CN112050942B - Optical fiber interference spectrum cavity length correction method based on phase compensation - Google Patents
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Abstract
The invention relates to the field of optical fiber sensor signal processing, and discloses an optical fiber interference spectrum cavity length correction method based on phase compensation. On the basis of a common demodulation method, a cavity length correction method based on phase difference compensation is provided. Firstly, preprocessing an original spectrum to obtain a real spectrum, and obtaining a cavity length A by using a common demodulation method; bringing the cavity length A into an interference formula to obtain a reconstructed spectrum A; calculating a phase difference A between the real spectrum and the reconstructed spectrum A by a cross-correlation method, and performing first cavity length correction by using the phase difference A to obtain a cavity length B; and obtaining a reconstructed spectrum B through the cavity length B, calculating a phase difference B between the reconstructed spectrum B and the real spectrum at the frequency spectrum characteristic frequency by using Fast Fourier Transform (FFT), and correcting the cavity length B by using the phase difference B to obtain the final cavity length. After the method is applied, the demodulation precision of the sensor cavity length is improved by nearly 10000 times, and the operation efficiency and the demodulation precision are greatly improved.
Description
Technical Field
The invention belongs to the field of optical fiber sensing signal processing, and particularly relates to a high-precision demodulation method for optical fiber interference spectrum cavity length.
Background
The optical fiber sensor based on the Fabry-Perot interference principle has the advantages of high sensitivity, small volume, electromagnetic interference resistance, simple manufacture, low cost and the like. As various sensors have been studied, the fiber-optic Fabry-Perot sensor has enabled the measurement of various physical quantities, such as temperature, pressure, strain, refractive index, gas concentration, vibration, underwater sound, etc. Since the interference spectrum generated by Fabry-Perot is quasi-sinusoidal, it is an important problem to realize high-precision large-dynamic-range measurement for the sensor.
The current interference spectrum demodulation technology is mainly divided into three categories: intensity, phase and optical path difference. The intensity method and the phase method have higher measurement accuracy, but the intensity method and the phase method can only realize parameter measurement in one interference period. When the amount of spectral shift exceeds one period, the variation of the parameter cannot be resolved, which limits the measurement range of the sensor. The optical path difference method solves the problem of cavity length demodulation in a large dynamic range of a spectrum by calculating the optical path of an interference spectrum, but the conventional optical path difference method has relatively low demodulation precision (such as a DGT method, an FFT method and a peak-to-peak method) and cannot realize high-precision demodulation of the cavity length. The method can achieve sub-nanometer demodulation precision, but the two methods realize high-precision cavity length demodulation by greatly increasing calculated amount, have slow operation speed and are difficult to meet the use requirements of some occasions. How to fully utilize information in a spectrum to realize rapid and accurate demodulation of a sensor is an important problem of the current optical fiber interference sensor.
Disclosure of Invention
The invention aims to improve the cavity length demodulation precision of a sensor by fully utilizing the information of a spectrum, and solves the problem of low cavity length demodulation precision of an interferometer in the related technology by fully utilizing the phase information of the spectrum into an optical path demodulation method. The invention provides a cavity length correction method based on a phase difference compensation technology.
The technical scheme of the invention is as follows: a cavity length correction method based on phase compensation comprises the following steps:
step 1, acquiring an original spectrum through a spectrometer, obtaining a real spectrum through filtering and normalization processing, and demodulating to obtain a cavity length A; substituting the cavity length A into the parameter OPD of the formula (1) to obtain a reconstructed spectrum A;
wherein OPD represents the cavity length obtained by demodulation, and lambda is the scanning wavelength of the spectrum;
step 2, calculating a phase difference A between the reconstructed spectrum A and the real spectrum by a cross-correlation phase difference calculation method;
step 3, correcting the cavity length A by using the phase difference A through a formula (2) to obtain a cavity length B;
wherein l0Is the length of the cavity to be corrected, l is the target cavity length,
the phase difference is obtained by comparing the phase difference,
represents the median of the spectral scanning wavelengths;
step 4, substituting the cavity length B into the parameter OPD of the formula (1) to obtain a reconstructed spectrum B;
step 5, calculating a phase difference B between the reconstructed spectrum B and the real spectrum by an FFT phase difference calculation method;
and 6, correcting the cavity length B by using the phase difference B through a formula (2) to obtain the final cavity length.
The cross-correlation phase difference calculation method comprises the following steps: and performing cross-correlation operation on the reconstructed spectrum A and the real spectrum to obtain a cross-correlation spectrum, judging the phase lead-lag relationship between the two spectrums through the cross-correlation spectrum, and calculating the phase difference between the two spectrums.
The FFT phase difference calculation method includes: and respectively carrying out FFT analysis on the reconstructed spectrum B and the real spectrum, and calculating the phase difference of the two spectra under the characteristic frequency.
Further, the demodulation method of step 1 is a DGT method, an FFT method or a peak-to-peak method.
Further, the error of the cavity length A and the real cavity length is smaller than
The invention has the beneficial effects that: by using the phase difference compensation technology, the cavity length demodulation precision of the sensor is greatly improved under the condition of increasing less calculation amount.
Drawings
FIG. 1 is a flow chart of a cavity length demodulation method based on a phase difference compensation technology.
Fig. 2 is a schematic diagram of the phase difference between the true spectrum and the reconstructed spectrum.
FIG. 3 cavity length demodulation error comparison before and after phase difference compensation; (a) demodulation errors of the DGT demodulation method under different cavity lengths; (b) compensating cavity length error distribution by a cross-correlation phase difference method on the basis of (a); (c) and (b) performing FFT phase difference compensation on the basis of the cavity length error distribution.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be fully described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only directed to the implementation of the solutions under a certain condition, and not to all the implementation cases. Other embodiments, which can be obtained by one skilled in the art without inventive step, based on the embodiments of the present invention, also belong to the protection scope of the present invention.
When incident light enters the interferometer from one side, the incident light is reflected and transmitted for multiple times in the interferometer to form multi-beam interference. For a common low finesse Fabry-Perot interferometer, it can be simplified as a dual beam interferometer due to its low end reflectivity. The light intensity distribution can be expressed by the following formula:
wherein I is the reflected light intensity of the FP interferometer; i is1The intensity of the light reflected from the first optical plane; i is2For the intensity of light transmitted through the first optical plane, reflected from the second optical plane, and transmitted through the first optical plane, OPD represents the optical cavity length of the sensor (the optical cavity length of the sensor can be expressed as the product of the refractive index in the optical cavity and the geometric length of the optical cavity, i.e., OPD ═ nl, where n is the refractive index of the medium inside the interferometer and l represents the cavity length of the sensor), and λ represents the scanning wavelength of the spectrum. When light is emitted from a low refractive index medium to a high refractive index medium, the light willA phase jump of size pi is generated. By substituting the light intensity data formula into the formula, the cavity length and phase information of the spectrum can be calculated. The invention corrects the cavity length demodulation error by using the phase difference between the real spectrum and the reconstructed spectrum, and improves the cavity length demodulation precision.
When the conventional method is used for demodulating the spectral cavity length of the sensor, errors exist between the demodulation cavity length and the actual cavity length due to frequency spectrum leakage or limited wavelength resolution, and the high-precision cavity length correction is realized by utilizing the phase difference information between the real spectrum and the reconstructed spectrum. There is a phase difference between the real spectrum and the reconstructed spectrum, and as shown in fig. 1, there is a linear correlation between the phase difference and the cavity length difference within the theoretical maximum compensation value range. When the cavity length error is very small, it can be considered that the phase of the interference spectrum changes without changing the period. By utilizing the relation between the phase difference and the cavity length difference, the cavity length demodulation of the high-precision sensor spectrum can be realized.
As shown in fig. 1, the cavity length correction method based on the phase difference compensation technology provided by the present invention specifically includes the following steps:
the first step is as follows: the raw spectrum obtained. The raw spectrum of the fiber FP interferometer refers to the light intensity corresponding to each wavelength within the scanned wavelength range obtained from the demodulator or spectrometer. Can be represented as a one-dimensional array. Due to the defects of the sensor and the influence of the environment, noise and amplitude change easily occur in the spectrum, which greatly influences the demodulation effect of the spectrum and causes adverse influence on the spectrum demodulation.
The second step is that: and denoising and normalizing the original spectrum to obtain a real interference signal. In order to reduce demodulation errors caused by spectral noise and amplitude variations, wavelet transform is used to denoise the signal. The wavelet decomposition can effectively eliminate noise under the condition of keeping the signal characteristics, and the influence on the signal in the noise reduction process is reduced to the maximum extent. For the amplitude change problem of the spectrum, an envelope waveform of a signal is obtained by Hilbert transform, and the signal is divided by the envelope to obtain a normalized signal. Endpoint effects may occur during this process and it is contemplated to use a Hilbert-Huang transform or to remove portions of the data points at both ends of the signal. By these two operations, the conversion of the original signal into a normalized real signal can be achieved.
The third step: and estimating the cavity length of the sensor. In this step, the cavity length value is estimated by using a conventional cavity length demodulation method (such as FFT method, DGT method, peak-to-peak method, etc.). In this step, it is possible to use any cavity length demodulation method within the theoretical maximum compensation value range. When the cavity length demodulation method is selected, attention must be paid to the error condition of the method in the cavity length range, otherwise, a phase jump phenomenon may occur to cause the demodulation error to increase, and the meaning of compensation is lost. For some occasions with high requirements on demodulation efficiency, the calculation amount of a demodulation algorithm needs to be considered.
The fourth step: and in the first phase difference compensation operation, the phase difference between the real spectrum and the reconstructed spectrum A is calculated by using a cross-correlation algorithm, and the phase difference is compensated to the cavity length, so that the cavity length demodulation precision is preliminarily improved. In this step, the reconstructed spectrum is obtained by substituting the cavity length a into equation (1). The cross-correlation operation is used to compare the phase lead-lag of the two signals, and the phase difference a between the two spectra. In order to reduce the amount of calculation, the abscissa corresponding to the main peak of the cross-correlation operation between the reconstructed spectrum a and the real spectrum can be directly compared with the midpoint of the cross-correlation operation sequence to determine the phase lead-lag and calculate the phase magnitude. The reason why the phase calculation in this step does not adopt the FFT method is that the phase obtained by the FFT analysis is an absolute phase, and when the cavity length difference is large, a phenomenon that the phase spans a period may occur, thereby affecting the phase compensation effect, and the final phase compensation effect directly depends on the effect of the first phase difference compensation operation. And multiplying the phase difference A and the compensation coefficient to compensate the cavity length A to realize the first correction of the cavity length, and obtaining the cavity length B. The compensation coefficient can be directly calculated by a theoretical formula, and can be used as the cavity length corresponding to one period of spectral change can be calculated
And calculating to obtain a compensation coefficient of the cavity length.
The fifth step: and performing a second phase compensation operation, wherein in the step, the spectral cavity length correction is performed after the phase difference between the real spectrum and the reconstructed spectrum B is obtained through FFT calculation. In the step, the main reason for calculating the phase by using the FFT method is that the phase calculation accuracy by using the FFT phase method is higher than that by using the conventional phase method under the condition that the difference between the cavity length errors of the two signals is small. The method comprises the steps of substituting the demodulation cavity length B obtained in the fourth step into a formula (1) to obtain a reconstructed spectrum B, searching a corresponding phase at a characteristic frequency of the spectrum to calculate the phase difference B of two signals, and after the fourth step of operation, locking an error in a certain range to judge whether the obtained phase difference B is correct or not, wherein the phase difference B of the two signals is very small. The phase difference B is then compensated to the cavity length B to obtain the final cavity length. The compensation factor is the same as the fourth step. Through twice compensation, the demodulation precision of the cavity length can be effectively improved.
In order to more intuitively represent the compensation effect of the sensor, a numerical simulation condition of cavity length demodulation errors before and after the phase compensation technology is applied is given in fig. 3, and in order to better embody the effect of the compensation method, the demodulation effect under the condition that the cavity length is 100-600 μm is given. Numerical simulations were performed based on the DGT method. It can be seen that when only the DGT method is used, the cavity length demodulation error is large, and the cavity length error exhibits a periodic attenuation variation with cavity length variation, with the error being approximately in the sub-micron order as shown in fig. 3 (a). After the first phase difference compensation, the cavity length error is reduced to the nanometer level, as shown in fig. 3 (b); after the second phase difference compensation, the cavity length error is reduced to sub-nanometer level, as shown in fig. 3 (c). After the phase compensation technology is applied, the cavity length demodulation precision is improved by 10000 times, and the technical effect is obvious. The method can be used for demodulating the double-beam interference spectrum with high precision and large dynamic range, and provides a technical basis for the practical application of the fiber Fabry-Perot interferometer and the Mach-Zehnder interferometer.
Claims (5)
1. The optical fiber interference spectrum cavity length correction method based on phase compensation is characterized by comprising the following steps of:
step 1, acquiring an original spectrum through a spectrometer, obtaining a real spectrum through filtering and normalization processing, and obtaining a cavity length L1 through a demodulation method; substituting the cavity length L1 into the parameter OPD of the formula (1) to obtain a reconstructed spectrum Y1;
wherein OPD represents the cavity length obtained by demodulation, and lambda is the scanning wavelength of the spectrum;
step 2, calculating a phase difference theta 1 between the reconstructed spectrum Y1 and the real spectrum by a cross-correlation phase difference calculation method;
step 3, correcting the cavity length L1 by using the phase difference theta 1 through a formula (2) to obtain a cavity length L2;
wherein l0Is the length of the cavity to be corrected, l is the target cavity length,
is the phase difference between the phase difference and the phase difference,
represents the median of the spectral scanning wavelengths;
step 4, substituting the cavity length L2 into the parameter OPD of the formula (1) to obtain a reconstructed spectrum Y2;
step 5, calculating a phase difference theta 2 between the reconstructed spectrum Y2 and the real spectrum by an FFT phase difference calculation method;
and 6, correcting the cavity length L2 by using the phase difference theta 2 through a formula (2) to obtain a final cavity length L3.
2. The method for correcting the cavity length of the optical fiber interference spectrum based on the phase compensation according to claim 1, wherein the cross-correlation phase difference calculation method comprises the following steps: and performing cross-correlation operation on the reconstructed spectrum Y1 and the real spectrum to obtain a cross-correlation spectrum, judging the phase lead-lag relationship between the two spectra through the cross-correlation spectrum, and calculating the phase difference between the two spectra.
3. The method for correcting the cavity length of the optical fiber interference spectrum based on the phase compensation as claimed in claim 1, wherein the FFT phase difference calculation method comprises: and respectively carrying out FFT analysis on the reconstructed spectrum Y2 and the real spectrum, and calculating the phase difference of the two spectra at the characteristic frequency.
4. The method for correcting the cavity length of the optical fiber interference spectrum based on the phase compensation of claim 1, wherein the demodulation method of step 1 is DGT method, FFT method or peak-to-peak method.
5. The method for correcting the cavity length of the optical fiber interference spectrum based on the phase compensation as claimed in claim 1, wherein the error between the cavity length L1 and the true cavity length is smaller than
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