and e. The measurement result from this invention is a consequence of the random scrambling approach which leads notably to a simple equation (42) that is valid for any FUT 18 and any pulse length according to theory, and of the associated signal processing. Embodiments of the invention can measure PMD over a range extending from a few hundredths of picoseconds to over 50 picoseconds and can be used to locate high PMD fiber sections with excellent spatial resolution.

Relationships and Differences with respect to Commonly-Owned Patent Applications

Commonly-owned International patent application number PCT/CA2006/001610 filed September 29, 2006, the content of document is incorporated herein by reference, discloses a method and apparatus for using an OTDR-based instrument for single-end measurement of cumulative PMD of a FUT by launching groups of pairs of series of light pulses, series in each pair having closely-spaced wavelengths, and processing corresponding OTDR traces to obtain the PMD at any distance z along the fiber.

The two-end PMD measurement method and apparatus embodying the present invention facilitates a two-ended measurement where the overall PMD and/or DGD at one or more particular wavelengths is required to be measured in an optical link, that may include (unidirectional) optical amplifiers. Accordingly, in embodiments of the present invention, a) the measurement is a "straight-through" measurement without reflection, and the pulse lengths are very long, leading to an excellent signal to noise ratio; b) the ("straight-through" or forward) DGD as a particular wavelength, which is not the case for the other applications; c) the measurement is unidirectional and hence can be used if unidirectional elements, such as optical amplifiers (comprising optical isolators), are placed within the link; d) the invention permits measurement in the presence of significant ASE generated by intervening optical amplifiers; e) the invention permits the concurrent determination of PMD and DGD(λ); f) the invention enables the concurrent determination of PMD according to both the rms and mean definitions, without assumptions on the FUT behavior; g) the invention can be adapted to permit rapid monitoring within a DWDM channel to detect sudden changes in DGD, thereby permitting correlation with possible observed system outages.

The single-end overall PMD measurement embodying the present invention addresses the situation where only the overall PMD is required to be measured by accessing one end of FUT. Accordingly, in such embodiments of the present invention, a) the FUT has at its distal end a localized reflection having a significant degree of reflectivity which is not in general the case for the above-cited commonly-owned applications; b) using two detectors for high accuracy and reliable measurements which is not in a case for the above-cited commonly-owned applications where only one detector is used; c) using long light pulses for one detector design for obtaining a long measurement distance or high dynamics which is not in a case for the above-cited commonly- owned applications where only short light pulse length of less than about five to ten times beating length is applied; and d) the detected backreflected pulses ("response pulses") have very nearly the same time duration as the pulses launched into the FUT, in contrast to the above-cited commonly-owned applications, where the backreflected signal is an impulse response corresponding to distributed backreflections induced by Rayleigh backscattering and possible spurious localized reflections along the length of the

FUT;

The present invention of single-end cumulative PMD measurement addresses the alternative situations where two detectors are used or two different input and output polarization controller are applied. Accordingly, in embodiments of the present invention, a) using two detectors for high accuracy and reliable measurements which is not in a case for the above-cited commonly-owned applications where only one detector is used; b) more accurately measurements to extract a normalized power so as to have a reliable PMD measurement result from FUT; c) auto-calibration of two detectors' electronic gains for a PBS based embodiment; and d) a rough cumulative PMD as function of fiber length may be obtained using only one group of closely-spaced wavelengths, whereas in the above-cited commonly- owned applications, at least two groups are required.

INDUSTRIAL APPLICABILITY The entire contents of the various patents, patent application and other documents referred to hereinbefore are incorporated herein by reference.

Although embodiments of the invention have been described and illustrated in detail, it is to be clearly understood that the same are by way of illustration and example only and not to be taken by way of the limitation, the scope of the present invention being limited only by the appended claims.

In contrast to known PMD measurement most techniques of two end measurement methods for currently most of commercial available PMD test and measurement instrument for field application requires a wide wavelength range, embodiments of the present invention of two-end PMD measurement can be applied for a both small and big wavelength ranges for DGD or PMD measurement.

Embodiments of the invention can permit measuring and monitoring of DGD or PMD within a narrow DWDM channel if there is any spare channel available. It can also permit rapid detecting sudden changes in DGD from a DWDM channel or any optical path, thereby permitting correlation with possible observed system outages.

Embodiments of the invention permit measurement of DGD or PMD in the 5 presence of significant ASE generated by intervening optical amplifiers.

Also, in contrast to known techniques which rely upon the FUT 18 being stable over a relatively long period of time, typically tens seconds to few minutes, embodiments of the present invention do not require such long term stability, e.g. only requiring over about tens or hundreds of μs or ms averaging time. This is because acquired powerso corresponding to different SOPs and/or wavelengths (over about tens or hundreds of μs or ms averaging time), are treated as statistically independent (pseudo-randomly scrambled), without assuming any deterministic relationship between them.

Also, a small equivalent laser linewidth may be used to achieve a high measurable PMD dynamic range (e.g. to have a maximum measurable PMD of about over 50 to 1005 ps). Therefore, as a consequence of these advantages, this two-end PMD measurement embodying the present invention can measure PMD from very small value (e.g. less than 0.1 ps) to very large value (e.g. larger than 50 to about 100 ps) with a high distance dynamic range for the FUT within a very short measurement time.

Also this two-end PMD measurement embodying the present invention can o measure PMD of the FUT with optical amplifiers.

For single-end overall PMD measurement, in contrast to known PMD measurement most techniques which rely upon two ended measurement methods for currently most of commercial available PMD test and measurement instrument, embodiments of the present invention for single-end overall PMD measurement only5 require to access one end, i.e. a single end overall or total PMD measurement solution.

Also, in contrast to known techniques which rely upon the FUT 18 being stable over a relatively long period of time, typically several minutes to several tens of minutes, embodiments of the present invention for single-end overall PMD measurement do not require such long term stability. This is because acquired powers corresponding to0 different SOPs and/or wavelengths (over about hundreds of milliseconds averaging time), are treated as statistically independent (pseudo-randomly scrambled), without assuming any deterministic relationship between them.

The use of very long pulses allows a much larger SNR and also the OTDR technique (in comparison of CW laser) removes any other light reflections that are not come from the position for the testing (e.g. the end of fiber). Also a small equivalent laser 5 linewidth may be used to achieve a high measurable PMD dynamic range (e.g. to have a maximum measurable PMD of about over 50 to 100 ps). Therefore, as a consequence of these advantages of using OTDR and long pulses, the single-end PMD measurement embodying the present invention can measure PMD from very small value (e.g. less than 0.1 ps) to very large value (e.g. larger than 50 to about 100 ps) with a high distance i o dynamic range for the FUT within a reasonable short measurement time.

For the single-end cumulative PMD measurement, in contrast to known techniques which use short pulses and/or rely upon the FUT 18 being stable over a relatively long period of time, typically several minutes to several tens of minutes, embodiments of the invention for the cumulative PMD measurement do not require such

15 long term stability. This is because OTDR traces corresponding to different SOPs and/or wavelengths (a few seconds averaging time), are treated as statistically independent (pseudo-randomly scrambled), without assuming any deterministic relationship between them.

The use of relatively long pulses allows a much larger SNR than otherwise

20 achievable for a given averaging time. This is because (i) the optical energy of the backreflected light is proportional to the pulse length; and (ii) the detector bandwidth can be smaller, allowing both the bandwidth and spectral density of the noise to be reduced. Therefore, the effects of longer pulse length on SNR are three-fold and multiplicative.

With long pulses, the maximum measurable PMD value can also be larger for the

25 following indirect reason: With short pulses, the "coherence noise" that superimposes over OTDR traces is larger. To reduce it when using short pulses, the "standard" solution is to increase the equivalent laser linewidth (the laser intrinsic linewidth as such, or alternatively, using dithering or other equivalent means). This limits the maximum measurable PMD. Therefore, as a consequence of these different advantages of using

30 long pulses, the POTDR embodying the present invention can measure large values of cumulative PMD, that typically are seen at large values of z, within a reasonable measurement time.

In all OTDR applications, the power of the light backreflected by the FUT 18 decreases as a function of the distance from which local backscattering occurs, because any FUT 18 has a non-zero loss (typically 0.2- 0.25 dB/km @ λ =1550 nm). The dynamic range of an OTDR can be defined as the maximum loss for which it is still possible to obtain a good measurement within some reasonable noise-induced uncertainty. Initial test results show a dynamic range of ~15 dB when using 100-ns pulses and 1-s averaging time of single traces, for a noise-induced uncertainty smaller than 10- 15%. Tests with a prototype according to Figure 3 A have shown that, with typical fiber loss (0.2-0.25 dB/km), a POTDR embodying this invention may reach up to 70 km with 200-ns pulses and 2-s averaging time. Similar or better performance it anticipated from the embodiments of Figures 3, 3B and 3C.

The combination of the above advantages, i.e., significantly relaxed stability requirement, much larger SNR (and hence measurement range) due to the longer pulse lengths, and a realistic maximum measurable PMD (such as 30 to 40 ps), make a POTDR embodying the present invention particularly suitable for "field measurements" of long, installed fibers, possibly even those including an aerial section.

References [1] CD. Poole, D. L. Favin, 'Polarization-mode dispersion measurements based on transmission spectra through a polarizer', Journal of Lightwave Technology, Vol. 12 (6), pp. 917-929 (1994).

[2] 'Method and apparatus for measuring polarization mode dispersion', United States

Patent 7,227,645 B2, Jun. 5, 2007. [3] N. Cyr, 'Polarization-mode dispersion measurement: generalization of the interferometric method to any coupling regime', Journal of Lightwave Technology, Vol.

22(3), pp. 794-805 (2004).

[4] 'Fiber optical dispersion method and apparatus', United States Patent 4,750,833, Jun.

14, 1988. [5] P.A. Williams, AJ. Barlow, C. Mackechnie, J.B. Schlager, 'Narrowband measurements of polarization-mode dispersion using the modulation phase shift technique', Proceedings SOFM, Boulder CO, 1998, pp. 23-26.

[6] R. Noe, et al, 'Polarization mode dispersion detected by arrival time measurement of polarization-scrambled light', Journal of Lightwave Technology, Vol. 20(2), pp. 229-235 (2002). [7] 'Monitoring Mechanisms for Optical Systems', United States Patent Applications Publication US 2005/0201751 Al, Sep. 15, 2005.

[8] S.X. Wang, A. M. Weiner, S.H. Foo, D. Bownass, M. Moyer, M. O'Sullivan, M. Birk, M. Boroditsky, 'PMD Tolerance Testing of a Commercial Communication System Using a Spectral Polarimeter', Journal of Lightwave Technology, Vol. 24 (11), pp. 4120-4126 (2006).

[9] 'Method and apparatus for polarization mode dispersion monitoring in a multiple wavelength optical system', United States Patent 7,203,428, April 10, 2007. [10] S. Wielandy, M. Fishteyn, B. Zhu, Optical performance monitoring using nonlinear detection', Journal of Lightwave Technology, Vol. 22(3), pp. 784-793 (2004). [11] N. Kikuchi, 'Analysis of signal degree of polarization degradation used as control signal for optical polarization mode dispersion compensation', Journal of Lightwave Technology, Vol. 19(4), pp. 480-486 (2001).

[12] F. Corsi, A. Galtarossa, L. Palmieri, M. Schiano, T. Tambosso, "Continuous-Wave Backreflection Measurement of Polarization Mode Dispersion Characterization", IEEE Photonics Technology Letters, Vol. 11 No. 4, April 1999, pp. 451 -453.

[13] A. Galtarossa, L. Palmieri, M. Schiano, T. Tambosso, "Single-End Polarization Mode Dispersion Measurement Using Backreflected Spectra Through a Linear Polarizer", IEEE/OS A J. Lightwave Technology, Vol. 17 No. 10, October 1999, pp. 1835-1842. [14] H. Sunnerud, B.-E. Olsson, M. Karlsson, P.A. Andrekson, J. Brentel "Polarization- Mode Dispersion Measurements Along Installed Optical Fibers Using Gated Backscattered Light and a Polarimeter", IEEE/OSA J. Lightwave Technology, Vol. 18 No. 7, July 2000, pp. 897-904. [15] H. Sunnerud, B.-E. Olsson, M. Karlsson, P.A. Andrekson, "Measurement of Polarization Mode Dispersion Accumulation Along Installed Optical Fibers", IEEE Photonics Technology Letters, Vol. 11 No. 7, July 1999, pp. 860-862. [16] US patent No. 6,229,599 (A. Galtarossa).

[17] H. Dong, P. Shum, J.G. Zhou, Y.D. Gong, "Single-end Spectral Resolved Measurement of Polarization Mode Dispersion in Optical Fibers", Paper JThA20, Optical Fiber Communications Conference, March 25-29, 2007, Anaheim, CA, USA. [ 18] US patent No. 6,724,469 (M. Leblanc).

[19] F.Corsi, A.Galtarossa, L.Palmieri, "Beat Length Characterization Based on Backscattering Analysis in Randomly Perturbed Single-Mode Fibers," Journal of Lightwave Technology, Vol. 17, No. 7, July 1999.

[20] A.Galtarossa, L.Palmieri, A.Pizzinat, M.Schiano, T.Tambosso, "Measurement of Local Beat Length and Differential Group Delay in Installed Single-Mode Fibers", Journal of Lightwave Technology, Vol. 18, No. 10, October 2000.

[21] A.Galtarossa, L.Palmieri, M.Schiano, T.Tambosso, "Measurement of Beat Length and Perturbation Length in Long Single-Mode Fibers," Optics Letters, Vol. 25, No. 6, March 15, 2000. [22] B. Huttner, B. Gisin, N. Gisin, "Distributed PMD measurement with a polarization- OTDR in optical fibers", Journal of Lightwave Technology, Vol. 17, pp. 1843-1948, Oct. 1999.

[23] US patent number 6,946,646 (Chen et al.) [24] US published patent application number 2004/0046955, Fayolle et al.

Claims

1. A method of measuring at least one polarization-related characteristic of an optical path (FUT) using light input means connected to the optical path at or adjacent a proximal end thereof, and light output means connected to the optical path at or adjacent either the proximal end thereof or a distal end thereof, the light input means comprising light source means for supplying at least partially polarized light and means for controlling the state of polarization (I-SOP) of said at least partially polarized light and injecting said light into the FUT, and output light means comprising means for extracting corresponding light from the FUT, analyzing means for analyzing the extracted light and detection means for detecting the analyzed light corresponding to the at least one transmission axis of the analyzer means (A-SOP) to provide transmitted coherent optical power at each wavelength of light in each of at least two groups of wavelengths, wherein the lowermost

and uppermost (λu) said wavelengths in each said group of wavelengths are closely-spaced and wherein the following three conditions are not all concomitantly met: h. the source and detection means are at the same end of the FUT; i. only one detector in the analyzing and detecting means is used; j. the light from the light source comprises principally temporal pulses having a spatial extent more than ten times the beat length of the FUT; and wherein the said group comprises a wavelength pair, said pair in each group corresponding to a small optical-frequency difference and defining a midpoint wavelength therebetween, and wherein the I-SOP and A-SOP are substantially constant for each said wavelength in each said group, and wherein at least one of the midpoint wavelength, I-SOP and A-SOP is different between the respective said groups, the method including the steps of: xvi. Computing the at least one difference in a measured power parameter corresponding to each wavelength in said wavelength pair for each of the said at least two groups, said measured power parameter being proportional to the power of the said analyzed and subsequently detected light, thereby defining a set of at least two measured power parameter differences; xvii. Computing the mean-square value of said set of differences; and xviii. Calculating the at least one polarization-related FUT characteristic as at least one predetermined function of said mean-square value, said predetermined function being dependent upon the said small optical frequency difference between the wavelengths corresponding to the said each at least said two pairs of closely-spaced wavelengths.

2. A method according to claim 1, wherein the said output light means is connected to the optical path at or adjacent the distal end of the FUT.

3. A method according to claim 2, wherein: a. each said group comprises wavelength pairs having substantially said prescribed midpoint wavelength, and b. the said at least one polarization-related FUT characteristic is the differential group delay (DGD) at the said midpoint wavelength.

4. A method according to claim 3 or claim 62, wherein the said measured power parameter is the computed normalized power T(v) , and said predetermined function can be expressed, for small optical-frequency differences (δυ), according to the following differential formula:

i SOP

where the constant a ^ = J— , and υ is the optical frequency corresponding to the said

midpoint wavelength.

5. A method according to claim 3 or claim 62, wherein the said measured power parameter is the computed normalized power T(v) , and the means square value computing step (ii) further comprises the computation of the relative variance (σ_r ²(v) ) of the normalized powers, according to the expression:

where the reference variance

= 1/12 and the said predetermined function then is determined, for small optical-frequency differences δυ, according to the following differential formula:

where the constant , and υ is the optical frequency corresponding to the said

midpoint wavelength.

6. A method according to claim 3 or claim 63, wherein the said measured power parameter is the computed relative power P_R(v) , and mean square value computing step (ii) comprises the steps of: a. computing the relative variance (σ_R ² (y) ) of the relative powers (relative transmitted signals); and b. computing the ratio of the mean-square difference from relative powers over said relative variance, c. said DGD being computed as a function of said ratio as said predetermined function that can be expressed as a differential formula for small optical-frequency differences δυ .

7. A method according to claim 3, wherein the said optical source means emits coherent light at two closely-spaced wavelengths separated by said small optical frequency difference about a prescribed midpoint wavelength;

8. A method according to claim 3, wherein a) the said light input means emits polarized broadband light, the spectral width of said broadband light encompassing the said small optical-frequency difference corresponding to the wavelength pair centered on said prescribed midpoint wavelength, b) said lowermost and uppermost wavelengths separated by said small optical frequency difference about a prescribed midpoint wavelength; c) the said analyzing and detection means includes spectral filter means, comprising a narrowband optical filter, the filter width being much less than the said small optical frequency difference, thereby rendering coherent the light selected therefrom; d) the said spectral filter means being operable to allow selection and subsequent detection of each of the wavelengths corresponding to the said groups comprising the said wavelength pair;

9. A method according to claim 8, wherein the said spectral filter means is operable to allow the contemporaneous selection and subsequent detection of each of the wavelengths corresponding to the said groups comprising the said wavelength pair, the selected filtered light corresponding to the two or more wavelengths being subsequently detected by respective two or more detectors.

10. A method according to claim 3 or claim 5, wherein: steps (i), (ii) and (iii) of the said method are repeated for each of at least two said midpoint wavelengths falling within a prescribed wavelength range, thereby providing a set of at least two calculated values of DGD each at a corresponding one of the at least two said midpoint wavelengths; the said optical-frequency difference between wavelengths in each group not necessarily being the same for each application of said method at different said midpoint wavelengths, said at least one predetermined function comprising at least one of the rms DGD value and mean DGD value of the DGD values at the different wavelengths.

11. A method according to claim 10, where said at least two said midpoint wavelengths falling within a prescribed wavelength range includes a large number of midpoint wavelengths, approximately uniformly distributed across the said prescribed wavelength range.

12. A method according to claim 2, wherein: a) each of said at least two groups of closely-spaced wavelengths being defined by a respective midpoint wavelength, and at least two of the said at least two groups having midpoint wavelengths that are different, b) the said at least one polarization-related FUT characteristic is the rms DGD (i.e. PMD) over a prescribed wavelength range;

13. A method according to claim 12, wherein the said measured power parameter is the computed normalized power T , wherein said predetermined function can be expressed, for small optical-frequency differences δυ, as the following differential formula:

PMD = ^^ - (AT²) πδv V \ '∞^p,λ

where the constant a = , ft — .

14. A method according to claim 12 or claim 62, wherein the said measured power parameter is the computed normalized power T(υ), and wherein the mean square value computing step (ii) includes the computation of the relative variance {σ_r ² ) of the normalized powers according to the expression:

where the reference variance

= 1 / 12 , the said predetermined function then being determined for small optical- frequency differences δυ according to the following differential formula:

9 where the constant, a = J— .

' 2

15. A method according to claim 14 or claim 63, wherein the said measured power parameter is the computed relative power P_R , and the mean square value computing step 5 (ii) comprises the steps of: a) computing the

) of the relative transmitted signals; and b) computing the ratio of the mean-square difference over said relative variance, said rms DGD computed as a function of said ratio as said predetermined function that is determined for small optical-frequency differences δυ, according to the i o differential formula:

where a relative variance (σ_R ) of the normalized powers is defined as:

\

15

16. A method according to claim 2 wherein: in each of at least one spectral acquisition step, at least a quasi-continuum of transmitted coherent optical powers as a function of optical frequency are detected and stored for further analysis in said step (i), said optical frequency spanning a prescribed wavelength 20 range, a) said measured power parameters are computed from said transmitted coherent optical powers ; b) none, either or both of the I-SOP and A-SOP vary with respect to the optical frequency and such respective variation, if present, is slow, such that both of I-SOP

25 and A-SOP, respectively, are substantially the same for each said group of closely- spaced wavelengths;

17. A method according to claim 2, wherein a) the said at least one spectral acquisition is one spectral acquisition; and b) the said at least one polarization-related FUT characteristic is the rms DGD (i.e. PMD) over said prescribed wavelength range.

18. A method according to claim 16 or claim 62, wherein the measured power parameter of step b) is a normalized power proportional to the analyzed and subsequently detected light power.

19. A method according to claim 18 or claim 63, wherein the measured power parameter of step b) is a relative power proportional to the analyzed and subsequently detected light power.

20. A method according to claim 18, wherein the said at least one spectral acquisition is at least two spectral acquisitions, wherein either or both of the I-SOP and A-SOP corresponding to at least some of the stored optical frequencies in at least one spectral acquisition are substantially different than the either or both of the I-SOP and A-SOP, respectively, for the corresponding said stored optical frequencies in at least a second sweep, said at least one predetermined function comprising at least one of a. the rms DGD value over a prescribed wavelength range; and b. when the said at least some of the stored optical frequencies correspond to the said midpoint wavelengths, the DGD at at least one of the said midpoint wavelengths.

21. A method according to claim 20, wherein a) the said at least one of the said midpoint wavelengths in b) is one said midpoint wavelength, and b) the said spectral acquisition encompasses said small optical-frequency difference corresponding to the wavelength pair centered on said midpoint wavelength.

22. A method according to claim 16, wherein a) said none, either or both is none; and b) the said at least one polarization-related FUT characteristic is the rms DGD (i.e. PMD) over said prescribed wavelength range.

23. A method according to claim 16, wherein the said optical source means is operable to sweep the optical frequency of the said coherent light substantially continuously, said sweep enabling said spectral acquisition and encompassing the prescribed wavelength range.

24. A method according to claim 16, wherein a) the said optical source means emits polarized broadband light, the spectral width of said broadband light encompassing the prescribed spectral range; b) the said analyzing and detection means includes spectral filter means, comprising a narrowband optical filter, the filter width being much less than the said small optical-frequency difference, such that the light selected therefrom is coherent; and c) the said spectral filter means is operable to sweep substantially continuously to sequentially select and subsequently detect each of the wavelengths corresponding to the said groups comprising the said wavelength pairs, said sweep enabling said spectral acquisition.

25. A method according to claim 16, wherein a) the said optical source means emits polarized broadband light, the spectral width of said broadband light encompassing the prescribed spectral range; and b) the said spectral filter means, comprising a spectrometer, spatially separates the spectrum of the incident light so as to allow the detection means to contemporaneously detect the wavelengths corresponding to the said wavelength pairs in said at least two groups, the different wavelengths being selectively detected by respective two or more detectors.

26. A method according to claim 1, where the said light extraction and processing means is connected to the optical path at or adjacent the proximal end of the FUT and there is provided a localized reflection at or adjacent the distal end of the FUT.

27. A method according to claim 26, wherein: a) each of said at least two groups of closely-spaced wavelengths being defined by a respective midpoint wavelength, and at least two of the said at least two groups having midpoint wavelengths that are different, and b) the said at least one polarization-related FUT characteristic is the rms forward DGD (i.e. PMD) over a prescribed wavelength range;

28. A method according to claim 26, wherein each group comprises series of optical pulses, each optical pulse in each series having a spatial extent less than the length of the FUT and having substantially the same wavelength as other pulses in the same said each series, and wherein the said measured power parameter is determined from an average of at least some of the optical pulses in each series.

29. A method according to claim 27 or claim 62, wherein the said measured power parameter is the computed normalized power T , and said predetermined function is determined, for small optical-frequency differences δυ, according to the following differential formula: a a

PMD = -+ — *- • / (AT² πδv \ ^{v l sop}'^λ

where the roundtrip factor a_n = J- and the constant α_ώ is dependent upon the respective

V o optical paths traversed by the forward-propagating light from the optical source and the detected backreflected light.

30. A method according to claim 27 or claim 62, wherein the said measured power parameter is the computed normalized power T , and the mean square value computing step (ii), compensates for the possible presence of unpolarized noise, such as spontaneous emission (SE) light, in the detected signal, by the steps of : a) computing the relative variance ( σ_r ² ) of the normalized transmitted signals; and b) computing the ratio of the mean-square difference over said relative variance, said rms DGD computed as a function of said ratio as said predetermined function being determined for small optical-frequency differences δυ, according to the following differential formula:

where the roundtrip factor a_rl = J- , the relative variance of the normalized powers is

defined as,

₂ 4 „ ,. . „ . |3 where the constant σ,₀ = — , the roundtrip factor a_rt = J- , and the constant a_ds is

o dependent upon the respective optical paths traversed by the forward-propagating light from the optical source and the detected backreflected light.

31. A method according to claim 27 or claim 63, wherein the said measured power parameter is the computed relative power P_R , and mean square value computing step (ii)5 comprises: a) computing

) of the relative transmitted signals; and b) computing the ratio of the mean-square difference over said relative variance, said rms DGD computed as a function of said ratio as said predetermined function that can be expressed as a differential formula for small optical-frequency differences0 δυ.

32. A method according to claim 26, wherein a. each said group comprises wavelength pairs having substantially said prescribed midpoint wavelength; b. the said at least one polarization-related FUT characteristic is the differential 5 group delay (DGD) at the said midpoint wavelength.

33. A method according to claim 32 or claim 62, wherein the said measured power parameter is the computed normalized optical power T(v) , and said predetermined function for small optical-frequency differences δυ, according to the following differential formula:

where the constant α_Λ is dependent upon the respective optical paths traversed by the forward-propagating light from the optical source and the detected backreflected light. .

34. A method according to claim 32 or claim 62, wherein the said measured power i o parameter is the computed normalized power T(v) , and mean square value computing step (ii), compensates for the possible presence of unpolarized noise, such as spontaneous emission light, in the detected signal, by: a) computing the relative variance ( σ) (v) ) of the normalized transmitted signals; and

15 b) computing the ratio of the mean-square difference over said relative variance, said rms DGD being computed as a function of said ratio as said predetermined function determined for small optical-frequency differences δυ, according to the following differential formula:

2 o where the relative variance of the normalized powers is defined as,

4 where the constant σ*₀ = — , and where the constant a_ds is dependent upon the respective

optical paths traversed by the forward-propagating light from the optical source and the detected backreflected light.

25

35. A method according to claim 32 or claim 63, wherein the said measured power parameter is the computed relative power P_R (v) , means square value computing step (ii) comprises the steps of : a) computing the

) of the relative transmitted signals; and b) computing the ratio of the mean-square difference over said relative variance, said 5 DGD computed as a function of said ratio as said predetermined function that can be expressed as a differential formula for small optical-frequency differences δυ.

36. A method according to claim 32, wherein: a. the said method is repeated for each of at least two said midpoint wavelengths i o falling within a prescribed wavelength range, thereby providing a set of at least two calculated values of round-trip overall DGD at the corresponding at least two said midpoint wavelengths; the said optical-frequency difference between wavelengths in each group not necessarily being the same for each application of said method at different said midpoint wavelengths; and

15 b. said polarization-related FUT characteristic additionally comprises at least one of: i. the average round-trip overall DGD value over the prescribed wavelength range, where the average is either or both of the root-mean square (rms) and mean, calculated from the individually measured round-trip overall DGD(v), and

20 ii. the average (forward) overall DGD value corresponding to the prescribed wavelength range, where the average is either or both of the root-mean square (rms) and mean, is calculated from the individually measured round-trip overall DGD(v,z) by including the appropriate roundtrip factor.

25

37. A method according to claim 36, wherein said at least two said midpoint wavelengths falling within a prescribed wavelength range include a large number of midpoint wavelengths, approximately uniformly distributed across the said prescribed wavelength range.

30

38. A method according to claim 1 , wherein: a. the said light output means is connected to the optical path at or adjacent the proximal end of the FUT; b. each group comprises at least one wavelength pair of series of light pulses, each series having the same I-SOP; c. the light pulses in each series of the pair have substantially the same wavelength; d. the said measured power parameter is the detected backreflected power as a function of distance along the FUT, this said measured power parameter being determined by: i. for each of at least some of the light pulses in each series of light pulses in each said group, analyzing and subsequently detecting light comprising at least one polarization component of the resulting backreflected signal caused by Rayleigh scattering and/or discrete reflections along the FUT to provide a corresponding impulse- response, said at least one polarization component being the same for each of the said series in said group, and converting each of the impulse-responses into a corresponding electrical impulse-response signal; ii. for each said series of light pulses in each said group, sampling and averaging the electrical impulse-response signals of said at least some of the light pulses to provide an OTDR trace as a function of time delay; iii. converting said OTDR trace as a function of time delay to an OTDR trace representing detected backreflected power as a function of distance.

39. A method according to claim 38, wherein: a. each of said at least two groups of closely-spaced wavelengths is defined by a respective center wavelength, this said center wavelength being the midpoint wavelength if the group comprises only two series corresponding to respective closely-spaced wavelengths, and at least two of the said at least two groups having center wavelengths that are different, and b. the said at least one polarization-related FUT characteristic is the cumulative PMD value over a prescribed wavelength range corresponding to a distance z along the FUT, this said cumulative PMD value being estimated from the cumulative rms round-trip DGD for the same said prescribed wavelength range.

40. A method according to claim 39 or claim 62, wherein the said measured power parameter is the computed normalized power as a function of distance z along the FUT, T{z), and said predetermined function is determined for small optical-frequency differences δυ, according to the following differential formula:

« - cz rη : r

PMD(z) = -= ^d- ^■ J (AT¹ (z)) π π δδvv V v \ \ ⁷/ ' SSOOΛPJ

where the roundtrip factor a_rt = J- , and where the constant a_ds is dependent upon the

V o respective optical paths traversed by the forward-propagating light from the optical source and the detected backreflected light. .

41. A method according to claim 39 or claim 62, wherein the said measured power parameter is the computed normalized power T(∑) , and the mean square value computing step (ii), compensates for the partial depolarization of the backreflected signal induced by the spatial extent of the light pulses by: a) computing the relative variance ( σ² (z) ) of the normalized transmitted signals; and b) computing the ratio of the mean-square difference over said relative variance, said cumulative PMD computed as a function of said ratio as said predetermined function that can be expressed, for small optical-frequency differences δυ as the following differential formula:

where the constant α_Λ is dependent upon the respective optical paths traversed by the forward-propagating light from the optical source and the detected backreflected light, .

the roundtrip factor a_rt - J- , and a relative variance of the normalized powers defined

V O as,

*■>- P _σ-T I & l\»"« ')/„SOPA -(πCj

4

5 where the constant σ?_n = — .

¹⁰ 45

42. A method according to claim 39 or claim 63, wherein the said measured power parameter is the computed relative power P_R (z) , and mean square value computing step (ii) comprises the steps of: o c) computing the relative variance (

) of the relative transmitted signals; and d) computing the ratio of the mean-square difference over said relative variance, said rms DGD being computed as a function of said ratio as said predetermined function that is determined, for small optical-frequency differences δυ, according to a differential formula. 5

43. A method according to claim 38, wherein: a) each said group comprises wavelength pairs having substantially said prescribed midpoint wavelength; and b) the said at least one polarization-related FUT characteristic is the differential o group delay (DGD) at the said midpoint wavelength.

44. A method according to claim 43 or claim 62, wherein the said measured power parameter is the computed normalized backreflected power T(v,z) , and mean square value computing step (ii), compensates for the partial depolarization of the 5 backreflected signal induced by the spatial extent of the light pulses by: a. computing the relative variance ( σ) (z, v) ) of the normalized transmitted signals; and b. computing the ratio of the mean-square difference over said relative variance, said rms DGD being computed as a function of said ratio as said predetermined function that is determined for small optical-frequency differences δυ, according to the following differential formula:

where the constant or _ώ is dependent upon the respective optical paths traversed by the forward-propagating light from the optical source and the detected backreflected light, and the relative variance of the normalized powers is defined as,

4 where the constant σ,l = — .

¹⁰ 45

45. A method according to claim 43 or claim 63, wherein the said measured power parameter is the computed relative power P_R{z,v) , may include an additional computing step in (ii) in the detected signal, the step comprising: a) computing

) of the relative transmitted signals; and b) computing the ratio of the mean-square difference over said relative variance, said DGD being computed as a function of said ratio as said predetermined function that can be expressed as a differential formula for small optical-frequency differences δυ.

46. A method according to claim 43, wherein: a) the said method is repeated for each of at least two said midpoint wavelengths falling within a prescribed wavelength range, thereby providing a set of at least two calculated values of round-trip DGD at the corresponding at least two said midpoint wavelengths, the said optical- frequency difference between wavelengths in each group not necessarily being the same for each application of said method at different said midpoint wavelengths, and said polarization-related FUT characteristic additionally comprises at least one of: iii. the average round-trip DGD(z) value over the prescribed wavelength range, where the average is either or both of the root-mean square

(rms) and the mean, calculated from the round-trip DGD(v,z); and iv. the average (forward) DGD value corresponding to the prescribed wavelength range, where the average is either or both of the root-mean square (rms) and the mean is calculated from the round-trip DGD(v,z) by including the appropriate roundtrip factor ;

47. A method according to claim 46, wherein said at least two said midpoint wavelengths falling within a prescribed wavelength range comprise a large number of midpoint wavelengths, approximately uniformly distributed across the said prescribed wavelength range.

48. A method according to any one of claims 3, 10, 12, 27, 32, 39 and 43, wherein either or both of each I-SOP and A-SOP, respectively, each corresponding to at least one said group of wavelengths, may be significantly different than its respective predecessor or0 successor, and is randomly or quasi-randomly selected on the Poincare sphere, this difference being such that over a sufficiently large number K of said groups, either or both of each I-SOP and A-SOP, respectively, are substantially uniformly distributed about the respective Poincare spheres. 5

49. A method according to any one of claims 3, 10, 12, 16, 27, 32, 39 and 43, wherein either or both of each I-SOP and A-SOP, respectively, each corresponding to at least one said group of wavelengths, is only slightly different than its respective predecessor or successor, this difference being such that over a sufficiently large number K of groups, either or both of each I-SOP and A-SOP, respectively, are substantially uniformly o distributed about the respective Poincare spheres.

50. A method according to any one of claims 3, 10, 12, 27, 32, 39 and 43, wherein either or both of the I-SOP and A-SOP comprise four distinct and I-SOPs and A-SOPs, respectively, said four distinct I-SOPs and A-SOPs, respectively, representing approximately mutually equidistantly spaced points on the Poincare sphere.

5 51. A method according to claim 48, wherein the said number K is greater than 10.

52. A method according to claim 49, wherein the said number K greater than 500,

53. A method according to any one of claims 4, 5, 13, 14, 15, 29, 30, 33, 34, 40, 41 ando 44, wherein said predetermined function can be expressed, for small optical-frequency differences δυ, as any formula that provides a numerical result that falls within an acceptable difference from the said following differential formula.

54. A method according to any one of claims 3, 10, 13, 27, 32, 39 or 43, wherein the said5 at least two groups of wavelengths comprises a number K of said groups of wavelengths, each comprising at least one wavelength pair, wherein the kth group is characterized by the SOP couple (I-SOPk; A-SOPk), where (I-SOPk) designates the injected state of polarization into the FUT and (A-SOPk) designates the said at least one transmission axis of the analyzing means, such that, for the K pairs corresponding to the K said groups, at o least two of said SOP couples are substantially different from others of said SOP couples.

55. A method according to claim 54, where the K said groups of wavelengths additional groups are injected, the said at least two of said SOP couples is at least a large 5 majority of the K said couples.

56. A method according to any one of claims 3, 10, 12, 27, 32, 39 or 43, wherein each said group of closely-spaced wavelengths comprises the detection of each wavelength in at least one additional repeated said wavelength pair, corresponding to an initial first0 wavelength pair, wherein the I-SOP and A-SOP for each of these additional repeated wavelength pairs are substantially the same within each said group, the computation of the at least one said polarization-related FUT characteristic including the detected signals for these additional repeated wavelength pairs.

57. A method according to claim 56, providing for the substantially contemporaneous detection of each said wavelength in the said additional repeated wavelength pair and the said corresponding initial wavelength pair in the detection means, the detection means separating the said analyzed transmitted light so as to comprise two portions of the same analyzed transmitted light, the said two portions being detected by two respective detectors.

58. A method according to claim 57, wherein the said each wavelength in the said additional repeated wavelength pair from the optical source means is detected sequentially in time with respect to each wavelength in the said corresponding initial wavelength pair in the detection means.

59. A method according to claim 56, wherein the said each wavelength in the said additional repeated wavelength pair from the optical source means is detected sequentially in time with respect to slightly different wavelength in the said corresponding initial wavelength pair in the detection means.

60. A method according to any one of claims 3, 10, 12, 27, 32, 39 or 43, wherein there is provided means to correlate the detected transmitted optical power with a respective one of the uppermost, lowermost and, when more the said group comprises more than two wavelengths, intermediate wavelengths in said group.

61. A method according to claim 60, wherein the said correlating means includes encoding the optical pulses using either or both of amplitude or pulse-frequency encoding.

62. A method according to any one of claims 4, 5, 13, 14, 15, 29, 30, 33, 34, 40, 41 or 42, wherein the measured power parameter of step (i) is a normalized power T proportional to the analyzed and subsequently detected light power, determined by one of the following methods: a) one polarization component of the light power is detected, conveniently using one detector, and then the normalized power is obtained for each wavelength of coherent light in each said group of wavelengths having at least two wavelengths, respectively, by dividing the power for that coherent light by the average of at least some, and preferably all, of the powers of the coherent light in the different groups; b) two orthogonal polarization components of the light power are detected simultaneously, conveniently using two detectors, and then the normalized power for each wavelength of coherent lights are obtained by dividing at least one of the powers corresponding to the two detected different polarization components for that coherent light by the sum of the powers corresponding to the two detected different polarization components for that coherent light; or by dividing a weighted difference of the powers corresponding to the two detected different polarization components for that coherent light by the sum of the powers corresponding to the two detected different polarization components for that coherent light; c) one polarization component and one optical power directly proportional to the output of light from the FUT are detected, conveniently using two detectors, and the normalized power corresponding to each wavelength of coherent lights obtained by first dividing the power for that wavelength of coherent light corresponding to the optical power detected from one polarization component of light by the power for that coherent light corresponding to the optical power directly proportional to the output of light to obtain a ratio representing the relative power for that coherent light, and dividing said relative power for that coherent light by the average of at least some, and preferably all of the relative powers in the different groups; d) using one detector plus one optical switch, two orthogonal polarization components of the light are detected at different times by the same detector where the optical switch is used to route the two orthogonal polarization components of the light to the same detector, and then the normalized power for each wavelength of coherent light is obtained by dividing at least one of the powers corresponding to the two detected different polarization components for that coherent light by the sum of the powers corresponding to the two detected different polarization components for that coherent light; or by dividing a weighted difference of the powers corresponding to the two detected different polarization components for that coherent light by the sum of the powers corresponding to the two detected different polarization components 5 for that coherent light; e) using one detector plus one optical switch, one polarization component and one optical power directly proportional to the light are detected at different times by the same detector where the optical switch is used to route one polarization component and optical power directly proportional to the output of light from the FUT to theo same detector, and the normalized power corresponding to each wavelength of coherent light obtained by first dividing the power for that wavelength of coherent light corresponding to the optical power detected from one polarization component of light by the power for that coherent light corresponding to the optical power directly proportional to the output light to obtain a ratio representing the relative5 power for that coherent light, and dividing said relative power for that coherent light by the average of at least some, and preferably all of the relative powers in the different groups.

63. A method according to any one of claims 6, 15, 19, 31, 35, 42 or 45, wherein the o measured power parameter of step (i) is a relative power P_R proportional to the analyzed and subsequently detected light power, determined by one of the following methods: a) One polarization component of the light power is detected, conveniently using one detector, and then the relative power is obtained for each wavelength of coherent light in each said group of wavelengths having at least two wavelengths,5 respectively, by dividing the power for that coherent light by the average of at least some, and preferably all, of the powers of the coherent light in the different groups; b) two orthogonal polarization components of the light are detected simultaneously, conveniently using two detectors, and then the relative power for each wavelength of coherent light is obtained by dividing at least one of the powers corresponding to the0 two detected different polarization components for that coherent light by the sum of the powers corresponding to the two detected different polarization components for that coherent light; or by dividing a weighted difference of the powers corresponding to the two detected different polarization components for that coherent light by the sum of the powers corresponding to the two detected different 5 polarization components for that coherent light; c) one polarization component and one optical power directly proportional to the output light from the FUT are detectedusing two detectors and the relative power corresponding to each wavelength of coherent light is obtained by dividing the power for that coherent light corresponding to the optical power detected from one i o polarization component of light by the power for that coherent light corresponding to the optical power directly proportional to the output of light to obtain a ratio representing the relative power for that coherent light; d) using one detector plus one optical switch, then two orthogonal polarization components of the light are detected at different times by the same detector where

15 the optical switch is used to route the two orthogonal polarization components of the light to the said one detector, and then the relative power for each wavelength of coherent light is obtained by dividing at least one of the powers corresponding to the two detected different polarization components for that coherent light by the sum of the powers corresponding to the two detected different polarization components for

20 that coherent light, or by dividing a weighted difference of the powers corresponding to the two detected different polarization components for that coherent light by the sum of the powers corresponding to the two detected different polarization components for that coherent light; e) using one detector plus one optical switch, one polarization component and one 25 optical power directly proportional to the light are detected at different times by the said one detector where the optical switch is used to route one polarization component and optical power directly proportional to the output light from the FUT to the said one detector, and the relative power corresponding to each wavelength of coherent light is obtained by dividing the power for that coherent light corresponding 30 to the optical power detected from one polarization component of light by the power for that coherent light corresponding to the optical power directly proportional to the output of light to obtain a ratio representing the relative power for that coherent light.

64. A method according to any one of claims 3, 10, 12 or 16, wherein: a) the at least one transmission axis of the analyzer means comprise two or more linearly-independent transmission axes; and b) the transmitted coherent optical powers from the plurality of said transmission axes are detected substantially simultaneously by corresponding detectors in the said detector means.

65. A method according to any one of claims 29, 30, 33, 34, 40, 41 or 44, where the

constant or . = I — if a common polarization scrambler is traversed by both the V 4 forward-propagating light from the optical source that is injected into the FUT and the

detected backreflected light, and a ^ if the said forward-propagating light and the

said detected backreflected light traverse independent polarization scramblers.

66. Measurement instrumentation, for measuring at least one polarization-related characteristic of an optical path (FUT), comprising: input light means for connection to the optical path at or adjacent a proximal end thereof, and output light means for connection to the optical path at or adjacent either the proximal end thereof or a distal end thereof for extracting, analyzing and detecting light that has travelled at least part of the FUT and providing corresponding electrical signals, and processing means for processing the electrical signals from the output light means to determine said at least one polarization-related characteristic; the light input means comprising light source means for supplying at least partially polarized light at each wavelength in at least two groups of wavelengths, and SOP controller means for controlling the state of polarization (I-SOP) of said at least partially polarized light and injecting said light into the FUT, wherein the lowermost (X₁) and uppermost (λu) of said wavelengths in each said group of wavelengths are closely-spaced, the said group comprises a wavelength pair, said pair in each group 5 corresponding to a small optical-frequency difference and defining a midpoint wavelength therebetween, and the SOP of the injected light and A-SOP are substantially constant for each said wavelength in each said group, and wherein at least one of the midpoint wavelength, I-SOP and A-SOP is different between theo respective said groups, and the output light means comprising: extraction and analysis means for extracting corresponding light from the FUT and analyzing the extracted light, and detection means for detecting the analyzed light corresponding to at least5 one transmission axis of the analyzer means (A-SOP) to provide transmitted coherent optical power at each wavelength of the analyzed light in each of said at least two groups of wavelengths, wherein the lowermost (λi) and uppermost (λu) said wavelengths in each said group of wavelengths are closely-spaced and wherein the following three o conditions are not all concomitantly met: k. the source and detection means are at the same end of the FUT; 1. only one detector in the analyzing and detecting means is used; m. the light from the light source comprises principally temporal pulses having a spatial extent more than ten times the beat length of the FUT; 5 the processing means being configured and operable for : xix. Computing the at least one difference in a measured power parameter corresponding to each wavelength in said wavelength pair for each of the said at least two groups, said measured power parameter being proportional to the power of the said analyzed and subsequently detected light, thereby defining a o set of at least two measured power parameter differences; xx. Computing the mean-square value of said set of differences; and xxi. Calculating the at least one polarization-related FUT characteristic as at least one predetermined function of said mean-square value, said predetermined function being dependent upon the said small optical frequency difference between the wavelengths corresponding to the said each at least said two pairs of closely-spaced wavelengths; and xxii. outputting the value of said at least one polarization-related FUT characteristic for display, transmission or further processing.

67. Light source apparatus for successively and repetitively generating coherent light at two or more closely spaced wavelengths, the apparatus comprising: an optical gain medium; at least two laser cavities, each cavity sharing a portion of their respective laser cavities, including the said optical gain medium; at least one output coupler permitting extraction of a fraction of the intra- cavity light corresponding to each said at least two laser cavities; a beam splitter for dividing the light into at least two spatially separated portions, each said at least two laser cavities corresponding to at least one of said at least two portions; a multichannel wavelength tunable bandpass filter means comprising at least two channels corresponding to different closely-spaced wavelengths, operable to accept light corresponding to each of the said at least two spatially separated portions into respective channels, and operable to wavelength tune the said channels in a synchronized manner; and a multichannel light blocking means, operable to permit the continuation of the optical path of not more than one said spatially separated light portions incident upon it and blocking all of the other light portions, the choice of light portion which is not blocked depending upon a parameter of the said multichannel light blocking means.

68. Apparatus according to Claim 67, wherein if the said at least one output coupler is two or more output couplers, the extracted light from each of the said two or more output couplers is subsequently combined into a common light path to provide an single output from the said light source apparatus.

5 69. Apparatus according to claim 67 or 68, wherein: the multichannel light blocking means is an optical chopper disc and motor to effect rotation thereof about an axis through the center of the disc and perpendicular to the plane of the disc, the said disc comprising holes arranged in a pre-determined manner; the said spatially separated portions of the light are spatially arranged so as to l o permit substantially unhindered passage of one of each portion through the said disc as a function of rotation angle of the disc; each of the portions of light passing substantially unhindered through the disc then completes the traversal of its respective cavity; and the disc is rotated at an approximately constant speed to successively and 15 repetitively permit passage of light portions corresponding to each said laser cavity, and to provide regular and repetitive time intervals during which no light passes the said disc; the apparatus being then operable to generate successively and repetitively at least two closely-spaced wavelengths.

CLAIMS FOR THE UNITED STATES AND CANADA ONLY

70. A method of measuring at least one polarization-related characteristic of

5 an optical path (FUT) using light input means connected to the optical path at or adjacent a proximal end thereof, and light output means connected to the optical path at or adjacent either the proximal end thereof or a distal end thereof, the light input means comprising light source means for supplying at least partially polarized light and means for controlling the state of polarization (I-SOP) of said at least partially polarized lighto and injecting said light into the FUT, and output light means comprising means for extracting corresponding light from the FUT, analyzing means for analyzing the extracted light and detection means for detecting the analyzed light corresponding to the at least one transmission axis of the analyzer means (A-SOP) to provide transmitted coherent optical power at each wavelength of light in each of at least two groups of wavelengths,5 wherein the lowermost (λ_\) and uppermost (λu) said wavelengths in each said group of wavelengths are closely-spaced; and wherein the said group comprises a wavelength pair, said pair in each group corresponding to a small optical-frequency difference and defining a midpoint wavelength therebetween, and wherein the I-SOP and A-SOP are substantially constant o for each said wavelength in each said group, and wherein at least one of the midpoint wavelength, I-SOP and A-SOP is different between the respective said groups, the method including the steps of: xxiii. Computing the at least one difference in a measured power parameter corresponding to each wavelength in said wavelength pair for each of the said at5 least two groups, said measured power parameter being proportional to the power of the said analyzed and subsequently detected light, thereby defining a set of at least two measured power parameter differences; xxiv. Computing the mean-square value of said set of differences; and xxv. Calculating the at least one polarization-related FUT characteristic as at least0 one predetermined function of said mean-square value, said predetermined function being dependent upon the said small optical frequency difference between the wavelengths corresponding to the said each at least said two pairs of closely-spaced wavelengths.

71. Measurement instrumentation, for measuring at least one polarization-related characteristic of an optical path (FUT), comprising: input light means for connection to the optical path at or adjacent a proximal end thereof, and output light means for connection to the optical path at or adjacent either the proximal end thereof or a distal end thereof for extracting, analyzing and detecting light that has travelled at least part of the FUT and providing corresponding electrical signals, and processing means for processing the electrical signals from the output light means to determine said at least one polarization-related characteristic; the light input means comprising light source means for supplying at least partially polarized light at each wavelength in at least two groups of wavelengths, and SOP controller means for controlling the state of polarization (I-SOP) of said at least partially polarized light and injecting said light into the FUT, wherein the lowermost (λι) and uppermost (λu) of said wavelengths in each said group of wavelengths are closely-spaced, the said group comprises a wavelength pair, said pair in each group corresponding to a small optical-frequency difference and defining a midpoint wavelength therebetween, and the SOP of the injected light and A-SOP are substantially constant for each said wavelength in each said group, and wherein at least one of the midpoint wavelength, I-SOP and A-SOP is different between the respective said groups, and the output light means comprising: extraction and analysis means for extracting corresponding light from the FUT and analyzing the extracted light, and n. detection means for detecting the analyzed light corresponding to at least one transmission axis of the analyzer means (A-SOP) to provide transmitted coherent optical power at each wavelength of the analyzed light in each of said at least two groups of wavelengths, wherein the lowermost (λι) and uppermost (λu) said wavelengths in each said group of wavelengths are closely-spaced; the processing means being configured and operable for : xxvi. Computing the at least one difference in a measured power parameter corresponding to each wavelength in said wavelength pair for each of the said at least two groups, said measured power parameter being proportional to the power of the said analyzed and subsequently detected light, thereby defining a set of at least two measured power parameter differences; xxvii. Computing the mean-square value of said set of differences; and xxviii. Calculating the at least one polarization-related FUT characteristic as at least one predetermined function of said mean-square value, said predetermined function being dependent upon the said small optical frequency difference between the wavelengths corresponding to the said each at least said two pairs of closely-spaced wavelengths; and xxix. outputting the value of said at least one polarization-related FUT characteristic for display, transmission or further processing.