TWI382149B - For path imbalance measurement of the two arms fiber optic interferomter - Google Patents

Description

Measurement of interference arm length difference between two-arm fiber optic interferometer

The invention relates to the measurement of the interference arm length difference of the dual-arm fiber interferometer (TAFOI), in particular to measuring the PI value by using a polarization-insensitive fiber optic Michelson interferometer (PIFOMI). The method is mainly to apply a current carrier signal to modulate the semiconductor laser source of the interferometer, and the interference signal length interference (PI) of the two-arm interferometer is used to output an interference signal (interference signal). Generating a carrier phase signal and expanding the interference signal to a harmonic component of the carrier phase signal frequency using a Bessel function, and then we use a specific relationship between the second and fourth harmonic components of the interfering signal ( The theory of two interference arm length imbalance (PI) measurements between the second and fourth harmonic components, which measures the path imbalance (PI) of several decimeters (0.1 m), making it Accuracy can reach millimeters.

The induced phase signal of the two arms fiber optic interferometric sensor (TAFOIS) requires linear demodulation (via the use of some demodulation techniques). Signal demodulation lines of commonly used dual-arm interferometric fiber optic sensors, including active homodyne with DC phase tracking (PTDC demodulation) and passive homodyne demodulation using phase generated carrier (passive homodyne demodulation using phase generated carrier, Referred to as PGC demodulation). There are many advantages to using PGC demodulation, such as wide dynamic range, good linearity, high sensitivity, and sensor multiplexing.

Therefore, PGC demodulation has been widely used for signal demodulation in dual-arm fiber interferometric sensors (TAFOIS). However, first of all, PGC demodulation must first generate a high frequency carrier phase signal of a fixed amplitude. A common method is to apply a current carrier signal to modulate the interferometer's semiconductor laser source, which is caused by the interference arm length imbalance (PI) of the two-arm interferometer. The output interference signal produces a fixed amplitude (2.37 rads) carrier phase signal, and the amplitude of the carrier phase signal is proportional to the PI of the unbalanced interferometer. In a multiplexed sensing system, multiple sensors share a semiconductor laser, and each sensor PI must be the same or very close to generate a carrier phase signal with the same amplitude, and the sensing phase of the PGC demodulation output of each sensor The signal can be maintained in an optimal condition. Therefore the accuracy of individual sensor path imbalance (PI) values (typically PI lengths up to 200 mm) must be in the range of mm. However, when the sensing fiber of the interference arm is made of loose tube fiber, or the length of the sensing fiber reaches several hundred meters, the error of the initial cutting fiber length may approach a few decimeters (0.1 m), so we need A method for measuring the range of PI can reach several decimeters, and the accuracy is in the range of a few millimeters.

Current methods for measuring large optical path differences (OPD) include the use of an optical low-coherence reflectometry (OLCR) and a millimeter optical time domain reflectometry (MM-OTDR). Both methods are based on the measurement of the high spatial resolution of the reflected lightwave signal, so the price of the instrument is very high.

Although the low coherence light wave reflectometer (OLCR) has a high resolution, the optical measurement range of the OPD is limited to a few centimeters.

On the other hand, the resolution of the millimeter lightwave time domain reflectometer (mm-OTDR) is limited to about 5 mm. Therefore, the above two methods cannot meet the previous requirements.

In the present invention, we propose a method of measuring path imbalance (PI) values (via an output interference signal using a fiber optic Michaelson interferometer (PIFOMI) without polarization susceptibility). We use a current carrier signal to modulate the semiconductor laser source of the interferometer. The interference arm length imbalance (PI) of the two-arm interferometer causes the output interference signal to generate a carrier phase. Signal, and by using the Bessel function to spread the interference signal to the harmonic component of the carrier phase signal frequency, then we use the specific between the second and fourth harmonic components of the interfering signal. Relationship derivation of two interference arm length imbalances (path The theory of imbalance/PI), which measures a few millimeters (0.1 m) of path imbalance (PI) to achieve an accuracy of millimeters.

Therefore, the inventor specifically detects the length of the optical fiber, uses an optical fiber interferometer with unbalanced arms, and modulates the semiconductor laser light source of the interferometer to output an interference signal to generate a carrier phase signal, and then uses the measurement interference. The method of harmonic components of the signal enables accurate measurement of the length of the fiber.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a method for measuring the length of an optical fiber, in particular, using a fiber optic optical Michelson interferometer (PIFOMI) without polarization sensitivity to compensate for the length of the two interference arms for precise measurement of the PI value.

The measurement of the interference arm length difference of the dual-arm fiber interferometer (TAFOI) of the present invention mainly utilizes the unbalanced arms formed by the A-arm and the B-arm of the fiber-optic optical Michelson interferometer (PIFOMI) without polarization sensitivity. The method for measuring the unbalanced PI value of the length of the two interference arms is mainly to apply a current carrier signal to modulate the semiconductor laser source of the interferometer, and the length of the interference arm of the two-arm interferometer is unbalanced (path Imbalance/PI), which causes the output interference signal to generate a carrier phase signal, and uses the Bessel function to expand the interference signal into the harmonic component of the carrier phase signal frequency, and then we use the interference signal. The specific relationship between the second and fourth harmonic components deduces the theory of two interference arm length imbalance (PI) measurements, which can measure several decimeters (0.1 m). The path imbalance (PI) makes it accurate to reach millimeters.

The difference of the interference arm length difference of the dual-arm fiber optic interferometer of the present invention is mainly that the A-arm and the B-arm respectively have a fiber to be detected and a reference fiber, and the phase is changed by the piezoelectric ceramic phase modulator provided by the B-arm. And in a certain period of time, the second and fourth harmonic components of the array are obtained to obtain the maximum interference signal, and the measured values of the PIs of the two arms of the array are respectively calculated, and averaged to obtain an average PI measurement value. The length of the fiber is measured and its measurement error value is effectively reduced after averaging.

Thus, in order for your examiner to fully understand the dual-arm fiber optic interferometer of the present invention (TAFOI) The measurement of the interference arm length difference is explained as follows:

One. Path Unbalance (PI) Measurement Theory for Dual-arm Fiber Optic Wave Interferometer

If the fiber optic micson interferometer is made of a regular single-mode fiber, the output interference signal has polarization-induced signal fading, which makes the signal amplitude sometimes strong. Sometimes weak. In order to avoid the effects of strong time and weak, a fiber optic optical Michelson interferometer (PIFOMI) without polarization sensitivity is used in the present invention to measure path imbalance (PI). The polarization-free fiber-optic Michelson interferometer structure is connected to the Faraday rotator mirrors (FRM) at the end of the two interference arms to eliminate signal-induced fading caused by polarization. We assume that the path-unbalance (PI) value of the fiber-optic Maison interferometer without polarization sensitivity is Δ L . Therefore, as shown in FIG. 3, a current modulation signal Δ i sin ω _c t is used to modulate the semiconductor laser light source of the interferometer, so that the output interference signal can generate a carrier phase signal. (This technique is a conventional technique and will not be repeated here). among them Refers to the carrier phase signal function with time t , Can be expressed as equation (1): among them , For the amplitude of the carrier phase signal, n is the refractive index of the core of the fiber in the above equation, c is the speed of light, and Δ i is the amplitude of the current modulated signal. It is the partial differential of the optical wave step frequency v to the current i (ie, the conversion factor of the current i of the semiconductor laser to the optical frequency v ), and ω _c is the angular frequency.

Furthermore, the current modulation signal Δ i sin ω _c t will simultaneously produce a light intensity modulation for the semiconductor laser. This light intensity modulation does not affect signal demodulation in PGC demodulation, but the effects of this light intensity modulation (used to measure path imbalance (PI)) must be considered.

It is assumed that the output power of the semiconductor laser is modulated from I ₀ to I ₀ (1+ a sin ω _c t ), a is the normalized intensity modulation coefficient, a and Δ i In proportion, the output interference signal I ( t ) of the PIFOMI with the unbalanced arm is obtained by the formula (2) (this technique is a conventional technique and will not be described here):

In the above equation, b is the light intensity coefficient (or optical proportional to the optical power), k is the fringe visibility of the PIFOMIS interference signal output, and the coefficients b are proportional to I ₀ . And phase biased (biased) It will change as the environment changes. According to the PGC-DCM demodulation theroy, the equation (2) can be obtained by Fourier series (Fourier series) to obtain the equation (3). This technique is a conventional technique and does not do much here. Brief description):

among them with The function is a Bessel function of the first kind, and the amplitudes of the four harmonic components with angular frequencies ω _c , 2 ω _c , 3 ω _c , 4 ω _c can be obtained from equation (3). , respectively, represented by A ( ω _c ), A (2 ω _c ), A (3 ω _c ), A (4 ω _c ), respectively, as follows:

As far as the above four formulas are concerned, when When we get the following results:

There are significant at a laser intensity modulation factor _{A (ω c), A (} 2 ω c) and A (4 ω _c), and A (3 ω _c) and a irrelevant. A (2 ω _c ), A (4 ω _c ) and a are proportional, so when a <<1 compared with A ( ω _c ) and A (3 ω _c ), A (2 ω _c ) and A (4 ω _c ) is a minor component. This means that A (2 ω _c ) and A (4 ω _c ) are easily affected by noise. The ratio of A ( ω _c ) / A (3 ω _c ) can be calculated as equation (12):

A ( ω _c ) / A (3 ω _c ) depends on a and ( It is subject to environmental changes, so the ratio of A ( ω _c ) / A (3 ω _c ) is not suitable for calculation , on the formula (4) ~ (7), when When you get the following formula:

From equations (13) to (16), when , A (ω _c) and A (3 ω _c) and a related; in addition A (2 ω _c) and A (4 ω _c) and a independent, and A (2 ω _c) and A (4 ω _c) each Don't reach their maximum value (due to Time ).

From equations (14) and (16), we find , the ratio of A (4 ω _c ) of A (2 ω _c ) depends only on the amplitude of the modulated phase signal And set. If Limited to an appropriate range, with Is a one-to-one function. The condition can be calculated by adding the DC bias of the piezoelectric ceramic phase modulator on the fiber arm of TAFOI, and the spectrum of the PIFOMI output interference signal I ( t ) can be analyzed by a frequency spectrum analyzer (FSA). 2 ω _c and 4 ω _c harmonic components to get Value, and then calculate the corresponding value. Usually the spectrum component measured by the spectrum analyzer is expressed in decibels. Therefore, in the following theoretical analysis, we prefer to use To replace .

Here we use the LabView software to calculate the function value (phase) of the first class of the shell function n( n =1~4). Between 0 and 6 rads (radian).

As shown in Figure 1, the four lines are from left to right. , , , . In theory ( Among the function values, with Is a one-to-one function, Figure 2 is Correct ( The function curve. Because A (2 ω _c ), A (4 ω _c ) and , Each is proportional. If the values of A (2 ω _c ) and A (4 ω _c ) are small, it will be severely disturbed by noise during the measurement, so it is possible to reduce the accuracy.

For example, if you consider , Situation, we can get . In order to reduce the impact of background noise and improve accuracy and stability, we will set an ideal experimental procedure to be arranged during the measurement process to determine Is at ( Let the values of A (2 ω _c ) and A (4 ω _c ) be close, not because of one of the values being too small and susceptible to noise), in other words: That is what we need The ideal range.

According to formula (1), The path imbalance (PI) value Δ L of the interferometer is proportional. We first select the modulation phase signal amplitude reference value of the appropriate interfering signal. (Generally choose ,therefore ) as a reference value for measuring Δ L afterwards. Due to the reference value It is not possible to measure directly, so the reference value is obtained. The method is to fabricate a standard polarization-free fiber optic optical Michelson interferometer (PIFOMI), utilizing its measurable dual-arm fiber length imbalance (PI) value Δ L _R (requires precision scale (ruler) Make accurate measurements) as a measurement Reference value. Then, we will properly adjust the DC current and modulation current amplitude applied to the semiconductor laser so that the PIFOMI output interference signal is close. Requirements. According to the function value of the first type of bezel function calculated by the LabView software, the measured Δ L _R value can be obtained. Reference value.

Thus, when measuring the path imbalance (PI) value (indicated by Δ L _D ) of an unknown PIFOMI, we maintain a DC current on the semiconductor laser. According to △ L _D and The ratio has two arguments as follows:

(a) if The current modulation signal Δ i ₀ sin ω _c t remains unchanged, and the amplitude of the modulation phase signal of the unknown interference signal is Said that it still meets The scope of the requirements.

when When the values of A (2 ω _c ) and A (4 ω _c ) become maximum values, the amplitude of the phase signal is modulated in the output interference signal of the interferometer as seen from equation (1). It is proportional to the path imbalance (PI) value Δ L _D of the interferometer. Therefore Δ L _D can be expressed as equation (17):

(b) if or At this time, the current modulation signal will be multiplied by a coefficient h to become h Δ i ₀ sin ω _c t , and the amplitude of the modulation phase signal of the unknown interference signal is Said that it still meets Requirements. So it can be clearly The scope is (ie using the coefficient h to adjust The scope is within the required range). when From equation (1), we obtain the amplitude of the phase signal modulated in the output interference signal of the interferometer. It is proportional to the path imbalance (PI) value Δ L _D of the interferometer. Therefore Δ L _D can be expressed as equation (18):

If the length of the arms of the interferometer is L and L ( L + Δ L ), because our technique is to directly measure Δ L , it is the second harmonic component of the second and fourth modulation phase frequencies in the interfering signal. Amplitude ratio Used to determine Δ L . Obviously It is independent of the size of the L value, so when L is large, it will not affect the accuracy, which is a big advantage.

two. Analysis of the impact of environmental noise on PI measurement

As mentioned above, if the second and fourth frequencies of the output signal of the interferometer (ie, A (2 ω _c ), A (4 ω _c )) are small, the measurement accuracy may be easily affected by noise. As far as the facts are concerned, even In the ideal range, When the ambient noise is large enough, it may still affect the second and fourth components, which in turn affects accuracy. If the single-frequency phase noise from the surrounding environment is The PIFOMI interferometric signal output I ( t ) of equation (2) can be expressed as equation (19):

After expanding the equation (19) in the Fourier series, the expansion formula containing the bezel function is obtained as:

Equation (20) can further obtain frequencies close to 2 ω _c and 4 ω _c harmonic amplitudes respectively with , can be known by:

Generally speaking, noise is composed of many kinds of frequencies. Therefore, we have a reasonable hypothesis. . As far as ω _en and ω _{c are} concerned, two arguments are discussed below:

(a) if ω _en << ω _c , then the noise pair with The impact can be ignored. when When A (2 ω _c ) and A (4 ω _c ) can be reduced to in equations (21) and (22):

Therefore, from equations (23) and (24), phase noise can be found. The effect is simply multiplied by the variation , the comparison formula (14) and formula (16) are less than 1. Therefore the ratio of A (2 ω _c )/ A (4 ω _c ) is still .

(b) If ω _en << ω _c does not hold and the noise is wide-band, we can especially consider these special frequencies ω _en = mω _c ( m is an integer less than or equal to 4) and ω _en = ω _c The noise component of / n ( n is an integer greater than or equal to 2) changes the A (2 ω _c ) and A (4 ω _c ) amplitude components, which in turn affects the measurement accuracy.

The obvious frequency noise ω _en = ω _c has the greatest influence on the measurement results. When ω _en = ω _c , the noise is assumed to be ,in case ,we got (Equation 19), and the amplitudes of the ω _c and 4 ω _c harmonics of equation (19) 2 are A (2 ω _c ) and A (4 ω _c ), respectively, as modified:

Deviation between equation (25) and equation (26) . Therefore the ratio of A (2 ω _c ) / A (4 ω _c ) will vary with phase noise amplitude And change, that is, the exact measurement required The relationship no longer exists.

Combining the conclusions of (a) and (b), because the frequency of the main main environmental noise is less than 5KHz, if the carrier phase signal frequency is properly increased to meet The impact of environmental noise can be significantly reduced. On the other hand, if we can effectively reduce the induced phase noise generated by environmental noise on the interferometer (for example, placing the interferometer on the vibration isolation optical platform and properly controlling the room temperature), Improve measurement accuracy.

three. Experiments and applications

As shown in Fig. 3, in the experiment, we used a fiber-optic optical Michelson interferometer (PIFOMI) without polarization sensitivity, and used a DFB laser diode as an interferometer light source with an operating current of 80 mA. The laser light generated by the aforementioned DFB laser diode 1 is connected to the first port 20 of the three-turn optical circulator 2 to reduce optical feedback. Then, the light source is output to the 2x2 fiber coupler 3 of the third port 阜21 of the three-way optical circulator 2, and is separately split to the arms of A and B of PIFOMI, and the piezoelectric ceramic is set on the B arm. The phase modulator 5 (PZT Phase modulator) forms a double-arm with unbalanced paths, and connects the fiber to be detected 50 (Sensing fiber) to the A port (B port), and connects the reference fiber of the standard measurement to the B port. 51 (Reference fiber) (or method code). The other end of the fiber to be detected 50 is connected to the Faraday rotator mirrors (FRM), and the other end of the reference fiber 51 is connected to another Faraday rotator 61 (FRM).

Therefore, when the laser light generated by the DFB laser diode (DFB laser diode) passes through the A-arm and the B-arm, respectively, and then passes through the optical fiber 50 to be detected, the reference fiber 51, and then the respective Faraday. The rotating mirrors 60, 61 (FRM) are respectively reflected by the optical fiber 50 to be detected, the reference optical fiber 51, and the A-arm and the B-arm, and then coupled through a 2x2 fiber coupler 3 to input a three-turn optical circulator 2 The second port 21 is then outputted via the third port 22 of the three-way optical circulator 2, and then converted into an electronic signal by an optical receiver 70. Then we use FSA to analyze the signal.

We use ILX3724B as the laser diode controller 10 to control the output light source of the aforementioned DFB laser diode 1, and generate a voltage modulation signal by the function generator 11 to modulate the ILX3724B, using the ILX3724B. The voltage conversion current function (current/voltage conversion ratio is 20 mA/V) is generated, and a current modulation signal Δ i sin ω _c t is generated to modulate the DFB laser diode 1 to output an interference signal to generate a carrier phase signal. . To reduce the effects of ambient noise, we use high frequency (10 kHz) current modulation signals and place the interferometer on the isolation optics platform. The interference signal input NI6250 DAQ card is converted into a digital signal, and then input into the personal computer PC to use the FSA function in the LabView software for spectrum analysis, thereby calculating the carrier phase signal. And the path imbalance (PI) value of the interferometer Δ L . This advantage is that the PC can be directly used for further analysis and calculation of the measurement results, and the equipment required for this method is relatively inexpensive.

In order to measure the path imbalance (PI) value of the fiber optic Michelson interferometer (PIFOMI) without polarization sensitivity, it must be satisfied Conditions such that A (2 ω _c ) and A (4 ω _c ) The value of the time is the maximum value before you can get The correct value. Phase Phase changes will occur with environmental conditions (such as temperature, vibration, and sound pressure). Therefore, we must use a Triangle wave generator to drive a PZT Phase modulator to generate a phase. Phase signal ( The amplitude must be much larger than π rads ), so that all phase biased becomes To ensure that within a triangle wave signal period, there must be several times The condition; at the same time, the FSA should continuously analyze the spectrum of the output interference signal to ensure almost accurate Value The condition is that the values of A (2 ω _c ) and A (4 ω _c ) become maximum values. The low frequency of the PZT phase modulator (typically DC to 1 kHz) has a fixed response value. The output interference signal of the PIFOMI can be measured using the FSA to obtain the response of the PZT phase modulator.

Here we use a function generator to generate a 1 kHz sine wave to the PZT phase modulator (the resonant frequency of the PZT phase modulator is much larger than 1 kHz), and we use the SR770 FSA to analyze this signal. As we slowly increase the amplitude, we find that the frequency components of 1 kHz and 3 kHz are the same at 4.415V (as shown in Figure 4). From Figure 1, the phase amplitude at 3.415 V is 3.054 rads. Therefore, the low frequency response of the PZT phase modulator is 0.69 rad/V. If the input signal of the phase modulator is a triangular wave with 5V amplitude (using a triangular wave) Is to produce a linear phase change), and the frequency is 10mHz (cycle is 100 seconds), as shown in Figure 5.

In 50 seconds (or half cycle), the phase of the PZT phase modulator changes to 6.92 rads, so there are two chances to reach ( m is an integer) corresponding Case.

Again, when At 300 seconds, it is long enough for the FSA to have many opportunities (at least 12) to analyze and calculate the interference spectrum and calculate Corresponding phase value .

This program will automatically calculate the output interference signal with multiple second harmonic spectral components as the maximum value between 300 seconds, and calculate by selecting five maximum values to get five phase values. Average five phase values, we get the average phase (k means the k-th experiment (k ^th time experiment), each required 300 seconds) as the result of this measurement. By this method, we can effectively reduce the impact of environmental noise and ensure measurement accuracy (ensure the corresponding measurement The best condition).

In the experiments (A) and (B) below, we performed five independent measurements for the path imbalance (PI) values of each of the polarization-free fiber-optic Maison interferometers (PIFOMI), and the results were (k=0~5), the average Can be expressed as:

And the corresponding standard deviation S of the five measurements is:

In order to achieve high reliability and stability, we will use The value of PI is calculated and compared to the difference in fiber length measured by a precision ruler.

In addition to this, the smaller standard deviation S represents the measured value It will be more reliable. On the other hand, a larger standard deviation S indicates that the measured value is less reliable, for example, the measurement may be affected by a larger environmental noise. Therefore, we can specify a reference value of the standard deviation S (for example, 0.5mm in this experiment) as a measure of the reliability of the measurement results.

The first step is to use a standard PI to correct the polarization-free fiber optic Michaelson interferometer (PIFOMI). The PIFOMI with standard PI is only a few meters long, so it is convenient to measure the PI exact length of the fiber with a ruler (we don't need to get the full length of the arms here, we only care about PI).

We use an optical connector on the standard PIFOMI's arms for easy testing. We must first test the response of the complete optical circuit using the standard PIFOMI, that is, measure the phase signal. And the correspondence between the path imbalance (PI) value ΔL of the interferometer under the current setting conditions, and using him as a reference to measure the PI between the other to-be-detected optical fiber 50 and the reference optical fiber 51.

When measuring, in order to obtain PI, the reference fiber 51 and the fiber to be detected 50 are attached to the arms of the PIFOMI by an optical connector. The three parts of our experiment are described as follows:

(A) PIFOMI's standard PI measurement

As shown in Figure 3, a standard PIFOMI is used. Its arms (referred to as A arm length L _A and B arm length L _B ) have an unbalanced (PI) value that has been accurately measured Δ L _R = L _A - L _B = 98.6 mm (required to be accurately measured by the ruler) as a reference for the measurement. Then we will properly adjust the DC current and modulation current amplitude applied to the semiconductor laser so that the PIFOMI output interference signal is close. Requirements. (which is Reached 4.2 rads). We found that a very low distortion function generator DS360 generates a 10 kHz modulation signal input with an amplitude of 200 mV into the ILX3724B laser diode controller. When the DCX current is set to 60.5 mA with the ILX3724B, the interference signal is output. The amplitude components of A (2 ω _c ) and A (4 ω _c ) are equal, that is, . The waveform of the output interference signal is shown in Fig. 6.

The triangular wave with a period of 10mHz and 5V amplitude is used to drive the PZT phase modulator, so that the output interference signal of PIFOMI has 12 chances to reach the maximum value of the second harmonic spectrum component in 300 seconds (ie, corresponding ).

when When, as shown in Fig. 7, the second and fourth harmonic spectral components of the output interference signal are at a maximum value, here we use the SR770 FSA to analyze this signal.

Correspondingly, when At the time, as shown in FIG. 8, the first and third harmonic spectral components of the output interference signal are at a maximum value.

As mentioned above, the program automatically selects five corresponding interfering signals within 300 seconds, wherein their second harmonic spectral components reach five maximum values, and the average phase of the five phase values is calculated as . In addition, the average phase of each of the five separate measurements (300 seconds for each measurement time) is 4.1328 rads, 4.1231 rads, 4.1246 rads, 4.1253 rads, and 4.1268 rads, as shown in Table 1-1. The phase values are averaged again to get the final average . We set the standard PIFOMI measurement phase signal at The corresponding PI length is △ L _R = 98.6 mm .

It can be imagined that when the amplitude of the modulated signal is 200 mV, the response of the standard PIFOMIS is 23.89 mm/rads. Based on this response, we can inversely calculate that the corresponding lengths of the five measurement phases of the standard PIFOMIS are 98.55 mm, 98.45 mm, 98.57 mm, 98.59 mm, and 98.63 mm, respectively. The standard deviation S = 0.031 mm, which is much smaller than the reference value S = 0.5 mm of the set standard deviation S.

(B) PIFOMI accuracy measurement of some PIs

In this experiment we made five pigtailed fibers with optical connectors at both ends, the length of which is accurately measured by the ruler as L ₁ =299.8 mm , L ₂ =219.5 mm , L ₃ =400.3 mm , L ₄ =538.2 mm , and L ₅ =6785 mm . We connect these fiber optic lines to the two arms of the standard PIFOMI (path unbalance Δ L _R = L _A - L _B = 98.6 mm ) to obtain seven different PI PIFOMIs, and the PI values are each L _{PI , 1} = L ₁ + L _B - L _A = 201.2 mm , L _{PI , 2} = L ₂ + L _A - L _B = 318.1 mm , L _{PI , 3} = L ₁ + L _A - L _B = 398.4 mm , L _{PI , 4} = L ₃ + L _A - L _B = 498.9 mm , L _{PI , 5} = L ₄ + L _A - L _B = 636.8 mm , L _{PI , 6} = L ₅ + L _A - L _B = 777.1 mm and L _{PI , 7} = L ₂ + L ₅ + L _A - L _B = 996.6 mm .

Therefore, when we still set the signal modulation amplitude of 10 kHz to 200 mV, the modulation phase signal amplitude of seven different PI PIFOMIs Far greater than 4.12rads. For example, for L _{PI , 1} = 201.2 mm , we can calculate The value reaches 8.4 rads, so the output interference signal waveform has ten extreme values in one cycle, as shown in Figure 9. because Can meet the best measurement situation , we will use a coefficient h to reduce the amplitude of the modulation signal to 200 (h) mV, and we can get effective The value is close to 4.2 rads (in order to meet this condition, we can get the waveform of the output interference signal as shown in Figure 6, with six extreme values) and then we can calculate the measured value L _{PI , m , measure} ( m =1 according to equation (18) ~7). The test values are similar to the standard PI measurements of PIFOMI, and the measured values are listed in Table 1-1 and Table 1-2. The difference _between all measured values is L _{differ , m} =| L _{PI , m} - L _{PI , m , measure} | and the standard deviation S _m are also listed in Table 1.

Among all the measured values in Table 1, the maximum value L _{differ , 7} is 3.9 mm, and the maximum value S ₅ is 0.49 mm. We can clearly see that when the PI value is large (such as L _{PI , 6} = 777.1 mm , L _{PI , 7} = 996.6 mm ), the L _{difference , m} value may also be larger (for L _{PI , 6} , L _{differ , 6} = 2.7 mm , for L _{PI , 7} L _{differ , 7} = 3.9 mm ). The main reason may be caused by slight nonlinearity in the current modulation process. In addition, when the PI is less than 600mm, we can get ( )with . In addition, the PIs of a general dual-arm fiber optic interferometric sensor (using a DFB laser diode as a light source) are mostly less than 200 mm. In our experiments, when the PI value is about 200mm, we get according to this test system. with .

(C) PIFOMI's PI measurement in practical sensing systems

For the application of the actual sensing system, when constructing the dual-arm fiber optic interferometer, the length balance between the two long-length sensing fiber arms (or fixed PI) is needed, so we must develop appropriate methods. The PI value between the fiber to be detected and the standard reference fiber with a long length is measured.

In this experiment, we made a reference fiber 51 with a diameter of 6 mm, a PE coating on the outer layer, and an optical connector at both ends, with a length of about 185 m. We can repeat a fiber 50 to be inspected having the same structure as the reference fiber, the length of which is close to or equal to the reference fiber 51.

First, according to the mark, the length of the fiber to be detected 50 is cut by about 20 cm longer than the length cut by the reference fiber 51, and the P-measurement system is used (the fiber to be detected 50 and the reference fiber 51 are respectively connected to the aforementioned A-arm and B-arm). ), we measure the length of the _PI Δ L _PI between the fiber to be tested and the reference fiber. The length of the fiber 50 to be detected that is too long is equal to (Δ L _PI -98.6 mm ). Then, the excess fiber length of the fiber to be inspected 50 is cut according to the test value, and an optical connector is fabricated at the end of the fiber to be inspected 50.

It is to be noted that the manufacturing process of the optical fiber 50 to be inspected must be accurately controlled such that the length of the optical fiber 50 to be detected is equal to the reference optical fiber 51. Finally, by using a PI measurement system (the fiber to be detected and the reference fiber are each connected to the A arm and the B arm), we measure the PI value between the fiber to be detected and the reference fiber. Similar test standard programming and PIFOMIS PI measurement, but the value of △ L _PI PI from the primary measurements (during 300 seconds) directly, as an application on actual sensing system must be efficient to reduce the measurement time.

In order to verify the reliability and stability of the PI measurement system, we performed three tests in three consecutive days. We obtained three (△ L _PI -98.6 mm ) values of 4.82 mm , 4.34 mm , and 4.71 mm , respectively. The difference between the maximum and minimum values of these measured values is close to 0.48 mm, and the standard deviation s is 0.27 mm. The PI value between the fiber to be tested and the standard reference fiber (average value is 4.62 mm) is mainly caused by the error caused by the process of cutting the fiber and manufacturing the connector when manufacturing the optical connector. In the future, we can modify this. The process is to reduce the length error of the PI. These experiments confirmed that the accuracy of the PI measurement system was only slightly affected when the length of the PIFOMI fiber arm was large (up to several hundred meters). This is a big advantage of this PI measurement system.

four. in conclusion

In summary, there are two main reasons why the PI value of the dual-arm fiber interferometer (TAFOI) is an important parameter. First, the phase noise of the interferometric signal output by the dual-arm fiber interferometer (TAFOI) is proportional to PI. In some applications, a near-zero PI value is necessary to reduce phase noise.

Second, the inductive phase signal of the dual-arm fiber interferometer (TAFOI) requires linear demodulation (eg, by using a PGC demodulator with many advantages), and a fixed PI value is necessary to generate the amplitude of the fixed carrier phase signal. The accuracy of the PI values for both applications (the length of the PI may reach 200 mm for PGC modulators) must be in the millimeter class. When the fiber to be tested is made of loose tube fiber or the length of the fiber to be tested exceeds several hundred meters, the length of the original fiber length may be several decimeters, so we need a PI detection range of several decimeters and its Accuracy may be measured in millimeters. Methods for measuring larger OPDs include the use of OLCR and mmOTDR. Although OLCR has a high resolution, its OPD measurement range is about a few centimeters. On the other hand, the resolution of mmOTDR is limited to approximately 5 mm. Therefore, neither of these methods can meet the aforementioned requirements. In the present invention, we propose a method to measure PI (via the output interference signal using PIFOMI). In the theoretical analysis, we use the Bayesian function to expand the interference signal into the harmonic component of the carrier phase signal frequency, using a specific The relationship between the second and fourth harmonic components of the interfering signal develops a theory to measure PI of PIFOMI. This method is capable of measuring a few centimeters of PI and its accuracy can reach millimeters.

In our experiments, when the PI is less than 600mm, we get according to the PI measurement system. with . Generally, the PIs of a dual-arm fiber optic interferometric sensor (using a DFB laser diode as a light source) are mostly less than 200 mm. Therefore, the PI measurement system proposed in this patent can meet the requirements in both the PI test range and the accuracy of the PI measurement requirements. In addition, in the application of the actual sensing system, the experiment also confirmed that even if the length of the fiber arm is up to several hundred meters, the accuracy of the PI measuring system is only slightly affected, which is also an important advantage of the PI measuring system proposed by this patent. .

1‧‧‧DFB laser diode

2‧‧‧Three-inch optical circulator

20‧‧‧The first port阜

21‧‧‧Second connection阜

22‧‧‧ Third connection阜

3‧‧‧2x2 fiber coupler (2x2 Fiber coupler)

A‧‧‧ arm

B‧‧‧ Arm

5 (PZT phase modulator) ‧‧‧Piezoelectric ceramic phase modulator

51 (Reference fiber) ‧‧‧ reference fiber

50 (Sensing fiber) ‧‧‧ fiber to be tested

60, 61‧‧ Faraday rotator mirrors (FRM)

70‧‧‧Optical receiver

Figure 1 is the first type of Bayesian function (n = 1 ~ 4) curve, based on the amplitude of the phase signal (0~6 rads).

Figure 2 is Curve, based on adjusting the amplitude of the phase signal (0~5.135rads).

Figure 3 is a path imbalance (PI) value measurement system for a fiber optic Michaelson interferometer (PIFOMI) without polarization sensitivity.

Figure 4 shows that the piezoelectric ceramic phase modulator on the fiber arm of PIFOMI uses a 1 kHz sine wave for modulation. The interference signal spectrum of the PIFOMI output is the same for the 1 kHz and 3 kHz frequency components when the sine wave amplitude is 4.415V. The phase amplitude is 3.054 rads at 4.415 V.

Fig. 5 is a triangular wave signal input to a piezoelectric ceramic phase modulator having an amplitude of 5 V and a period of 100 seconds.

Figure 6 shows PIFOMI in phase signal The output interferes with the signal waveform. In the 100 microsecond period, the interference signal waveform has six extreme values (including maximum and minimum).

Figure 7 is at The interference signal spectrum of the PIFOMI output, the maximum of the 2nd and 4th harmonic spectral components.

Figure 8 is at The interference signal spectrum of the PIFOMI output under conditions, the maximum of the first and third harmonic spectral components.

Figure 9 shows the PIFOMI signal at the phase The output interferes with the signal waveform. In the 100 microsecond period, the interferometric signal has 10 extreme values (including maximum and minimum).

Figure 10 is a measurement result, which includes Table 1-1 and Table 1-2.

1‧‧‧DFB laser diode

2‧‧‧Three-inch optical circulator

20‧‧‧The first port阜

21‧‧‧Second connection阜

22‧‧‧ Third connection阜

3‧‧‧2x2 fiber coupler (2x2 Fiber coupler)

A‧‧‧ arm

B‧‧‧ Arm

5 (PZT Triangle wave generator) ‧‧‧Piezoelectric ceramic phase modulator

51 (Reference fiber) ‧‧‧ reference fiber

50 (Sensing fiber) ‧‧‧ fiber to be tested

60, 61‧‧ Faraday rotator mirrors (FRM)

70‧‧‧Optical receiver

Claims (12)

The measurement of the interference arm length difference of a two arms fiber optic interferometer (TAFOI) includes at least a two-arm fiber optic interferometer, two optical fibers, and a semiconductor carrier using a current carrier signal to modulate the interferometer The light source is formed by the two fiber interference arm length imbalance (PI) of the two-arm interferometer to form two interference arm length imbalance values Δ L (ie, PI value), and the interference signal output by the interferometer (interference signal) generating a carrier phase signal, and expanding the interference signal outputted by the interferometer to obtain a harmonic component of a carrier phase signal frequency including a first class of bessel function (Bessel function of the first kind), and Interfering with the signal to obtain the amplitude of the four harmonic components of the carrier phase signal, and then using the amplitude ratio of the second and fourth harmonic components of the phase angle frequency in the interference signal to calculate the two interferences arm length imbalance value △ L, this method can measure several decimeters (0.1M) the degree of imbalance fiber paths, it is possible to accuracy Mm. The measurement of the interference arm length difference of the dual-arm fiber optic interferometer (TAFOI) according to the scope of claim 1 of the patent application, wherein a current modulation signal of Δ i sin ω _c t can be used to modulate the semiconductor laser source of the interferometer , the output interference signal will generate a carrier phase signal (among them Refers to the carrier phase signal function with time t , For the amplitude of the carrier phase signal, n is the refractive index of the fiber axis, c is the speed of light, and Δ i is the current modulated signal amplitude, and Is the partial differential of the optical wave step frequency v to the current i , ω _c is the angular frequency); at the same time, the output power intensity of the semiconductor laser changes from I ₀ to I ₀ (1+ a sin ω _c t ) ( a is normalized) Light intensity modulation coefficient), a proportional to Δ i , has the output interference signal I ( t ) of the PIFOMI of the unbalanced arm, (where b is the light intensity coefficient and k is the fringe visibility of the PIFOMI interferometric signal output). According to the PGC-DCM demodulation theroy, I ( t ) can be obtained by Fourier series (Fourier series). The amplitudes of the four harmonic components of ω _c , 2 ω _c , 3 ω _c , and 4 ω _c are : among them with The function is the first class of the Bayesian function (Bessel function of the first kind), when the control When you get: then Ratio is only dependent on the amplitude of the modulated phase signal It may be (and a do not care). when Limited to (among them Within the appropriate range, with Is a one-to-one function; and control The method can be completed by adding the DC bias of the piezoelectric ceramic phase modulator on the fiber arm of TAFOI, and analyzing the spectrum of the PIFOMI output interference signal I ( t ) by a frequency spectrum analyzer (FSA). 2 ω _c and 4 ω _c harmonic components to get Value, and then calculate the corresponding value. Measurement of the interference arm length difference of the dual-arm fiber optic interferometer (TAFOI) according to item 2 of the patent application scope, wherein the harmonic components of 2 ω _c and 4 ω _c are obtained Value Replaced to facilitate calculations. Measurement of the interference arm length difference according to the two-arm fiber optic interferometer (TAFOI) described in the second paragraph of the patent application, in order to reduce the influence of background noise and improve accuracy and stability, it will be in the experimental procedure of measurement determine Is at Within the range (ie, A (2 ω _c ) and A (4 ω _c ) have close values, and will not be affected by noise due to one of them being too small), in other words: It is the ideal range. Measurement of the interference arm length difference of the dual-arm fiber optic interferometer (TAFOI) according to item 4 of the patent application scope, wherein the path imbalance (PI) value of the fiber optic Michaelson interferometer (PIFOMI) for measuring the polarization-free sensitivity Must meet Conditions such that A (2 ω _c ) and A (4 ω _c ) The value of the time is the maximum value before you can get Correct value; however, phase The phase change will occur with environmental conditions (such as temperature, vibration, and sound pressure). Therefore, it is necessary to drive the piezoelectric ceramic phase modulator (PZT Phase modulator) with a periodic voltage signal to generate a phase signal. (among them The amplitude must be greater than π rads ) so that all phase biased becomes To ensure that within the voltage signal period T , it must be reached several times For the ideal voltage signal, for example, a triangle wave can be used; at the same time, the FSA should continuously analyze the spectrum of the output interference signal to ensure almost accurate Value The condition is that the values of A (2 ω _c ) and A (4 ω _c ) are the maximum values. The measurement of the interference arm length difference of the dual-arm fiber optic interferometer (TAFOI) according to item 5 of the patent application scope, wherein a plurality of voltage signal periods T can be selected The second harmonic spectral component is the maximum output interference signal to calculate the plurality of output interference signals to obtain a plurality of phase values, and averaged to obtain an average phase By using the average phase To replace Calculating the interference arm length imbalance value Δ L can effectively reduce the influence of environmental noise and ensure measurement accuracy. Measurement of the interference arm length difference of the dual-arm fiber optic interferometer (TAFOI) according to item 6 of the patent application scope, wherein the interference signal is selected to be plural The second harmonic component of the time is the maximum output interference signal to calculate the average phase When choosing 5 The second harmonic spectral component is the maximum output interference signal to calculate the average phase When you get a fairly accurate measurement. A method for measuring a difference in interference arm length of a dual-arm fiber optic interferometer (TAFOI) according to claim 1 of the patent application, wherein a piezoelectric ceramic phase modulator is used to generate a phase signal to modulate the phase signal Condition, when The values of A (2 ω _c ) and A (4 ω _c ) are the maximum values. A dual-arm fiber optic interferometer (TAFOI) measuring the difference in the length of the interfering arm, comprising at least: a fiber optic micson interferometer (PIFOMI) without polarization susceptibility to measure the PI value, and the aforementioned optical fiber optics of the non-polarization susceptibility The interferometer (PIFOMI) consists of two Faraday rotator mirrors (FRM) that eliminate polarization fading; one of the arms of the aforementioned polarization-free fiber-optic Maison interferometer (PIFOMI) Piezoelectric ceramic phase modulator (PZT Phase modulator), the interference arm length imbalance value Δ L of the interferometer, by applying a current carrier signal to modulate the semiconductor laser source of the interferometer and interfering with the interferometer output The signal generates a carrier phase signal, and the interference signal outputted by the interferometer is expanded to obtain a harmonic component of a carrier phase signal frequency including a first type of Bessel function of the first kind, and the interference signal is used to Obtaining the amplitude of the four harmonic components of the carrier phase signal, adjusting the phase difference by the piezoelectric ceramic, and extracting the complex array in the interference signal The amplitude ratio of the second and fourth harmonic components of the modulation phase angular frequency is the maximum value to calculate the measured value of the length difference of the complex array interference arm (ie, the PI value), and averaged to serve as the interference arm length difference. The measured value, using the average measured value of the interference arm length difference, can effectively reduce the influence of environmental noise and ensure the accuracy of the measured PI value. The measurement of the interference arm length difference of the dual-arm fiber optic interferometer (TAFOI) according to claim 9 of the patent application scope, wherein a piezoelectric ceramic phase modulator (PZT Phase modulator) provided by one of the PIFOMI arms is used to modulate the difference The phase signal of the arm. Measurement of the interference arm length difference according to the dual-arm fiber optic interferometer (TAFOI) described in claim 9 of the patent application, wherein the standard non-polarization-sensitive fiber optic optical interferometer (PIFOMI) has an unbalanced path The difference in fiber length is measured by an accurate technique (using a precision scale) with a reference value Δ L _{R of} the interference arm length imbalance. Measure the interference arm length difference of the dual-arm fiber interferometer (TAFOI) according to the scope of claim 9 and measure the two fiber-optic interference arms using a standard polarization-free fiber optic optical Michelson interferometer (PIFOMI) Length imbalance value Δ L _D , determined in the experimental procedure of the measurement Is at Within the scope of in Ideal range, where with For the aforementioned first class of shell color functions, Is the amplitude of the carrier phase signal. The experimental procedure in the measurement is arranged as follows: (a) when The current modulation signal Δ i ₀ sin ω _c t remains unchanged, modulating the phase signal amplitude Still consistent Under the condition of the range; △ L _D can be The relationship is obtained, where Δ L _R is the reference value of the interference arm length imbalance, Δ i ₀ is the current modulation signal amplitude, ω _c is the angular frequency, and t is the time. The amplitude of the phase signal generated by the current interferometer through current modulation, The phase signal amplitude generated by the current modulation of the fiber interferometer to be tested; (b) or The current modulation signal is multiplied by a coefficient h to become h Δ i ₀ sin ω _c t , so that the amplitude of the modulation phase signal is Still consistent Range; at this time △ L _D can be The relationship is obtained.