High-resolution FPI spectrum demodulation method

Abstract

The invention discloses a high-resolution FPI spectrum demodulation method, and relates to the field of optical fiber sensing. Comprising the following steps: acquiring an FPI interference spectrum, and performing pretreatment, including spectrum standardization, wave number conversion and wave number domain interpolation, on the acquired spectrum; performing FFT (Fast Fourier Transform) on the interpolated spectrum to obtain an amplitude spectrum and a phase spectrum; roughly estimating the F-P cavity length through a corrected amplitude spectrum Buneman algorithm; and the F-P cavity length is accurately calculated in combination with the phase spectrum. The FPI sensor demodulated according to the method can realize real-time monitoring of various environmental parameters including vibration, pressure and temperature, and compared with other demodulation methods, the method provided by the invention has the characteristics of high resolution, small calculation amount and large dynamic range, and has stable performance under the condition of low signal-to-noise ratio.

Description

Technical Field

[0001] The present invention relates to the field of optical fiber sensing technology, and more specifically, to a high-resolution FPI spectrum demodulation method. Background Art

[0002] Due to the characteristics of fiber optic sensors such as anti-electromagnetic interference, fast response, and small size, fiber optic sensing technology is very suitable for monitoring various environmental parameters including vibration, pressure, and temperature. After years of development and application, fiber optic sensing technology has covered a variety of application fields, such as structural health monitoring, aircraft status monitoring, oil and gas pipeline monitoring, etc.

[0003] Compared with other sensors with different measurement principles, interferometric fiber optic sensors have become a research hotspot in the field of fiber optic sensing due to their high sensitivity and strong multiplexing. Fabry-Perot interferometer (FPI) fiber optic sensor is an optical sensor device that measures changes in environmental physical quantities based on the principle of multi-beam interference. The interference spectrum of a single FPI sensor is cosine-shaped, with a single frequency component and a variety of demodulation methods. The current mainstream demodulation method is based on the phase demodulation principle. The change in the length of the Fabry-Perot (FP) cavity in the FPI sensor is demodulated according to the phase information of the spectrum, thereby realizing the sensing of the environment around the sensor. The methods include spectral peak tracking method, phase generation carrier method, cross-correlation demodulation method, fast Fourier transform (FFT) demodulation method, etc. This type of demodulation method has the advantages of high resolution and good stability, but the mode hopping problem caused by phase ambiguity limits the dynamic range of demodulation.

[0004] The Fourier transform demodulation method collects the FPI interference spectrum in the wavenumber domain and performs Fourier transform, searches for the peak of the Fourier spectrum to find the frequency of the interference spectrum, and then solves the cavity length. There are two types of demodulation methods. One is to calculate the sensor cavity length directly based on the frequency estimation method, and the other is to calculate the cavity length based on the frequency and phase information of the Fourier spectrum. The former has simple steps and fast demodulation speed, but the accuracy and resolution are not high; although the latter has high resolution and robustness, in order to solve the mode hopping problem in the demodulation process, the algorithm complexity is increased, which is not conducive to real-time processing. Summary of the invention

[0005] In view of the defects of the prior art, the purpose of the present invention is to solve the problem that the current FPI sensor demodulation algorithm based on phase demodulation cannot take into account the resolution, dynamic range and demodulation rate at the same time.

[0006] To achieve the above technical objectives, the present invention proposes a high-resolution FP cavity length demodulation method, comprising the following steps:

[0007] Collecting the interference spectrum of the FPI sensor and performing standardization processing, wherein the interference spectrum carries information of the environmental parameters to be measured;

[0008] The standardized interference spectrum is subjected to wavenumber conversion and wavenumber domain interpolation processing to obtain a uniformly discrete wavenumber spectrum;

[0009] The spectral function form of the wavenumber spectrum is transformed and FFT is performed to obtain the spectrum amplitude spectrum and phase spectrum;

[0010] Based on the frequency spectrum amplitude spectrum obtained by FFT transformation, the amplitude spectrum peak index and the estimated value of the FP cavity length are determined;

[0011] Based on the frequency spectrum phase spectrum obtained by FFT transformation, the accurate value of the FP cavity length is calculated according to the amplitude spectrum peak index and the estimated value of the FP cavity length. The change of the cavity length reflects the change of the surrounding environment of the FPI sensor.

[0012] Furthermore, the step of spectrum standardization processing includes:

[0013] Remove the light source envelope from the interferometric spectrum of the FPI sensor;

[0014] Remove the DC component from the interference spectrum of the FPI sensor;

[0015] The amplitude of the interference spectrum of the FPI sensor is normalized.

[0016] Furthermore, the wavenumber-converted spectrum is linearly interpolated to obtain a uniformly discrete wavenumber spectrum.

[0017] Furthermore, the spectral function form of the transformed wavenumber spectrum refers to converting the spectrum from a trigonometric function form to an exponential form.

[0018] Furthermore, the method of determining the amplitude spectrum peak index and the estimated value of the FP cavity length based on the frequency spectrum amplitude spectrum obtained by FFT transformation includes:

[0019] Obtain the frequency spectrum amplitude spectrum according to FFT transformation, and determine the index of the amplitude spectrum peak;

[0020] The Buneman frequency estimation algorithm is used to determine an estimate of the actual location of the peak;

[0021] Determining a corrected estimate of the actual position of the peak based on the index and the estimate;

[0022] The FP cavity length is estimated based on the corrected estimate of the actual position of the peak.

[0023] Furthermore, the determining of the corrected estimated value of the actual position of the peak value according to the index and the estimated value includes:

[0024] Determine the difference between the peak index of the amplitude spectrum and the estimated value of its actual position. When the difference is within the threshold δ, the estimated value of the actual position No need to correct, directly use it as the corrected estimate

[0025] When the difference exceeds the threshold range, the spectrum is frequency shifted so that the difference between the new amplitude spectrum peak index and the estimated value of its actual position after the frequency shift is within the threshold δ range. Subtract the frequency shift rδ and use it as the corrected estimate Where r is the frequency direction factor and δ is the threshold of the difference between the amplitude spectrum peak index and its actual position.

[0026] Furthermore, the frequency spectrum phase spectrum obtained based on FFT transformation, according to the amplitude spectrum peak index and the estimated value of the FP cavity length, calculates the exact value of the FP cavity length, including:

[0027] Determine the number of cycles: During the first demodulation, determine the relative phase of the corresponding frequency component according to the index at the peak of the amplitude spectrum, and calculate the number of 2π cycles of the absolute phase and relative phase difference of the frequency component in combination with the estimated value of the FP cavity length; for subsequent demodulations, compare the amplitude spectrum peak index obtained this time with that obtained in the previous demodulation, determine the compensation phase value based on the comparison result, and determine the number of cycles in combination with the relationship between the relative phase obtained after the current phase compensation and that obtained in the previous demodulation;

[0028] Based on the amplitude spectrum peak index, relative phase and number of cycles, the exact value of the FP cavity length is calculated.

[0029] Furthermore, the compensation phase value is used to compensate for the change in the phase of the corresponding frequency component when the spectrum amplitude spectrum peak index changes. The formula of the compensation phase value is as follows:

[0030]

[0031] Among them, p b and p a is the peak index of the amplitude spectrum obtained this time and last time, is the compensation phase.

[0032] Furthermore, the number of cycles is used to unwind the phase of the frequency component corresponding to the spectrum peak index of the spectrum amplitude spectrum. The formula for determining the number of cycles is as follows, combining the relationship between the current compensation phase and the relative phase obtained by the previous demodulation:

[0033]

[0034] Among them, a b and a a is the number of cycles obtained this time and last time, and is the relative phase corresponding to the peak index of the amplitude spectrum obtained this time and last time, is the compensation phase.

[0035] The number of cycles is always an integer. When the FP cavity length changes within a certain range, the number of cycles remains unchanged, and the relative phase changes accordingly. When the FP cavity length changes more than a certain range, both the relative phase and the number of cycles change accordingly.

[0036] Furthermore, the exact value of the FP cavity length is calculated based on the amplitude spectrum peak index, relative phase and number of cycles, and the formula is as follows:

[0037]

[0038] Among them, l e is the exact value of the FP cavity length, k0 is the wavenumber coordinate of the minimum wavenumber spectrum, k1 is the wavenumber coordinate of the maximum wavenumber spectrum, p is the peak index of the amplitude spectrum, is the relative phase of the frequency component corresponding to the peak index of the amplitude spectrum, is the number of cycles, [.] is the rounding symbol.

[0039] Compared with other prior arts, the present invention has the following beneficial effects:

[0040] The present invention aims at the defects of the prior art, corrects the general frequency estimation algorithm and solves the mode hopping problem caused by phase ambiguity in the general phase demodulation algorithm, and greatly expands the dynamic range of demodulation while ensuring high demodulation resolution and accuracy. In addition, compared with other methods, the demodulation method of the present invention has low algorithm complexity and high portability, and can realize real-time demodulation of sensors in software and hardware at the same time. Therefore, the present invention can provide a practical technical solution for high-speed, high-resolution, and large-range optical fiber sensing monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a flow chart of the high-resolution FPI spectral demodulation method proposed in the present invention.

[0042] Figure 2 The present invention provides a flow chart of the method for correcting frequency estimation.

[0043] Figure 3 A flow chart of iteratively determining parameter values ​​required to solve the FP cavity length proposed by the present invention.

[0044] Figure 4 This is the simulated spectrum after standardization provided by the present invention.

[0045] Figure 5This is the simulated frequency spectrum amplitude spectrum after FFT transformation provided by the present invention.

[0046] Figure 6 To simulate the resolution of demodulating the FP cavity length by the demodulation method of the present invention.

[0047] Figure 7 The demodulation method of the present invention is simulated to compare the accuracy with the general frequency estimation algorithm and phase estimation algorithm.

[0048] Figure 8 The invention provides an optical path acquisition system for vibration experiments.

[0049] Fig. 9 This is the cavity length fluctuation of the FPI vibration sensor in static state.

[0050] Fig.10 This is the cavity length fluctuation histogram of the FPI vibration sensor in static state.

[0051] Fig.11 is the relationship between the FP cavity length of the FPI vibration sensor and the set acceleration. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical scheme and advantages of the present invention clearer, the content of the present invention will be described in detail and completely in conjunction with the accompanying drawings and embodiments. Obviously, the embodiments described are only representative embodiments, which are only part of the embodiments of the present invention, not all of the embodiments. The selected embodiments are used to illustrate the present invention, but cannot be used to limit the present invention. In addition, those skilled in the art may combine or combine different embodiments of the present invention or technical features of different embodiments without conflict.

[0053] The present invention proposes a high-resolution FPI spectrum demodulation method, comprising the following steps: Figure 1 As shown:

[0054] S1, collecting the interference spectrum of FPI, and performing standardization processing on the interference spectrum.

[0055] In a specific implementation of the present invention, the interference spectrum of FPI is collected. Due to the low reflectivity of the end faces at both ends of the FP cavity, the multi-beam interference in the cavity can be simplified to low-fineness double-beam interference. The spectrum is similar to a cosine function. The relationship between the light source intensity and the output light intensity after FPI reflection interference is expressed as:

[0056]

[0057] Where I1(λ) is the interference light intensity spectrum formed by the light from the light source after being reflected by the FPI, I0(λ) is the light source spectrum, λ is the wavelength, γ is the interference fringe visibility, l is the FP cavity length, It is the initial phase of the spectrum, which is mainly affected by the optical path difference of the double reflection surfaces. u represents the refractive index of the medium in the FP cavity. Generally, the medium is air, and u=1.

[0058] The obtained FPI interference spectrum is standardized to make the spectral distribution more similar to the cosine function. Optionally, a set of light source spectra are collected and saved in advance, and the collected spectrum data is divided by the light source spectrum data to obtain the FPI interference spectrum with the light source envelope removed. Formula (1) is rewritten as:

[0059]

[0060] Where I2(λ) is the interference spectrum after removing the light source envelope.

[0061] The spectral data after de-envelopment is averaged, and the FPI interference spectrum without DC is obtained after the average value is subtracted from the spectral data. Formula (2) is rewritten as:

[0062]

[0063] Where I3(λ) is the interference spectrum after DC removal.

[0064] Take the maximum value of the spectral data after removing the DC, divide the spectral data by the maximum value, and get the normalized FPI interference spectrum, which is expressed as:

[0065]

[0066] Among them, I(λ) is the normalized and finally standardized FPI interference spectrum.

[0067] S2, perform wavenumber transformation and wavenumber domain interpolation on the standardized spectrum.

[0068] In a specific implementation of the present invention, according to the correspondence between wavenumber and wavelength, the interference spectrum data after standardization is converted from the wavelength domain to the wavenumber domain, and the FPI interference spectrum in the wavenumber domain (referred to as wavenumber spectrum) is expressed by the formula:

[0069]

[0070] Wherein, k is the wave number, k = 2π / λ.

[0071] Since the wavenumber intervals obtained by the transformation are not uniform, it is not convenient to perform FFT conversion. The wavenumber spectrum is interpolated using a linear interpolation method with good portability to obtain a uniform discrete wavenumber spectrum. For simplicity, u=1 is omitted and the formula is expressed as:

[0072]

[0073] Among them, I(n) is a uniformly discrete wavenumber spectrum, n is the ordinal number of the interpolation point, N is the total number of interpolation points, k0 is the minimum wavenumber coordinate, and Δk is the distance between the two ends of the spectral wavenumber coordinate.

[0074] S3, transform the spectrum function form and perform FFT transformation to obtain the spectrum amplitude spectrum and phase spectrum.

[0075] In a specific implementation of the present invention, after the interpolation process is completed, the spectral function form is first transformed to convert the wavenumber spectral data from a trigonometric function form to an exponential form.

[0076] In this embodiment, the wave number spectrum data is subjected to Hilbert transformation to convert the wave number spectrum data from cosine form to sine form, and equation (6) is transformed into:

[0077]

[0078] Furthermore, according to the Euler formula, combined with equations (6) and (7), the spectral data is converted from the sine trigonometric function form to the exponential analytical form, which is expressed as follows:

[0079]

[0080] Here, i represents the imaginary unit.

[0081] Then, the spectrum analysis data is transformed by FFT, and the spectrum spectrum after transformation is expressed by the formula:

[0082]

[0083] Where ξ is the abscissa of the FFT spectrum.

[0084] According to the FFT transformation results, the frequency spectrum amplitude spectrum and phase spectrum are obtained.

[0085] S4, determining an estimated value of the FP cavity length based on the frequency spectrum amplitude spectrum obtained by FFT transformation in step S3.

[0086] In a specific implementation of the present invention, the actual position of the peak of the spectrum amplitude spectrum is denoted as f, and the frequency of the corresponding FPI interference spectrum is expressed by the formula:

[0087]

[0088] According to formula (10), formula (9) can be rewritten as:

[0089]

[0090] The peak position f of the amplitude spectrum may not be an integer. It is recorded as being between m and m+1, and the corresponding amplitudes F(m) and F(m+1) are determined. The modulus is obtained as follows:

[0091]

[0092] Solving equation (12) together, we can obtain the estimated value of the peak position of the spectrum amplitude spectrum:

[0093]

[0094] The above formula (13) is the Buneman frequency estimation formula. The estimation of the FPI interference spectrum frequency by formula (12) has limitations. When f is close to an integer, the estimation error is large. Therefore, this frequency estimation method is modified, as follows: Figure 2 As shown, let p be the peak index of the amplitude spectrum, p is an integer, and calculate the difference between the peak index of the amplitude spectrum and the estimated value of its true position, denoted as d, d is expressed by the formula:

[0095]

[0096] Obviously, d<1.

[0097] The δ parameter is set as a basis for judging the distance between the index and the actual position, and optionally, δ = 1 / 3. The spectrum is processed differently according to δ.

[0098] When d>δ, the true frequency is located in the center area of ​​two adjacent frequency points, and the estimated value determined by formula (13) is The revised estimate

[0099] When d≤δ, the true frequency is close to a certain frequency point, and the original spectrum is appropriately frequency shifted so that the frequency of the new spectrum is located in the central area of ​​two adjacent frequency points. The corrected peak position estimate is then obtained through the Buneman frequency estimation algorithm.

[0100] Specifically, the frequency direction factor r is determined and expressed as:

[0101]

[0102] In the above, r=1 indicates a positive direction, and r=-1 indicates a negative direction.

[0103] In addition, the frequency shift factor is determined based on the same basis as the distance between the index and the actual position. The frequency shift factor is set to 1 / 3 so that after the spectrum is shifted, the frequency of the new spectrum is located in the center area of ​​two adjacent frequency points.

[0104] Multiply the original spectrum data expressed by formula (8) by the frequency shift factor, and the spectrum after frequency shift is expressed by the formula:

[0105]

[0106] Repeat the Buneman frequency estimation steps to obtain the estimated value after frequency shift compensation The corrected peak position estimate is obtained by subtracting the frequency shift rδ. The formula is:

[0107]

[0108] Finally, the rough estimate of the FP cavity length is calculated according to formula (10), which is expressed as:

[0109]

[0110] S5, based on the frequency spectrum phase spectrum obtained by FFT transformation in step S3, and according to the rough estimation value of the FP cavity length in step S4, calculate the precise value of the FP cavity length.

[0111] According to formula (11), the frequency spectrum phase spectrum is expressed as:

[0112]

[0113] When ξ=f, the phase corresponding to f at the peak of the spectrum amplitude spectrum is expressed by the formula:

[0114]

[0115] From formula (19), we can see that the spectrum phase spectrum is linear. Therefore, according to formula (19), Φ f The phase Φ with the adjacent spectrum peak point p The relationship is expressed by the formula:

[0116] φ f =Φ p +(-π)·(fp)#(21)

[0117] Since the FFT phase spectrum has phase winding, the absolute phase and relative phase of each frequency point differ by an integer multiple of 2π cycles, so Φ p It can be expressed as:

[0118]

[0119] in, is the corresponding relative phase on the phase spectrum, Φ p is the corresponding absolute phase on the phase spectrum, and a is the number of 2π cycles between the absolute phase and the relative phase.

[0120] By combining equations (18), (20), (21) and (22), we can obtain the estimated value of a, which can be expressed as:

[0121]

[0122] Where k1 is the wavenumber coordinate with the maximum wavenumber spectrum, is the initial phase of the spectrum, p is the spectrum peak index, is the relative phase corresponding to the spectrum peak index of the spectrum amplitude.

[0123] Since the actual a is an integer, the estimated value of a is rounded. Substitute the rounded estimated value into formula (23) again to calculate the exact value of the FP cavity length, which is expressed as:

[0124]

[0125] Among them, [.] indicates rounding, preferably rounding down.

[0126] The FP cavity length result obtained by solving equation (24) has high resolution and accuracy, but there will be phase ambiguity caused by spectral noise, and the solved a will have a jump problem. Therefore, based on it, the result of the previous demodulation is used to iteratively determine the parameter value required for solving the FP cavity length this time to avoid phase ambiguity. The process is as follows: Figure 3 shown.

[0127] During the first demodulation, the amplitude spectrum peak index and the estimated value of the FP cavity length are determined based on the spectrum amplitude spectrum obtained by FFT transformation. In subsequent demodulations, only the amplitude spectrum peak index needs to be determined. This processing method greatly reduces the execution time of the algorithm.

[0128] Specifically, during the first demodulation, based on the frequency spectrum amplitude spectrum obtained by FFT transformation and the estimated value of the FP cavity length, the number of 2π cycles of the difference between the absolute phase and the relative phase is calculated by formula (23).

[0129] In the subsequent demodulation, the amplitude spectrum peak indexes obtained by the two demodulations are compared to determine whether the peak position has changed. If it has changed, the phase change is compensated according to formula (21). The compensation phase is expressed by the formula:

[0130]

[0131] Among them, p b and p a is the peak index of the amplitude spectrum obtained twice before and after, is the compensation phase.

[0132] In the subsequent demodulation, the relative phases corresponding to the amplitude spectrum peak indices obtained by the two demodulations are compared, and the phase is unwrapped to obtain the 2π cycle number of the difference between the absolute phase and the relative phase, which is expressed as:

[0133]

[0134] Among them, a b and a a is the number of cycles obtained this time and last time, and It is the relative phase corresponding to the peak index of the amplitude spectrum obtained this time and last time.

[0135] Therefore, in the subsequent demodulation, according to the obtained amplitude value peak index p, relative phase and the number of cycles, the exact value of the FP cavity length is calculated by equation (24).

[0136] Embodiment 1: Demodulate the simulated spectrum according to the demodulation method proposed in the present invention. Simulate and construct the FPI interference spectrum, and add additive white noise as the spectrum noise. The spectrum data length is 256.

[0137] The FP cavity length is fixed to 550 μm, the spectral signal-to-noise ratio is 25 dB, and the interference spectrum of the FPI is demodulated according to the demodulation method proposed in the present invention.

[0138] Specifically, according to step S1, the spectrum is standardized. The processed spectrum is shown in FIG. Figure 4 shown.

[0139] Further, according to step S2, the spectrum after the normalization process is subjected to wave number conversion and wave number domain interpolation process. The length of the spectrum data after the interpolation process is 512.

[0140] Further, according to step S3, the interpolated wavenumber spectrum is transformed into a spectrum function form and FFT transformation is performed. The spectrum amplitude spectrum after FFT transformation is shown in the following example: Figure 5 shown.

[0141] Further, according to step S4, based on the frequency spectrum amplitude spectrum obtained by FFT transformation, during the first demodulation, the estimated value of the FP cavity length is determined, and during subsequent demodulation, the amplitude spectrum peak index is determined.

[0142] Further, according to step S5, based on the frequency spectrum phase spectrum obtained by FFT transformation, the precise value of the FP cavity length is calculated according to the estimated value of the FP cavity length obtained by the first demodulation or the amplitude spectrum peak index obtained by subsequent demodulation.

[0143] The FP cavity length is fixed to 550 μm, the spectral signal-to-noise ratio range is 50-10 dB, the interval is 5 dB, the spectrum is demodulated 10,000 times, the noise added each time is random, and the mean square error of the demodulation results of 10,000 times is used to represent the resolution. The demodulation accuracy of the present invention under different spectral signal-to-noise ratios is compared. Figure 6 As shown. Figure 6It can be seen that the resolution of demodulation is negatively correlated with the spectral signal-to-noise ratio. When the signal-to-noise ratio is greater than 40 dB, the resolution does not change much with the increase of the signal-to-noise ratio. When the spectral quality is high, the resolution of demodulation can reach the level of hundreds of picometers, and when the spectral quality is low, the resolution can also be maintained at the nanometer level at 15 dB. Therefore, the demodulation method proposed in the present invention has a very high resolution and has stable performance under low signal-to-noise ratio conditions.

[0144] The spectral signal-to-noise ratio is fixed at 30 dB, the FP cavity length varies from 300 to 500 μm, with an interval of 0.1 μm, and the maximum error between the demodulation cavity length and the set cavity length is used to represent the accuracy. The demodulation accuracy of the present invention is compared with that of the general Buneman frequency estimation algorithm and the general full phase demodulation algorithm. Figure 7 As shown. Figure 7 It can be seen that the general Buneman frequency estimation algorithm has low accuracy, and although the general phase demodulation algorithm has high accuracy, there is a problem of demodulation result jumps caused by phase ambiguity, and the demodulation range is limited. In comparison, the demodulation method proposed in the present invention has a large dynamic range and the same high accuracy as phase demodulation.

[0145] Example 2: Practically apply the demodulation method proposed in the present invention to demodulate the FPI vibration sensing spectrum to obtain corresponding acceleration information.

[0146] Specifically, an FPI vibration sensor is prepared, and the elastic structure of the sensor enables it to sense environmental vibration. Figure 8 The optical path acquisition system shown includes a broadband light source, a circulator, and a grating spectrometer. The broadband light source light carries the interference information of the FP cavity after being reflected by the FPI sensor. After passing through the grating spectrometer, an interference spectrum is formed. The interference spectrum is demodulated according to the steps S1-S5 described above to obtain the FP cavity length information, corresponding to the acceleration of the vibration.

[0147] The FPI vibration sensor was fixed on the vibration table. The demodulation system sampling rate was 1kHz. The cavity length change of the FP cavity was monitored within 60s in a static state. The cavity length fluctuation was recorded as follows: Fig. 9 As shown in the figure, the histogram of cavity length fluctuation distribution is as follows Fig.10 After calculation, the mean square error of the measured data is 0.27nm, and the stability is ±1nm.

[0148] The vibration frequency of the vibration table is set to 500 Hz, the acceleration range is set to 5g-50g, and the collected FPI interference spectrum is demodulated at every 5g interval. The relationship between the relative change of the FP cavity length and the acceleration is as follows: Fig.11As shown in the results, it can be seen that the FP cavity length is linearly related to the acceleration of external vibration. Based on this relationship, the acceleration can be solved. After calculation, the maximum difference between the measured acceleration and the set acceleration is 0.25g. Therefore, the algorithm proposed in the present invention can achieve high-resolution and high-precision demodulation in practical applications.

[0149] Obviously, the above is only a representative embodiment of the present invention, and the present invention is not limited to the above embodiment. Any deformation formed by simply deriving, modifying, and improving the contents disclosed in the present invention without performing creative work should be regarded as within the scope of protection of the present invention.

Claims

1. A high-resolution FPI spectrum demodulation method, characterized in that: include: Collecting the interference spectrum of the FPI sensor and performing standardization processing, wherein the interference spectrum carries information of the environmental parameters to be measured; The standardized interference spectrum is subjected to wavenumber conversion and wavenumber domain interpolation processing to obtain a uniformly discrete wavenumber spectrum; The spectral function form of the wavenumber spectrum is transformed and FFT is performed to obtain the spectrum amplitude spectrum and phase spectrum; Based on the frequency spectrum amplitude spectrum obtained by FFT transformation, the amplitude spectrum peak index and the estimated value of the FP cavity length are determined; Based on the frequency spectrum phase spectrum obtained by FFT transformation, the accurate value of the FP cavity length is calculated according to the amplitude spectrum peak index and the estimated value of the FP cavity length. The change of the cavity length reflects the change of the surrounding environment of the FPI sensor.

2. The high-resolution FPI spectrum demodulation method according to claim 1, characterized in that: The steps of spectral standardization include: Remove the light source envelope from the interferometric spectrum of the FPI sensor; Remove the DC component from the interference spectrum of the FPI sensor; The amplitude of the interference spectrum of the FPI sensor is normalized.

3. The high-resolution FPI spectrum demodulation method according to claim 1, characterized in that: The wavenumber-converted spectrum is then linearly interpolated to obtain a uniformly discrete wavenumber spectrum.

4. The high-resolution FPI spectrum demodulation method according to claim 1, characterized in that: The spectral function form of the transformed wavenumber spectrum refers to converting the spectrum from a trigonometric function form to an exponential form.

5. The high-resolution FPI spectrum demodulation method according to claim 1, characterized in that: The frequency spectrum amplitude spectrum obtained based on FFT transformation determines the amplitude spectrum peak index and the estimated value of the FP cavity length, and the FP cavity includes: Obtain the frequency spectrum amplitude spectrum according to FFT transformation, and determine the index of the amplitude spectrum peak; The Buneman frequency estimation algorithm is used to determine an estimate of the actual location of the peak; Determining a corrected estimate of the actual position of the peak based on the index and the estimate; The FP cavity length is estimated based on the corrected estimate of the actual position of the peak.

6. The high-resolution FPI spectrum demodulation method according to claim 5, characterized in that: The step of determining the corrected estimated value of the actual position of the peak value according to the index and the estimated value comprises: Determine the difference between the peak index of the amplitude spectrum and the estimated value of its actual position. When the difference is within the threshold δ, the estimated value of the actual position No need to correct, directly use it as the corrected estimate When the difference exceeds the threshold range, the spectrum is frequency shifted so that the difference between the new amplitude spectrum peak index and the estimated value of its actual position after the frequency shift is within the threshold δ range. Subtract the frequency shift rδ and use it as the corrected estimate Where r is the frequency direction factor and δ is the threshold of the difference between the amplitude spectrum peak index and its actual position.

7. The high-resolution FPI spectrum demodulation method according to claim 1, characterized in that: The frequency spectrum phase spectrum obtained based on FFT transformation, according to the amplitude spectrum peak index and the estimated value of the FP cavity length, calculates the exact value of the FP cavity length FP cavity, including: Determine the number of cycles: During the first demodulation, determine the relative phase of the corresponding frequency component according to the index at the peak of the amplitude spectrum, and calculate the number of 2π cycles of the absolute phase and relative phase difference of the frequency component in combination with the estimated value of the FP cavity length; for subsequent demodulations, compare the amplitude spectrum peak index obtained in this demodulation with that obtained in the previous demodulation, determine the compensation phase value according to the comparison result, and determine the number of cycles in combination with the relationship between the relative phase obtained after the current phase compensation and that obtained in the previous demodulation; the number of cycles is an integer; Based on the amplitude spectrum peak index, relative phase and number of cycles, the exact value of the FP cavity length is calculated.

8. The high-resolution FPI spectrum demodulation method according to claim 7, characterized in that: The compensation phase value is used to compensate for the change in the phase of the corresponding frequency component when the spectrum amplitude spectrum peak index changes. The formula of the compensation phase value is as follows: Among them, p b and p a is the peak index of the amplitude spectrum obtained this time and last time, is the compensation phase.

9. The high-resolution FPI spectrum demodulation method according to claim 7, characterized in that: The number of cycles is used to unwind the phase of the frequency component corresponding to the spectrum peak index of the spectrum amplitude spectrum. The formula for determining the number of cycles based on the relationship between the current compensation phase and the relative phase obtained by the previous demodulation is as follows: Among them, a b and a a is the number of cycles obtained this time and last time, and is the relative phase corresponding to the peak index of the amplitude spectrum obtained this time and last time, is the compensation phase.

10. The high-resolution FPI spectrum demodulation method according to claim 7, characterized in that: The exact value of the FP cavity length is calculated based on the amplitude spectrum peak index, relative phase and number of cycles, and the formula is as follows: Among them, l e is the exact value of the FP cavity length, k0 is the wavenumber coordinate of the minimum wavenumber spectrum, k1 is the wavenumber coordinate of the maximum wavenumber spectrum, p is the peak index of the amplitude spectrum, is the relative phase of the frequency component corresponding to the peak index of the amplitude spectrum, is the initial phase of the FPI interferometer spectrum, is the number of cycles, [.] is the rounding symbol.

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