GB2391935A

GB2391935A - Compact non-linear interferometer with ultrahigh sensitivity

Info

Publication number: GB2391935A
Application number: GB0209976A
Authority: GB
Inventors: Jolyon Mark De Freitas
Original assignee: Individual
Current assignee: Individual
Priority date: 2002-04-19
Filing date: 2002-04-19
Publication date: 2004-02-18
Anticipated expiration: 2022-04-19
Also published as: GB2391935B; GB0209976D0

Abstract

A compact interferometer is described which has an ultrahigh sensitivity response to small linear displacement or optical pathlength changes in general. The high sensitivity is achieved by rotating the orthogonally polarised heterodyne input states through angle R, and therefore deliberately frequency mixing the heterodyne components in a specific format in both arms of a polarising interferometer. In an additional treatment, the sensitivity is further enhanced by mixing the orthogonally polarised output beam into a given ratio in the polariser-analyser placed in front of the measurement photodetector.

Description

i 1. Field of invention

This invention relates to optical interferometry and to the precision measurement of linear displacement or optical pathlength change such as those used in stylus-based profilometers, extensometers, gravitational wave detectors, optical heterogeneity, optical metrology and other applications where extremely high sensitivity and low noise are needed. In particular, this invention relates to the apparatus and method for the measurement of small linear displacementsJoptical pathlength changes with very high sensitivity. The high sensitivity is achieved by deliberately mixing heterodyne signals in a specific format in both arms of a polarising interferometer.

2. Background

The measurement of linear displacement is often done by means of the standard Michelson interferometer. Michelson apparatus can be placed into two major categories: heterodyne and homodyne types, which may be subcategorised into broad beam and narrow beam interferometers. Within each sub-category we find a further two sub-categories, namely, polarising and non-polarising interferometer types. In general, a Michelson interferometer of one type can be converted to another by managing the tradeoffs.

In its most general form, and without reference to interferometer types, the input beam into the Michelson interferometer is first split in a beamsplitter, then recombined in the said beam-splitter after being reflected in the arms of the interferometer. The recombined beams are mixed in a photodetector or charge-

coupled device where interferometric fringes are recorded or detected. Signal processing can be either in real time or off-line.

In narrow beam, polarising interferometers, for example, the sensitivity of the interferometer is often improved optically by allowing both measurement and reference beams to traverse the interferometer anns in several round trips. If the number of round trips is N. then the sensitivity is increased by N. The drawback, though not limiting, is that the interferometer working range is reduced by N also.

Furthermore, the sensitivity can also be increased by what has been called 'resolution extension' electronics, where the phase difference to be measured is multiplied up using phase-locked loops and other techniques.

In the invention claimed herein, the apparatus and technique involve, but are not limited to, a narrow beam, polarising heterodyne interferometer. By rotating the heterodyne states about the input beam, the sensitivity of the interferometer can be enhanced significantly. However, the tradeoff between the interferometer working range and sensitivity becomes evident. The sensitivity response of the interferometer is therefore non- linear. The advantages of this invention are its extremely high sensitivity, compactness, and relatively low cost.

3. Detailed description

Fig. 1 shows one embodiment of the non-linear interferometer. Light la from a heterodyne source 1, such as a heterodyne laser diode or Zeeman heterodyne laser source, is orthogonally linearly polarised and passes through a half-wave plate 2 to produce beam la'. The heterodyne beam la' is then split by non-polarising bearn-

splitter 3 into two beams, a reference beam la" and a measurement beam lb. Each of the two linearly polarised components of me beam la (and consequently la', la" and lb) carries a unique frequency so that the difference in frequency between the two polarisation states is small, usually ranging from a few Lutz to tens of MHz. This type of frequency assignment to a polarisation state is usually referred to as 'polarisation frequency coding'. The half-wave plate 2 is used to orient and set me heterodyne mixing angle, R of the orthogonally polarised states of the beam la, relative to one of the axes of the polarising beam- splitter 5. Heterodyne mixing occurs in the interferometer and will be explained below. The reference beam la" passes through a polariser-mixer 16 set at 45 to both polarisation states before entering a photodetector 4 to yield the reference signal 12.

On entering polarising beam-splitter 5, the polarisation-coded heterodyne beam lb is split further into two beams 1c and Id. The intensity ratio between lc and Id is determined by the angular orientation R. set by halfwave plate 2, and the y-axis, say, of the polarisation beam-splitter S. Moreover, Ic and Id contain components of both heterodyne frequencies, often referred to as 'frequency mixing'. The extent of frequency mixing depends on angular setting, R. Beam lb has time-dependent complex electric vectors S'(,t) and 82(2,t) corresponding to the two heterodyne frequencies. Beam Ic is horizontally polarised and have electric field vectors proportional to the projection of the electric field

vectors onto the x-axis of the polarisation beam-splitter 5, i.e. horizontal: 8 cos R -

82sinR. Beam Id is vertically polarised and have electric field strength proportional

to the projection of the electric field vectors onto the y-axis of the polarisation beam-

splitter 5, i.e. vertical: C' sin R + 82 COS R. See details in Fig. 2. Clearly, a mixing of the two complex frequencies corresponding to B' and 82 occurs, and the ratio of the mixing intensities is (1 - sin 2) /(1 + sin 2R), assuming the magnitudes of the electric vectors are equal and no differential absorption.

Beam lc traverses a quarter-wave plate 11 where it is transformed into right circularly polarised light lc' towards plane mirror 6. After reflection in 6 it is left circularly polarised and passes through quarter-wave plate 11 whence it is transformed into vertically polarised light travelling towards beam-splitter 5. Beam lc going towards 5 is transmitted by the said beam-splitter and forms the vertically polarised component of beam le. Beam Id traverses through a quarter-wave plate 10 where it is transformed into left circularly Polaris light Id' towards plane mirror 7. After reflection in 7 it is right circularly polarised and passes through quarter-wave plate 10 whence it is transformed into horizontally polarised light travelling towards beam-

splitter 5. Beam Id going towards 5 is transmitted by the said beamsplitter and forms the horizontally polarised component of beam le.

z

The phase difference between the returning wavefronts lc and Id is the dynamical phase 6, given by Id 11, where d is the difference in pathlengths over the round trips taken by beams lc and Id, n is the refractive index of the material traversed by the two beams, and is the wavelength of the light source. If the vertical component (fusing+ 82cosR) in Id is the measurement arm of the interferometer, and undergoes a linear displacement, d over and beyond the reference arm (i.e. horizontal component), or a change in refractive index n, through the measurement path, or there is a change in the wavelength X, then the vertical component is proportional to (fusing+ 82cosR)ei6.

Beams lc and Id returning from mirrors 6 and 7 recombine in beam-splitter 5 to form beam Is going towards polariser-mixer 8 whose transmission axis is set at angle (3 to the vertical component of the beam le. If angle = 45 , then equal fractions of the electric fields in the orthogonally polarised beam Is are mixed and detected in

photodetector 9 to give the measurement signal 13. The ac part of the reference and measurement signals, 12 and 13 respectively, are fed into a phase-meter 14 where a phase up is measured and indicated.

The measured phase, up = tan'[sec2Rtan8] where is the dynamical phase corresponding to the linear displacement, d in the measurement arm. For appropriate values of R. the dynamical phase is amplified by a factor tan'[sec2Rtand]/. This factor is (see 2R) for values of close to, or equal to zero. Fig. 3 shows the interferometric characteristic response plotted against 6, for R = 40 . The grey line (in Fig. 3) shows the characteristic of a standard linear interferometer where there is no frequency mixing. Fig. 4 shows the relationship between the interferometer gain and dynamical phase, 8. The range A, over which the slope of the characteristic response of the interferometer is greater than or equal to l is = tan'(). For the characteristic shown in Fig. 3, the range is + 22.6 .

The measurement signal amplitude at 13, at worst case, is proportional to cos 2R. The worst-case scenario occurs when the dynamical phase = 0. Although the amplitude of the measurement signal is not generally important in digital applications, h could be important if analogue processing is used. And moreover, in digital applications where a zerocrossing technique is utilised the signal still needs to have a reasonable signal-to-noise ratio to register the crossing. Fig. shows the relationship between interferometer gain and angle, R. Clearly, as R gets closer to 45 there is a significant increase in the gain, but the signal amplitude cos2R, and consequently the mixing ratio (1 - sin 2R) /(1 + sin 2R), are practically zero and no signal is observed. As such only reasonable values for R are practical. For example, at R = 40.8 , the measurement signal modulation depth observed at the photodetector 9, is about 15%, but may still be useful if the initial input intensity is relatively high.

The sensitivity of the interferometer may further be improved by setting to be different from 45 . However, this is done at the expense of reducing the modulation depth furler for values of close to zero. In this case, the measured phase, <p = tan' [see 2R tan /(l - tan 2R cot 20 see ) ] where the symbols have their usual meanings. The problem of optimising on the polariser-mixer for maximum

sensitivity is equivalent to making 1- tan 2R cot 20 secd90 the smallest possible value subject to the constraints set by R and go, where the latter is the value of the dynamical phase at which the measured phase meter response is 90 . For a given R. the optimised polariser angle, Op' should be slightly greater than :tan[tan2Rsecd90]. The maximum gain, achieved when the dynamical phase is close to zero, is sec2R/(ltan2Rcot20); this also happens to be the slope of the interferometer characteristic response at the said phase. For example, Fig. 6 shows the interferometer gain versus dynamical phase for R = 40.8 , and (Hopi = 42 , whereas Fig. 7 shows the characteristic interferometer non-linear response and modulation depth for the said conditions in comparison to the response when the polariser-mixer angle is at 45 . Note that the increase in gain comes at the expense of the modulation depth at zero dynamical phase. Furthermore, note that if = -42 an entirely different characteristic response is obtained which may also be utilised.

In general, the reflecting means 6 and 7, may be retro-reflectors and the quarter-wave plates 10 and 11, may be removed entirely so that the beam is returned towards the source as occurs in some metrological optical sources. Furthermore, the interferometer is designed for use over short ranges (+ 45 ) about the zero dynamical phase position and as such needs to be 'zeroed'. This can be done by using the reference arm of the interferometer to bring the device into a zero position. These alternative embodiments and interpretations are evident to those skilled in the art.

Claims

4. Claims

1. An interferometer system for measuring linear displacement, refractive index changes, or changes in optical path comprising: a. a means for introducing polarisation-coded heterodyne light into the system; b. a means for rotating the said beam in 1 (a) about its input direction; c. a means for splitting the said beam in l(a) so as to obtain a reference beam and a measurement beam; d. interferometric means constituting a nonlinear response whereby the said measurement beam in l(c) is exploited to realise the measurement of linear displacement, refractive index changes, and/or optical path-length changes; e. interferometric means of 1 (d) further comprising: i. a means for splitting the said measurement beam in l(c) into separate orthogonally linearly polarised beams so that each of the said beams contains components of both heterodyne frequencies; ii. light reflecting means for the said beams in l(e)(i); iii. a means Or recombining the orthogonally polarised beams in l(e)(i) into a single beam; iv. a means for mixing the recombined beams in 1(e)(iii) so as to detect a ratio of components of the said orthogonally polarised beams; v. a means for detecting optical intensities corresponding to fringes l resulting from the said mixing in I (e)(iv); f. a means for detecting optical intensities associated with the said reference beam in l(c); g. a means for processing electronic signals associated with the detection of optical intensities in I(e)(v) and l(f) converting them into linear displacement, refractive index change, or optical path-length change;

2. Notwithstanding Claim I, the said means for the introduction of heterodyne light

into the system in l(a) comprises a light source emitting orthogonally polarised light whose polarisation states carry a unique frequency.

3. Notwithstanding Claims 1 and 2, the said means for splitting the light beams in I (e)(i) and the means for reflection in l(e)(ii) comprise a polarising beam-splitter with moveable plane mirrors optically aligned to the working beams of the said interferometer so that the dynamical phase may be controlled, including the setting of the relative position of the zero dynamical phase.

4. Notwithstanding Claims I to 3, the said interferometric means of l(d) and l(e) comprise orthogonally linearly polarised components of the input measurement beam whose states of polarization at the input to the polarising beam-splitter are: a. in the plane of the input surface of the said beam-splitter; b. angularly displaced at an angle relative to one of the beam-splitter axes and in the plane of the input surface of the said beam-splitter; c. whose axis of rotation is coincident with the direction of the said input beam;

5. Notwithstanding Claim 1, the said means for mixing in l(e)(iv) comprises a polariser-analyser at a fixed angle to the axes of the said orthogonally polarised components in l(e)(iii).

6. Notwithstanding Claims 1 to 4? the said interferometric means in l(d) may also comprise a polarised-coded non-orthogonally linearly polarised input beam.

7. Notwithstanding Claims I to 6, the said interferometric means in l(d) may also comprise a polarising beam-splitter with polarization leakage into output beams.