Parameter calibration method and system of four-photoelastic modulator type Mueller matrix polarization system

Abstract

The invention relates to a precision optical measuring instrument calibration technology, and discloses a parameter calibration method and system for a four-photoelastic modulator type Mueller matrix polarization system, and the method comprises the steps: carrying out a polarization experiment; introducing an analysis arm base vector and a polarization arm base vector containing dynamic parameters, and establishing a calculation model of the light intensity signals, the base vectors and a light intensity projection matrix; through a polarization experiment and a calculation model, dynamic parameters in base vectors of a polarization detection arm and a polarization starting arm are calibrated by using a nonlinear regression method, and the dynamic parameters comprise the peak retardation, the modulation frequency and the initial phase of the photoelastic modulator. Furthermore, a matrix containing static parameters of the system is obtained through a characteristic value calibration method and is directly used for measurement, and the static parameters comprise the azimuth angle of the polarization element and the static delay amount of the photoelastic modulator. According to the method, the base vector is introduced, the light intensity is detected through nonlinear regression projection, the calibration of dynamic parameters is realized, then the static parameters are calibrated by using the characteristic values, the operation is simple and convenient, and the calibration precision is high.

Description

Technical Field

[0001] The present invention belongs to the technical field related to calibration of precision optical measuring instruments, and more specifically, relates to a parameter calibration method and system for a four-photoelastic modulator type Mueller matrix polarization system. Background Art

[0002] The four-photoelastic modulator Mueller matrix polarimeter can measure the full Mueller matrix information of the sample in one measurement, and can characterize more complex optical properties such as sample anisotropy and depolarization. This type of polarimeter can obtain the Mueller matrix of the sample under the corresponding wavelength and incident angle conditions through the time modulation of four photoelastic modulators. It has the advantages of simple modulation, wide spectral coverage, and good system stability. However, the measurement accuracy of the four-photoelastic modulator polarimeter is greatly affected by the calibration results. Therefore, in actual use, it is necessary to accurately calibrate the parameters of the photoelastic modulator and the azimuth angle of the polarization element in the system.

[0003] Traditional calibration methods are usually based on a clear system model. By extracting the frequency domain components related to the system parameters, the measurement system is calibrated based on the relationship between the specific frequency domain components and the system parameters. The calibrated azimuth error of the polarization element is used to further adjust the installation error of the polarization element, so a precise rotation stage is required. This calibration method requires multiple phase-locked amplifiers to reduce the influence of spectral leakage and high-frequency components. At the same time, its calibration accuracy also has certain requirements on the system parameters themselves. For example, the peak delay of the photoelasticity, if the deviation is too large, will seriously affect the calibration effect. At the same time, the above calibration steps are relatively cumbersome.

[0004] Therefore, there is an urgent need for a simple calibration method with high tolerance to system deviations so that it can be applied to the four-photoelastic Mueller matrix polarimeter measurement system. Summary of the invention

[0005] In response to the above defects or improvement needs of the prior art, the present invention provides a parameter calibration method and system for a four-photoelastic modulator-type Mueller matrix polarization system, which is used to solve the problem that the existing parameter calibration method suitable for a four-photoelastic Mueller matrix polarimeter measurement system has complicated calibration steps and high requirements on system parameters for calibration accuracy.

[0006] To achieve the above-mentioned object, according to one aspect of the present invention, a parameter calibration method of a four-photoelastic modulator type Mueller matrix polarization system is provided, wherein the polarization system comprises a light source module, a polarizing arm, a sample position, an analyzer arm, a collecting lens and a detector arranged in sequence along an optical path, the polarizing arm comprises a polarizer, a first photoelastic modulator and a second photoelastic modulator arranged in sequence, and the analyzer arm comprises a third photoelastic modulator, a fourth photoelastic modulator and an analyzer arranged in sequence; the parameter calibration method comprises:

[0007] Perform a polarization experiment based on the polarization system and collect an experimental light intensity signal;

[0008] The analyzer arm basis vector and the polarizer arm basis vector, which contain the dynamic parameters of the polarization system, are introduced, and a calculation model of the light intensity signal about the analyzer arm basis vector, the light intensity projection matrix and the polarizer arm basis vector is established.

[0009] Based on the polarization experiment and the calculation model of the light intensity signal, the dynamic parameters of the polarization system in the analyzer arm basis vector and the polarizing arm basis vector are calibrated by a nonlinear regression method;

[0010] The dynamic parameters of the polarization system include the peak delay, modulation frequency and initial phase of each photoelastic modulator.

[0011] According to the parameter calibration method of the four-photoelastic modulator type Mueller matrix polarization system provided by the present invention, the polarization arm basis vector and the polarizing arm basis vector are established based on the sine and cosine functions of the dynamic delay part in the phase delay of the photoelastic modulator and their products.

[0012] According to the parameter calibration method of the four-photoelastic modulator Mueller matrix polarization system provided by the present invention, the polarization arm basis vector S A and the polarizing arm basis vector S W The specific formula is as follows:

[0013]

[0014] in, represents the dynamic delay part of the phase delay of the photoelastic modulator, The subscripts 1 to 4 in the figure represent the numbers of the photoelastic modulators; F, v, They are the peak delay, frequency and initial phase of the photoelastic modulator respectively.

[0015] According to the parameter calibration method of the four-photoelastic modulator type Mueller matrix polarization system provided by the present invention, based on the polarization experiment and the calculation model of the light intensity signal, the dynamic parameters of the polarization system in the polarization arm basis vector and the polarizing arm basis vector are calibrated by a nonlinear regression method, and the light intensity projection matrix is ​​calibrated by a nonlinear regression method, which specifically includes:

[0016] Determine the initial values ​​of the dynamic parameters of the polarization system and the intensity projection matrix;

[0017] Starting from the initial value, with the purpose of minimizing the error between the calculated value of the light intensity signal and the experimental value in the polarization experiment, the parameters in the calculation model of the light intensity signal are optimized, and finally the parameters in the calculation model of the light intensity signal are calibrated, including the dynamic parameters of the polarization system and the light intensity projection matrix.

[0018] According to the parameter calibration method of the four-photoelastic modulator Mueller matrix polarization system provided by the present invention, determining the initial values ​​of the dynamic parameters of the polarization system and the light intensity projection matrix specifically includes:

[0019] Determining the initial value of the peak delay of each photoelastic modulator according to the control voltage of each photoelastic modulator in the polarization experiment;

[0020] Determine the initial value of the modulation frequency and the initial value of the initial phase of each photoelastic modulator according to the control signal of each photoelastic modulator in the polarization experiment and the experimental light intensity signal;

[0021] The initial value of the light intensity projection matrix is ​​determined by random generation.

[0022] According to the parameter calibration method of the four-photoelastic modulator type Mueller matrix polarization system provided by the present invention, a polarization experiment is performed based on the polarization system, and an experimental light intensity signal is collected, which specifically includes: selecting multiple calibration samples and performing polarization experiments respectively; accordingly, the parameter calibration method also includes:

[0023] The analyzer arm analysis matrix and polarizer arm modulation matrix containing the static parameters of the polarization system are introduced, and the calculation model of the light intensity projection matrix with respect to the analyzer arm analysis matrix, the sample Mueller matrix and the polarizer arm modulation matrix is ​​established;

[0024] The light intensity projection matrices corresponding to a plurality of calibration samples are calibrated by a nonlinear regression method;

[0025] Based on the calculation model of the light intensity projection matrix, the light intensity projection matrix of multiple calibration samples is solved using the eigenvalue calibration method to obtain the polarization arm analysis matrix and the polarization arm modulation matrix, completing the calibration of the static system parameters of the system.

[0026] The static system parameters of the system include the azimuth angle of the polarizer, the azimuth angle of the analyzer, the azimuth angles of each photoelastic modulator, and the static delay amount of each photoelastic modulator.

[0027] According to the parameter calibration method of the four-photoelastic modulator Mueller matrix polarization system provided by the present invention, the calculation model of the light intensity signal and the calculation model of the light intensity projection matrix are shown as follows:

[0028] I(t)=S A ·B·S W =S A ·A·M S ·W.S. W ;

[0029] Where, I(t) is the light intensity signal; S A is the basis vector of the analysis arm; S Wis the basis vector of the polarizing arm; B is the light intensity projection matrix; M S is the Mueller matrix of the sample; A is the analysis matrix of the polarization arm; W is the modulation matrix of the polarization arm.

[0030] According to the parameter calibration method of the four-photoelastic modulator type Mueller matrix polarization system provided by the present invention, the multiple calibration samples include air and at least two non-air samples;

[0031] Solving the analysis matrix of the polarization arm and the modulation matrix of the polarization arm specifically includes:

[0032] The intensity projection matrices of multiple calibration samples are processed to obtain a transition matrix, which is constructed as follows:

[0033]

[0034] Where + represents the Moore-Penrose generalized inverse, the Mueller matrix element of air is the unit matrix, the light intensity projection matrix of air is B0, and the light intensity projection matrix of other samples is B S,j ;M S,j represents the Mueller matrix of the jth non-air sample, C W is the transition matrix corresponding to the polarizing arm, C A is the transition matrix corresponding to the analyzer arm;

[0035] Based on the transition matrix, determining the Mueller matrix elements of each non-air sample by an eigenvalue calibration method;

[0036] vectorizing the transition matrix to construct a matrix of linear equations for each non-air sample;

[0037] Based on the Mueller matrix elements of each non-air sample and the linear equation system matrix of all non-air samples, the polarization arm analysis matrix and the polarization arm modulation matrix are determined by the eigenvalue calibration method.

[0038] According to the parameter calibration method of the four-photoelastic modulator type Mueller matrix polarization system provided by the present invention, based on the linear equation matrix of all non-air samples, the polarization arm analysis matrix and the polarization arm modulation matrix are determined by the eigenvalue calibration method, which specifically includes:

[0039] Based on the linear equation matrix corresponding to the matrix A of all non-air samples, the eigenvector corresponding to the zero eigenvalue is solved, and the analysis matrix A of the analysis arm is determined based on the eigenvector;

[0040] Based on the linear equation matrix corresponding to the matrix W of all non-air samples, the eigenvector corresponding to the zero eigenvalue is solved, and the polarizing arm modulation matrix W is determined based on the eigenvector.

[0041] According to another aspect of the present invention, a parameter calibration system for a four-photoelastic modulator type Mueller matrix polarization system is provided, the system comprising a memory and a processor, the memory storing a computer program, and the processor executing any one of the above-described parameter calibration methods for a four-photoelastic modulator type Mueller matrix polarization system when executing the computer program.

[0042] In general, compared with the prior art, the above technical solutions conceived by the present invention provide a parameter calibration method and system for a four-photoelastic modulator type Mueller matrix polarization system:

[0043] 1. It is proposed to introduce the basis vectors of the polarizing arm and the analyzing arm, and transform the calculation model of the light intensity signal into the expression form of the basis vector and the light intensity projection matrix. Based on the polarization experimental data, the detection light intensity is projected by nonlinear regression, and the system dynamic parameters in the basis vector can be calibrated. This calibration method only needs to perform polarization experiments to obtain the experimental light intensity signal, which is simple to operate and does not require strict modeling of the system model, thus avoiding the system error introduced by the modeling deviation and having high calibration accuracy.

[0044] 2. The proposed calibration method uses full-time basis vectors and projects the detection light intensity through nonlinear regression, which avoids the spectrum leakage caused by Fourier transform in traditional methods, avoids the use of multiple lock-in amplifiers, saves costs, and improves the accuracy of system calibration;

[0045] 3. No need to consider the coupling between the parameters in the modulation matrix and the analysis matrix, the system can be calibrated as a whole, which reduces the difficulty of system calibration; combined with the eigenvalue calibration method, only a few calibration samples need to be measured. Compared with the traditional method, there is no need to know the accurate information of the samples, the calculation results are more accurate and robust, and the calibration process is simpler;

[0046] 4. Calibration method By measuring a series of calibration samples, the in-situ calibration of the system can be achieved. At the same time, it is a complete calibration, which includes all system parameters in the system and is applicable to any valid azimuth configuration. One measurement can obtain all Mueller matrix elements, which can effectively improve the final measurement accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 1 is a schematic diagram of the optical path of a transmission system of a four-photoelastic modulator Mueller matrix polarizer according to an embodiment of the present invention;

[0048] Figure 2 1 is a schematic diagram of the optical path of a reflective system of a four-photoelastic modulator Mueller matrix polarizer according to an embodiment of the present invention;

[0049] Figure 3 is a flow chart of the calibration algorithm principle in an embodiment of the present invention;

[0050] Figure 4 This is a result diagram of light intensity fitting of multiple reference samples calibrated when 27 dB noise is added to the detection light intensity in an embodiment of the present invention, taking the configuration in Table 1 as an example;

[0051] Figure 5 In the embodiment of the present invention, the configuration in Table 1 is used as an example, and when 27 dB noise is added to the detection light intensity, the comparison between the Mueller matrix elements of the multi-azimuth sample and the reference value is measured by the calibration method proposed by the present invention;

[0052] Figure 6 In the embodiment of the present invention, the configuration in Table 1 is used as an example, and when 27 dB noise is added to the detection light intensity, the Mueller matrix element error of the sample is measured using the calibration method proposed by the present invention;

[0053] Throughout the drawings, the same reference numerals are used to denote the same elements or structures, wherein:

[0054] 101 - light source, 102 - collimating lens, 103 - polarizer, 104 - first photoelastic modulator, 105 - second photoelastic modulator, 106 - sample position, 107 - third photoelastic modulator, 108 - fourth photoelastic modulator, 109 - polarizer, 110 - collecting lens, 111 - detector. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0056] See also Figure 1 and Figure 2 The four-photoelastic modulator Mueller matrix polarization system, i.e., the polarizer, specifically includes a direct system and a reflective system. The optical path principle diagram of the four-photoelastic modulator Mueller matrix polarizer direct system is shown in the figure. Figure 1As shown. The configuration of the instrument is light source 101, collimating lens 102, polarizer 103, first photoelastic modulator 104, second photoelastic modulator 105, sample position 106, third photoelastic modulator 107, fourth photoelastic modulator 108, analyzer 109, collecting lens 110, and detector 111. Among them, the light source 101 and the collimating lens 102 form a light source module to provide a parallel illumination beam to the system; the polarizer 103, the first photoelastic modulator 104 and the second photoelastic modulator 105 form a polarizing arm to modulate the polarization state of the light beam incident on the sample; the third photoelastic modulator 107, the fourth photoelastic modulator 108 and the analyzer 109 form an analyzer arm to analyze the polarization state of the outgoing light after passing through the sample. The four photoelastic modulators are driven by their respective controllers and collect light intensity signals by controlling the detector.

[0057] The optical path principle diagram of the oblique-incidence system of the four-photoelastic modulator Mueller matrix polarizer, i.e. the reflective system, is as follows: Figure 2 As shown. The configuration of the instrument is light source 101, collimating lens 102, polarizer 103, first photoelastic modulator 104, second photoelastic modulator 105, sample position 106, third photoelastic modulator 107, fourth photoelastic modulator 108, analyzer 109, collecting lens 110, detector 111. The calibration of the oblique-incidence system is based on the calibration of the straight-through system. The isotropic film sample is measured to complete the calibration. At the same time, the system incident angle is calibrated. This is not the main innovation of the present invention. Therefore, when calibrating, taking the transmission type as an example, its calibration principle is also applicable to the reflection type system. The specific calibration scheme is as follows. Figure 3 shown.

[0058] This embodiment provides a parameter calibration method for a four-photoelastic modulator Mueller matrix polarization system, and the parameter calibration method includes:

[0059] Perform a polarization experiment based on the polarization system and collect an experimental light intensity signal;

[0060] The analyzer arm basis vector and the polarizer arm basis vector, which contain the dynamic parameters of the polarization system, are introduced, and a calculation model of the light intensity signal about the analyzer arm basis vector, the light intensity projection matrix and the polarizer arm basis vector is established.

[0061] Based on the polarization experiment and the calculation model of the light intensity signal, the dynamic parameters of the polarization system in the analyzer arm basis vector and the polarizing arm basis vector are calibrated by a nonlinear regression method;

[0062] The dynamic parameters of the polarization system include the peak delay, modulation frequency and initial phase of each photoelastic modulator.

[0063] The parameter calibration method provided in this embodiment does not need to establish a strict and accurate model, does not need a phase-locked amplifier to extract specific frequency components, and has no rigid pre-requirements for system parameters. By introducing two basis vectors, where the basis vectors contain all the dynamic system parameters of the system, the continuously modulated light intensity signal is projected into a light intensity projection matrix, and the parameters in the basis vectors can be obtained through a nonlinear regression method, thereby realizing the acquisition and calibration of the system dynamic parameters.

[0064] Further, a polarization experiment is performed based on the polarization system to collect an experimental light intensity signal, specifically including: selecting a plurality of calibration samples and performing polarization experiments respectively; accordingly, the parameter calibration method also includes:

[0065] The analyzer arm analysis matrix and polarizer arm modulation matrix containing the static parameters of the polarization system are introduced, and the calculation model of the light intensity projection matrix with respect to the analyzer arm analysis matrix, the sample Mueller matrix and the polarizer arm modulation matrix is ​​established;

[0066] The light intensity projection matrices corresponding to a plurality of calibration samples are calibrated by a nonlinear regression method;

[0067] Based on the calculation model of the light intensity projection matrix, the light intensity projection matrix of multiple calibration samples is solved using the eigenvalue calibration method to obtain the polarization arm analysis matrix and the polarization arm modulation matrix, completing the calibration of the static system parameters of the system.

[0068] The static system parameters of the system include the azimuth angle of the polarizer, the azimuth angle of the analyzer, the azimuth angles of each photoelastic modulator, and the static delay amount of each photoelastic modulator.

[0069] The light intensity projection matrix constructed in this embodiment contains all the system static parameters and the Mueller matrix information of the sample. Through a series of calibration sample measurements and eigenvalue calibration methods, the calibrated modulation matrix of the polarizing arm and the analysis matrix of the analyzing arm are obtained, thereby completing the calibration of the system static system parameters.

[0070] When the optical model of the system is established based on the Jones-Mueller matrix principle, the parameters to be calibrated include: (1) the azimuth angles of the polarizer, analyzer and four photoelastic modulators; (2) the peak delay, modulation frequency, initial phase and static delay of each of the four photoelastic modulators. According to the properties of the above system parameters, they are divided into dynamic system parameters and static system parameters. Dynamic system parameters refer to parameters that may change in each measurement, including the peak delay, modulation frequency and initial phase of each photoelastic modulator. The above parameters may fluctuate in each measurement due to environmental influences and unstable control. Static system parameters refer to parameters that remain stable in each measurement, including the azimuth angle information of the polarization element in the system and the static delay of each photoelastic modulator. Because each polarization element in the four-photoelastic modulation Mueller matrix polarimeter remains fixed, the static delay of the photoelastic modulator is only related to the material and its geometric shape.

[0071] The calibration method proposed in this embodiment expands the eigenvalue calibration method and makes it applicable to the four-photoelastic modulator Mueller matrix polarimeter measurement system. This method can standardize all parameters to be calibrated, including: (1) dynamic system parameters in the basis vector, including the peak delay, modulation frequency and initial phase of each photoelastic modulator. (2) The Mueller matrix of the calibration sample and its azimuth information. (3) The modulation matrix and the analysis matrix, which contain the static system parameters of the four-photoelastic modulator Mueller matrix polarimeter, such as the azimuth information of each polarization element and the static delay of the photoelastic modulator.

[0072] Specifically, this embodiment divides the parameters to be measured into two parts for calibration. The first step is to calibrate the dynamic system parameters and the light intensity projection matrix in the basis vector through the nonlinear regression method. The second step is to calibrate the polarizing arm modulation matrix W and the analyzing arm analysis matrix A through the eigenvalue calibration method. The technical solution of the present invention is further illustrated by specific embodiments below.

[0073] In this embodiment, the plurality of calibration samples include air and at least two non-air samples; specifically, when the polarization system is a straight-through system, the calibration samples include air, a polarizer with an azimuth angle of 0°, a polarizer with an azimuth angle of about 90°, and a quarter-wave plate with an azimuth angle of about 30°. When the polarization system is an oblique-incidence system, i.e., a reflective system, the calibration samples include air, a polarizer with an azimuth angle of 0°, and an isotropic film. The calibration process is as follows: Figure 3 As shown:

[0074] In step 1, the four calibration samples are placed in the sample position 106 in sequence, aligned with the light path, and the data collection of the light intensity signal is completed. In the straight-through mode, the light intensity signal result of the reference sample is recorded as Where i = 1, 2, 3, 4, corresponding to air, polarizer with azimuth angle of 0°, polarizer with azimuth angle of about 90° and quarter wave plate with azimuth angle of about 30°. Under oblique incidence, the light intensity signal result of the reference sample is recorded as Where i=1, 2, 3, corresponding to air, polarizer with an azimuth angle of 0°, and isotropic film, respectively.

[0075] In step 2, for a single measurement sample, the theoretical calculation model of the measurement light intensity signal I(t) collected by the detector is:

[0076]

[0077] Among them, S in Represents the Stokes vector of the light source, M P 、M S 、M A are the Mueller matrices of the polarizer, sample and analyzer, respectively, C (δ) represents the Mueller matrix of the phase retarder with a phase delay of δ, θ P and θ A are the azimuth angles of the polarizer and analyzer, θ k and δ k (t)(k=1,2,3,4)represent the azimuth angle and phase delay of the kth photoelastic modulator, where the phase delay of the photoelastic modulator is: Where F, v, δ0 is the peak delay, frequency, initial phase and static delay of the photoelastic modulator. It should be noted that sufficient data points should be ensured and a suitable sampling frequency should be selected to satisfy the Nyquist sampling theorem to ensure that the collected signal is not distorted, to ensure the success rate of subsequent light intensity fitting, and to reduce the impact of random noise on the calibration results.

[0078] In step 3, it is necessary to select appropriate basis vectors, where the basis vector of the deflection arm is S W (t), the basis vector of the analysis arm is S A (t), the analyzer arm basis vector and the polarizing arm basis vector are specifically established based on the system model of the polarizing arm and the analyzer arm, that is, on the basis of Formula 1, by selecting the sine and cosine functions of the dynamic delay part of the phase delay of the photoelastic modulator and their products. For each time t, S W (t) is a 9×1 vector, S A (t) is a 1×9 vector, and a 9×9 intensity projection matrix B is obtained from the time-domain continuously modulated intensity signal:

[0079] I(t)=S A ·B·S W =S A ·A·MS ·W.S. W (2)

[0080]

[0081]

[0082] in, represents the dynamic delay part of the phase delay of the photoelastic modulator, The subscripts 1 to 4 represent the numbers of the photoelastic modulators; the basis vectors contain all the dynamic system parameters in the system, A and W are the polarization arm analysis matrix and the polarizing arm modulation matrix respectively, and B is the light intensity projection matrix. A is a 9×4 matrix, W is a 4×9 matrix, and B is a 9×9 matrix. The polarizing arm modulation matrix W contains the azimuth parameters of the polarization element in the polarizing arm and the static delay parameters of the photoelastic modulator; the polarization arm analysis matrix A contains the azimuth parameters of the polarization element in the polarization arm and the static delay parameters of the photoelastic modulator. The above formula 1 is the system model of the well-known four-photoelastic modulation type Mueller matrix polarimeter, which can be written in the form of formula 2 by introducing basis vectors.

[0083] In step three, the dynamic system parameters in the basis vector are calibrated by a nonlinear regression method, and the light intensity projection matrix B is obtained at the same time. This process requires finding a suitable initial value. There is an approximate linear relationship between the peak delay amount and the control voltage. The peak delay amount initial value close to the true value can be obtained by the control voltage, that is, the peak delay amount initial value of each photoelastic modulator is determined according to the control voltage of each photoelastic modulator in the polarization experiment. The initial value of the photoelastic frequency and initial phase can be obtained from the reference signal of the photoelastic control, specifically the signal output by the controller of the photoelastic modulator, together with the signal output by the photodetector for detecting the light intensity, through a multi-channel acquisition card or an oscilloscope, that is, according to the control signal of each photoelastic modulator in the polarization experiment and the experimental light intensity signal, the modulation frequency initial value and initial phase initial value of each photoelastic modulator are determined. B, as the projection of the light intensity signal on the selected basis vector, has good recognition, so a randomly generated 9×9 matrix can be selected as its initial value, that is, the initial value of the light intensity projection matrix can be determined by randomly generating, for example, a 9×9 matrix with a size in the range of 0-1 can be randomly selected.

[0084] Based on the polarization experiment and the calculation model of the light intensity signal, the dynamic parameters of the polarization system in the analyzer arm basis vector and the polarizing arm basis vector are calibrated by a nonlinear regression method, and the light intensity projection matrix is ​​calibrated by a nonlinear regression method, specifically including:

[0085] Determine the initial values ​​of the dynamic parameters of the polarization system and the intensity projection matrix;

[0086] Starting from the initial value, with the purpose of minimizing the error between the calculated value of the light intensity signal and the experimental value in the polarization experiment, the parameters in the calculation model of the light intensity signal are optimized, and finally the parameters in the calculation model of the light intensity signal are calibrated, including the dynamic parameters of the polarization system and the light intensity projection matrix.

[0087] In step 4, a light intensity projection matrix can be obtained for each calibration sample. The light intensity projection matrix of each calibration sample can be expressed as follows, where the Mueller matrix element of air is the unit matrix, and its light intensity projection matrix is ​​B0, and the light intensity projection matrix of other samples is B S,j :

[0088] B0=A·W (5.1)

[0089] B S,j =A·M S,j W (5.2)

[0090] In step 5, the intensity projection matrices of multiple calibration samples are processed to obtain a transition matrix, and the construction of the transition matrix is ​​as follows:

[0091]

[0092] Among them, + represents the Moore-Penrose generalized inverse, M S,j represents the Mueller matrix of the jth non-air sample, C W is the transition matrix corresponding to the polarizing arm, C A is the transition matrix corresponding to the polarization arm. By constructing the transition matrix, the polarization arm analysis matrix A and the polarization arm modulation matrix W are constructed into different equations, which is convenient for subsequent separate processing and calculation.

[0093] In step six, based on the transition matrix, the Mueller matrix elements of each non-air sample are determined by the eigenvalue calibration method. Specifically, in theory, the characteristics of the transition matrix are consistent with the eigenvalues ​​of the calibration sample, but the transition matrix C is a 9×9 matrix, and it is difficult to find accurate eigenvalues ​​due to errors. Therefore, when calculating the eigenvalues ​​of the calibration sample, it is necessary to select the 4×4 submatrix of the light intensity projection matrix to calculate the transition matrix or select the 4×4 submatrix of the transition matrix to calculate the eigenvalues ​​of the calibration sample, and then accurately calibrate the Mueller matrix elements of the calibration sample based on the eigenvalues ​​of the calibration sample.

[0094] Here, any one of the two transition matrices can be selected. Specifically, when selecting a 4×4 submatrix from a 9×9 matrix, the elements located in the first row and first column of the 9×9 matrix need to be selected. Further, considering that the static delay of the photoelastic modulator is generally small, the elements in the second row and second column are avoided. In addition, when an element in one row of the 9×9 matrix is ​​selected, the same number of elements in the corresponding column should be selected. Based on this, elements are selected in the 9×9 matrix to form a 4×4 submatrix. The eigenvalue of the submatrix is ​​the eigenvalue of the calibration sample, and the calculation accuracy is high.

[0095] In step seven, the transition matrix is ​​vectorized to construct a linear equation matrix for each non-air sample. Furthermore, when the non-air sample includes a polarizer and a wave plate, solving the analysis matrix of the analyzer arm and the modulation matrix of the polarizing arm also includes: based on the linear equation matrix of each non-air sample, calibrating the azimuth angle of the non-air sample.

[0096] Specifically, the Mueller matrix elements of the calibration sample obtained in the above step six are mainly the characteristic information of the Mueller matrix, but do not include the azimuth information; it is necessary to solve the calibration azimuth based on the linear equations to obtain the complete Mueller matrix, and then solve the linear equation matrix based on the complete Mueller matrix to obtain the polarization arm analysis matrix and the polarization arm modulation matrix. Taking the direct-through system as an example, the selected calibration samples include polarizers and wave plates. The complete Mueller matrix contains their azimuth information and characteristic information. Here, the azimuth of the 0° polarizer is used as a reference. The azimuths of the 90° polarizer and the 30° wave plate may have deviations due to installation errors, so they also need to be accurately solved. That is, the Mueller matrix M of the 0° polarizer S,1 =M P , the Mueller matrix M of the 90° polarizer S,2 =R(-θ S2 )·M P ·R(θ S2 ), the Mueller matrix M of the 30° wave plate S,3 =R(-θ S3 )·M C (δ)·R(θ S3 ), where θ S2 and θ S3 These are the exact azimuth angles of the 90° polarizer and 30° wave plate respectively.

[0097] When solving the azimuth of the calibration sample by the traversal method, it is necessary to vectorize the above transition matrix and construct a linear equation system, as shown in formulas (7.1)-(7.2); then the linear equation system matrices corresponding to the same matrix to be solved for all non-air samples are arrayed to obtain the linear equation system matrix K corresponding to the matrix W for all non-air samples. W And the linear equation matrix K corresponding to the matrix A for all non-air samplesA , taking the straight-through system as an example, as shown in formulas (8.1)-(8.2). It can be known that K A and K W There are 36 eigenvalues ​​in the , from large to small, they are λ1>…λ 35 >λ 36 . Select the linear equation matrix K A or K W The smallest ratio of two eigenvalues ​​in 36 / λ 35 The minimum is used as the evaluation criterion to optimize the optimal azimuth angle of the non-air sample to be obtained.

[0098]

[0099] in, represents the Kronecker product of two matrices, and vec(·) represents the vectorization of the matrix. i represents the identity matrix of order i, eig(·) represents the eigenvalue of the matrix to be solved, argmin{·} represents the minimum value to be solved, represents the optimal value of the azimuth angle θ, which is the azimuth calibration value of all non-air calibration samples, H W is the linear equation matrix corresponding to the matrix W for a single non-air reference sample, H A is the linear equation matrix corresponding to the matrix A for a single non-air reference sample, K W is the matrix of linear equations corresponding to the matrix W for all non-air reference samples, K A is the matrix of linear equations corresponding to matrix A for all non-air reference samples.

[0100] The present invention solves the modulation matrix and the analysis matrix through the eigenvalue calibration method, and calibrates the azimuth information or error of the polarization element in the system, without further feedback adjustment of the azimuth error, thereby reducing the difficulty and complexity of system implementation.

[0101] The present invention can be used not only in a straight-through four-photoelastic Mueller matrix polarization system, but also in an oblique-incident four-photoelastic Mueller matrix polarization system. It only needs to measure the isotropic film sample on the basis of the straight-through measurement of air and 0-degree polarizer to complete the calibration and calibrate the system incident angle at the same time.

[0102] In step eight, based on the Mueller matrix elements of each non-air sample and the linear equation matrix of all non-air samples, the polarization arm analysis matrix and the polarization arm modulation matrix are determined by the eigenvalue calibration method. Specifically, based on the linear equation matrix corresponding to the matrix A of all non-air samples, the eigenvector corresponding to the zero eigenvalue is solved, and the polarization arm analysis matrix A is determined based on the eigenvector; based on the linear equation matrix corresponding to the matrix W of all non-air samples, the eigenvector corresponding to the zero eigenvalue is solved, and the polarization arm modulation matrix W is determined based on the eigenvector.

[0103] What needs to be solved is to solve the eigenvector corresponding to the zero eigenvalue of the K matrix through the complete light intensity projection matrix or transition matrix. Specifically, the solution value of A is K A The result of rearranging the eigenvectors corresponding to the zero eigenvalue of the matrix. The solution value of W is K W The result of rearranging the eigenvectors corresponding to the zero eigenvalues ​​of a matrix.

[0104] The present invention provides a four-photoelastic modulator type Mueller matrix polarimeter system calibration and measurement method, and all system parameters are calibrated in two steps. The first step is to calibrate the dynamic system parameters of the system by a nonlinear regression method, and simultaneously obtain the light intensity projection matrix. The second step is to calibrate the static system parameters by an eigenvalue calibration method. This method introduces two novel basis vectors to project the continuous modulation spectrum in the time domain into a time-independent light intensity projection matrix by a nonlinear regression method. By measuring a series of samples, based on the eigenvalue eigenvector and matrix related theory, a matrix containing system configuration information is obtained to achieve system calibration. Compared with the existing calibration method, this method does not rely on an accurate system model, can calibrate all system parameters in the system under any effective azimuth configuration, and has the advantages of simple calibration operation, high calibration accuracy, strong anti-noise ability, and wide adaptability.

[0105] The method comprises the following steps:

[0106] Measure a series of calibration samples to collect sufficient intensity information for multiple calibration samples.

[0107] A basis vector containing dynamic system parameters and a light intensity projection matrix containing static system parameters and sample information are introduced to construct a new model. The dynamic system parameters in the basis vector are calibrated through the nonlinear regression method, and the discrete light intensity projection matrix is ​​obtained.

[0108] The light intensity projection matrix of the calibration sample is processed using the eigenvalue calibration method to obtain the modulation matrix of the polarizing arm and the analysis matrix of the analyzing arm, thereby completing the calibration of the static system parameters of the system.

[0109] Furthermore, in another embodiment, a parameter calibration system for a four-photoelastic modulator type Mueller matrix polarization system is provided, the system comprising a memory and a processor, the memory storing a computer program, and the processor executing any one of the above-described parameter calibration methods for the four-photoelastic modulator type Mueller matrix polarization system when executing the computer program.

[0110] The specific calibration and measurement method process is as follows:

[0111] In the transmission-type calibration, the zero degree of the 0° azimuth polarizer of the calibration sample can be used as the reference zero degree. The calibrated azimuths in this embodiment are all relative azimuths with respect to the 0° azimuth polarizer of the calibration sample, and can be used as absolute angles in the transmission-type system. The azimuths of the calibrated devices in the following text are no longer stated as relative azimuths. The system configuration is as shown in Table 1.

[0112] Table 1 System Configuration Table

[0113]

[0114] Turn on four photoelastic modulators to measure air, a polarizer with an azimuth angle of 0°, a polarizer with an azimuth angle of about 90°, and a 1 / 4 wave plate with an azimuth angle of about 30°.

[0115] The basis vectors of formulas (3) and (4) are introduced, where the initial value of the peak delay is selected from the reference value on the photoelastic modulator controller, which is based on the approximate linear relationship between the peak delay and the control voltage, obtained by applying the control voltage, the initial values ​​of the frequency and initial phase are obtained through the reference signal, and the initial value of the light intensity projection matrix is ​​a randomly generated 9×9 real number matrix. Then, according to formula (2), the measured frequency domain light intensity is fitted to obtain the dynamic system parameters and the light intensity projection matrix in the basis vector, Figure 4 This is the light intensity fitting effect of this step. Under the interference of 27dB random noise, the light intensity can still be accurately fitted.

[0116] According to the obtained light intensity projection matrix, the modulation matrix and analysis matrix are obtained by the eigenvalue calibration method, that is, the calibration of the static system parameters is realized. In order to verify the accuracy of the calibration results, multi-azimuth polarizers and 1 / 3 wave plates are selected as the samples to be tested for simulation verification. The light intensity projection matrix of the sample to be tested is also obtained by the nonlinear regression method. When the modulation matrix and analysis matrix have been calibrated, the Mueller matrix of the sample to be tested is solved analytically. Figure 5 is a comparison between the Mueller matrix of the sample to be tested and the reference value measured based on the calibration method of the present invention, Figure 6 The Mueller matrix error of the sample to be tested is measured based on the calibration method of the present invention. Under the interference of 27dB noise, the measurement error is within 0.6%.

[0117] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A parameter calibration method for a four-photoelastic modulator type Mueller matrix polarization system, wherein: The polarization system comprises a light source module, a polarizing arm, a sample position, an analyzer arm, a collecting lens and a detector which are sequentially arranged along the optical path, wherein the polarizing arm comprises a polarizer, a first photoelastic modulator and a second photoelastic modulator which are sequentially arranged, and the analyzer arm comprises a third photoelastic modulator, a fourth photoelastic modulator and an analyzer which are sequentially arranged; the parameter calibration method comprises: Perform a polarization experiment based on the polarization system and collect an experimental light intensity signal; The analyzer arm basis vector and the polarizer arm basis vector, which contain the dynamic parameters of the polarization system, are introduced, and a calculation model of the light intensity signal about the analyzer arm basis vector, the light intensity projection matrix and the polarizer arm basis vector is established. Based on the polarization experiment and the calculation model of the light intensity signal, the dynamic parameters of the polarization system in the analyzer arm basis vector and the polarizing arm basis vector are calibrated by a nonlinear regression method; The dynamic parameters of the polarization system include the peak delay, modulation frequency and initial phase of each photoelastic modulator.

2. The parameter calibration method of the four-photoelastic modulator type Mueller matrix polarization system as claimed in claim 1, characterized in that: The analyzing arm basis vector and the polarizing arm basis vector are specifically established based on the sine and cosine functions of the dynamic delay part in the phase delay of the photoelastic modulator and their products.

3. The parameter calibration method of the four-photoelastic modulator type Mueller matrix polarization system as claimed in claim 2, characterized in that: The analyzer arm basis vector S A and the polarizing arm basis vector S W The specific formula is as follows: in, represents the dynamic delay part of the phase delay of the photoelastic modulator, The subscripts 1 to 4 in the figure represent the numbers of the photoelastic modulators; F, v, They are the peak delay, frequency and initial phase of the photoelastic modulator respectively.

4. The parameter calibration method of the four-photoelastic modulator type Mueller matrix polarization system as claimed in claim 1, characterized in that: Based on the polarization experiment and the calculation model of the light intensity signal, the dynamic parameters of the polarization system in the analyzer arm basis vector and the polarizing arm basis vector are calibrated by a nonlinear regression method, and the light intensity projection matrix is ​​calibrated by a nonlinear regression method, specifically including: Determine the initial values ​​of the dynamic parameters of the polarization system and the intensity projection matrix; Starting from the initial value, with the purpose of minimizing the error between the calculated value of the light intensity signal and the experimental value in the polarization experiment, the parameters in the calculation model of the light intensity signal are optimized, and finally the parameters in the calculation model of the light intensity signal are calibrated, including the dynamic parameters of the polarization system and the light intensity projection matrix.

5. The parameter calibration method of the four-photoelastic modulator type Mueller matrix polarization system as claimed in claim 4, characterized in that: Determining the initial values ​​of the polarization system dynamic parameters and the light intensity projection matrix specifically includes: Determining the initial value of the peak delay of each photoelastic modulator according to the control voltage of each photoelastic modulator in the polarization experiment; Determine the initial value of the modulation frequency and the initial value of the initial phase of each photoelastic modulator according to the control signal of each photoelastic modulator in the polarization experiment and the experimental light intensity signal; The initial value of the light intensity projection matrix is ​​determined by random generation.

6. The parameter calibration method of the four-photoelastic modulator type Mueller matrix polarization system as claimed in claim 4, characterized in that: Based on the polarization system, a polarization experiment is performed to collect an experimental light intensity signal, specifically including: selecting a plurality of calibration samples and performing polarization experiments respectively; accordingly, the parameter calibration method also includes: The analyzer arm analysis matrix and polarizer arm modulation matrix containing the static parameters of the polarization system are introduced, and the calculation model of the light intensity projection matrix with respect to the analyzer arm analysis matrix, the sample Mueller matrix and the polarizer arm modulation matrix is ​​established; The light intensity projection matrices corresponding to a plurality of calibration samples are calibrated by a nonlinear regression method; Based on the calculation model of the light intensity projection matrix, the light intensity projection matrix of multiple calibration samples is solved using the eigenvalue calibration method to obtain the polarization arm analysis matrix and the polarization arm modulation matrix, completing the calibration of the static system parameters of the system. The static system parameters of the system include the azimuth angle of the polarizer, the azimuth angle of the analyzer, the azimuth angles of each photoelastic modulator, and the static delay amount of each photoelastic modulator.

7. The parameter calibration method of the four-photoelastic modulator type Mueller matrix polarization system as claimed in claim 6, characterized in that: The calculation model of the light intensity signal and the calculation model of the light intensity projection matrix are shown in the following formula: I(t)=S A ·B·S W =S A ·A·M S ·W·S W ; Where, I(t) is the light intensity signal; S A is the basis vector of the analysis arm; S W is the basis vector of the polarizing arm; B is the light intensity projection matrix; M S is the Mueller matrix of the sample; A is the analysis matrix of the polarization arm; W is the modulation matrix of the polarization arm.

8. The parameter calibration method of the four-photoelastic modulator type Mueller matrix polarization system as claimed in claim 7, characterized in that: The plurality of calibration samples includes air and at least two non-air samples; Solving the analysis matrix of the polarization arm and the modulation matrix of the polarization arm specifically includes: The intensity projection matrices of multiple calibration samples are processed to obtain a transition matrix, which is constructed as follows: Where + represents the Moore-Penrose generalized inverse, the Mueller matrix element of air is the unit matrix, the light intensity projection matrix of air is B0, and the light intensity projection matrix of other samples is B S,j ;M S,j represents the Mueller matrix of the jth non-air sample, C W is the transition matrix corresponding to the polarizing arm, C A is the transition matrix corresponding to the analyzer arm; Based on the transition matrix, determining the Mueller matrix elements of each non-air sample by an eigenvalue calibration method; vectorizing the transition matrix to construct a matrix of linear equations for each non-air sample; Based on the Mueller matrix elements of each non-air sample and the linear equation system matrix of all non-air samples, the polarization arm analysis matrix and the polarization arm modulation matrix are determined by the eigenvalue calibration method.

9. The parameter calibration method of the four-photoelastic modulator type Mueller matrix polarization system as claimed in claim 8, characterized in that: Based on the linear equation matrix of all non-air samples, the analysis matrix of the polarization arm and the modulation matrix of the polarization arm are determined by the eigenvalue calibration method, including: Based on the linear equation matrix corresponding to the matrix A of all non-air samples, the eigenvector corresponding to the zero eigenvalue is solved, and the analysis matrix A of the analysis arm is determined based on the eigenvector; Based on the linear equation matrix corresponding to the matrix W of all non-air samples, the eigenvector corresponding to the zero eigenvalue is solved, and the polarizing arm modulation matrix W is determined based on the eigenvector.

10. A parameter calibration system for a four-photoelastic modulator type Mueller matrix polarization system, characterized in that: The system includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the parameter calibration method of the four-photoelastic modulator type Mueller matrix polarization system described in any one of claims 1 to 9 is performed.

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