A parameter calibration method and system of a four photoelastic modulator type Mueller matrix polarization system

Abstract

The present application relates to precision optical measuring instrument calibration technology, disclose a kind of four photoelastic modulator type mueller matrix polarization system parameter calibration method and system, the method comprises: conducting polarization experiment;Introducing the detection polarization arm base vector and polarizing arm base vector containing dynamic parameters, establish the calculation model of light intensity signal and these base vectors and light intensity projection matrix;Through polarization experiment and calculation model, the dynamic parameters in detection polarization arm and polarizing arm base vector are calibrated using nonlinear regression method, these dynamic parameters include the peak retardation of photoelastic modulator, modulation frequency and initial phase.Further, the matrix containing system static parameters is obtained by eigenvalue calibration method, directly used for measurement, static parameters include the azimuth angle of polarization element and the static retardation of photoelastic modulator.The method introduces base vector, realizes the calibration of dynamic parameters by detecting light intensity through nonlinear regression projection, then the static parameters are calibrated using eigenvalue, easy to operate, and high calibration accuracy.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of precision optical measuring instrument calibration, and more particularly to a parameter calibration method and system for a four photoelastic modulator type Mueller matrix polarization system. BACKGROUND

[0002] The four photoelastic modulator type Mueller matrix polarimeter can measure the full Mueller matrix information of a sample by one measurement, and can represent more complex optical characteristics such as anisotropy and depolarization of the sample. The four photoelastic modulator type Mueller matrix polarimeter can obtain the Mueller matrix of the sample under the corresponding wavelength and incident angle conditions through the time modulation of the four photoelastic modulators, and has the advantages of simple modulation, wide spectral coverage, and good system stability. However, the measurement accuracy of the four photoelastic modulator type Mueller matrix polarimeter is greatly affected by the calibration results, so in actual use, the parameters of the photoelastic modulators and the azimuth angle of the polarization elements in the system need to be accurately calibrated.

[0003] The traditional calibration method is usually based on an explicit system model, and the frequency domain components related to the system parameters are extracted, and then the calibration of the measurement system is completed according to the relationship between the specific frequency domain components and the system parameters. The azimuth angle error of the polarization element calibrated is used to further adjust the installation error of the polarization element, so a precise rotary displacement table is required. In order to reduce the influence of spectral leakage and high frequency components, multiple lock-in amplifiers are required in this calibration method, and the calibration accuracy also has certain requirements for the system parameters themselves, such as the peak delay of the photoelasticity. If the deviation is too large, it 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 and high-tolerance calibration method for system deviation, which is suitable for the four photoelastic Mueller matrix polarimeter measurement system. SUMMARY

[0005] In view of the above defects or improvement needs of the prior art, the present application provides a parameter calibration method and system for a four photoelastic modulator type Mueller matrix polarization system, which solves the problems of the prior art that the calibration steps of the parameter calibration method suitable for the four photoelastic Mueller matrix polarimeter measurement system are relatively cumbersome, and the calibration accuracy has high requirements for system parameters.

[0006] To achieve the above-mentioned purpose, according to one aspect of the present application, a parameter calibration method for a four photoelastic modulator type Mueller matrix polarization system is provided, wherein the polarization system includes a light source module, a polarizing arm, a sample site, a detection arm, a collection lens and a detector arranged in sequence along the light path, the polarizing arm includes a polarizer, a first photoelastic modulator and a second photoelastic modulator arranged in sequence, and the detection arm includes a third photoelastic modulator, a fourth photoelastic modulator and a detection polarizer arranged in sequence; the parameter calibration method comprises:

[0007] performing a polarization experiment based on the polarization system, and collecting an experimental light intensity signal;

[0008] introducing a polarimetric arm basis vector and a polarizing arm basis vector containing dynamic parameters of the polarization system, and establishing a calculation model of the light intensity signal with respect to the polarimetric arm basis vector, a light intensity projection matrix, and the polarizing arm basis vector;

[0009] based on the polarization experiment and the calculation model of the light intensity signal, calibrating the dynamic parameters of the polarization system in the polarimetric arm basis vector and the polarizing arm basis vector through a nonlinear regression method;

[0010] The dynamic parameters of the polarization system include a peak retardation, a modulation frequency, and an 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 application, the polarimetric arm basis vector and the polarizing arm basis vector are specifically established based on a sine function and a product thereof of a dynamic delay part in a phase retardation of a contained photoelastic modulator.

[0012] According to the parameter calibration method of the four-photoelastic-modulator-type Mueller matrix polarization system provided by the application, the polarimetric arm basis vector S A and the polarizing arm basis vector S W are specifically as shown in the following formula:

[0013]

[0014] wherein, a dynamic delay part in a phase retardation of a photoelastic modulator is represented, subscripts 1-4 of S are a peak retardation, a frequency, and an initial phase of the photoelastic modulator in sequence.

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

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

[0017] starting from the initial values, optimizing parameters in the calculation model of the light intensity signal for the purpose of minimizing an error between a calculation value of the light intensity signal and an experimental value in the polarization experiment, and finally calibrating the parameters in the calculation model of the light intensity signal, that is, the dynamic parameters of the polarization system and the light intensity projection matrix.

[0018] The parameter calibration method of the four photoelastic modulator type Mueller matrix polarization system provided by the application determines the initial value of the dynamic parameters of the polarization system and the light intensity projection matrix, and specifically comprises the following steps:

[0019] According to the control voltage of each photoelastic modulator in the polarization experiment, the initial value of the peak retardation of each photoelastic modulator is determined.

[0020] According to the control signal of each photoelastic modulator in the polarization experiment and the experimental light intensity signal, the initial value of the modulation frequency and the initial phase of each photoelastic modulator are determined.

[0021] The initial value of the light intensity projection matrix is determined in a random generation manner.

[0022] The parameter calibration method of the four photoelastic modulator type Mueller matrix polarization system provided by the application is based on the polarization experiment of the polarization system, and the experimental light intensity signal is collected, specifically comprising the following steps: a plurality of calibration samples are selected, and polarization experiments are respectively performed; correspondingly, the parameter calibration method further comprises:

[0023] The polarization analysis matrix of the polarization system and the polarization modulation matrix of the polarizer are introduced, and a calculation model of the light intensity projection matrix with respect to the polarization analysis matrix of the polarization system, the sample Mueller matrix and the polarization modulation matrix of the polarizer is established.

[0024] The light intensity projection matrix corresponding to each of the plurality of calibration samples is calibrated by a nonlinear regression method.

[0025] Based on the calculation model of the light intensity projection matrix, the polarization analysis matrix and the polarization modulation matrix of the polarizer are solved by using the eigenvalue calibration method to obtain the light intensity projection matrix of the plurality of calibration samples, and the calibration of the static system parameters of the system is completed.

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

[0027] The calculation model of the light intensity signal and the calculation model of the light intensity projection matrix provided by the application are as follows:

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

[0029] Wherein, I(t) is the light intensity signal; S A is the analyzer base vector; S WB is the basis vector of the starting arm; M is the light intensity projection matrix; S denoted as the Mueller matrix of the sample; A is the analyzer matrix; W is the modulator matrix.

[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] The specific steps to obtain the analyzer arm analysis matrix and the starter arm modulation matrix include:

[0032] The transition matrix is ​​obtained by processing the light intensity projection matrices of multiple calibration samples. The construction of the transition matrix is ​​shown below:

[0033]

[0034] Where + represents the Moore-Penrose generalized inverse, the Mueller matrix element of air is the identity 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 C represents the Mueller matrix of the j-th non-air sample. W It is the transition matrix corresponding to the starting arm, C A It is the transition matrix corresponding to the bias detection arm;

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

[0036] The transition matrix is ​​vectorized to construct a linear equation matrix for each non-air sample;

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

[0038] The parameter calibration method for 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, determines the analyzer arm analysis matrix and the polarizer arm modulation matrix through the eigenvalue calibration method, specifically including:

[0039] Based on the linear equation system matrix corresponding to matrix A for all non-air samples, solve for the eigenvector corresponding to the zero eigenvalue, and determine the bias detection arm analysis matrix A based on the eigenvector.

[0040] Based on the linear equation system matrix corresponding to matrix W for all non-air samples, solve for the eigenvector corresponding to the zero eigenvalue, and determine the starting arm modulation matrix W based on the eigenvector.

[0041] According to another aspect of the present application, there is provided a parameter calibration system of a four photoelastic modulator type Mueller matrix polarization system, the system comprising a memory and a processor, the memory storing a computer program, and the processor executing the computer program to perform the parameter calibration method of the four photoelastic modulator type Mueller matrix polarization system according to any one of the above aspects.

[0042] In general, compared with the prior art, the present application provides a parameter calibration method and system of a four photoelastic modulator type Mueller matrix polarization system:

[0043] 1. The introduction of the polarizing arm basis vector and the polarizing arm basis vector is proposed, and the calculation model of the light intensity signal is converted into the expression form of the basis vector and the light intensity projection matrix, so that based on the polarization experimental data, the projection of the detected light intensity is performed through the nonlinear regression method, and the system dynamic parameters in the basis vector can be calibrated and obtained. The calibration method only needs to perform polarization experiments to obtain experimental light intensity signals, is simple to operate, does not need to strictly model the system model, avoids the system error introduced due to the modeling deviation, and has high calibration precision;

[0044] 2. The calibration method proposed uses a full-time basis vector, and the projection of the detected light intensity is performed through the nonlinear regression method, thereby avoiding the spectral leakage caused by the Fourier transform in the traditional method, saving the cost by avoiding the use of multiple lock-in amplifiers, and improving the precision of system calibration;

[0045] 3. Without considering the coupling between the parameters in the modulation matrix and the analysis matrix, the system calibration is realized by taking the modulation matrix and the analysis matrix as a whole, thereby reducing the difficulty of system calibration; and compared with the traditional method, the calibration method combining the eigenvalue calibration method only needs to measure a few calibration samples, does not need to know the accurate information of the sample, the calculation result is more accurate and robust, and the calibration process is simpler;

[0046] 4. The calibration method can realize in-situ calibration of the system by measuring a series of calibration samples, and the calibration is complete and contains all the system parameters in the system, so that the calibration method is suitable for any effective azimuth angle configuration, one measurement can obtain all the Mueller matrix elements, and the final measurement precision can be effectively improved. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 is a transmission type system optical path principle diagram of a four photoelastic modulator type Mueller matrix polarization instrument in an embodiment of the present application;

[0048] Figure 2 is a reflection type system optical path principle diagram of a four photoelastic modulator type Mueller matrix polarization instrument in an embodiment of the present application;

[0049] Figure 3 is a calibration algorithm principle flowchart in an embodiment of the present application;

[0050] Figure 4 This is a graph showing the light intensity fitting results of multiple reference samples calibrated, with the configuration in Table 1 as an example in this embodiment of the invention, and 27dB of noise added to the detected light intensity.

[0051] Figure 5 This embodiment of the invention uses the configuration in Table 1 as an example. Under the condition that 27dB noise is added to the detected light intensity, the comparison between the Mueller matrix elements of the multi-azimuth angle sample and the reference value is obtained by the calibration method proposed in this invention.

[0052] Figure 6 In this embodiment of the invention, taking the configuration in Table 1 as an example, the Mueller matrix element error of the sample is measured using the calibration method proposed in this invention when 27dB noise is added to the probe light intensity.

[0053] In all the accompanying 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-Analyzer, 110-Collecting lens, 111-Detector. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0056] Please see Figure 1 and Figure 2 The four-electro-optical-modulator type Mueller matrix polarization system, also known as a polarimeter, specifically includes a direct-through system and a reflective system. The optical path diagram of the direct-through system of the four-electro-optical-modulator type Mueller matrix polarimeter is shown below. Figure 1The configuration of the instrument is light source 101, collimating lens 102, polarizer 103, first photoelastic modulator 104, second photoelastic modulator 105, sample site 106, third photoelastic modulator 107, fourth photoelastic modulator 108, analyzer 109, collection lens 110, and detector 111 in sequence. Among them, the light source module is composed of light source 101 and collimating lens 102, which provides a parallel illumination beam for the system; the polarizing arm is composed of polarizer 103, first photoelastic modulator 104 and second photoelastic modulator 105, which is used to modulate the polarization state of the light beam incident on the sample; the analyzing arm is composed of third photoelastic modulator 107, fourth photoelastic modulator 108 and analyzer 109, which is used to analyze the polarization state of the light beam after passing through the sample. The four photoelastic modulators are driven by their respective controllers, and the light intensity signals are collected by the control detector.

[0057] The oblique incidence system of the four photoelastic modulator type Mueller matrix polarimeter is a reflection system, and the optical path principle diagram is as shown in Figure 2 The configuration of the instrument is light source 101, collimating lens 102, polarizer 103, first photoelastic modulator 104, second photoelastic modulator 105, sample site 106, third photoelastic modulator 107, fourth photoelastic modulator 108, analyzer 109, collection lens 110, and detector 111 in sequence. The calibration of the oblique incidence system is based on the calibration of the straight-through system, and the calibration of the isotropic film sample is completed, and the incident angle of the system is calibrated. This is not the main innovation point of the present application, so when calibrating, taking the transmission type as an example, the calibration principle is also applicable to the reflection system, and the specific calibration scheme is as shown in Figure 3 .

[0058] The embodiment provides a parameter calibration method of a four photoelastic modulator type Mueller matrix polarization system, and the parameter calibration method comprises the following steps:

[0059] Based on the polarization system, a polarization experiment is carried out, and an experimental light intensity signal is collected;

[0060] The analyzer arm base vector and the polarizing arm base vector containing the dynamic parameters of the polarization system are introduced, and a calculation model of the light intensity signal with respect to the analyzer arm base vector, the light intensity projection matrix and the polarizing arm base 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 base vector and the polarizing arm base vector are calibrated by a nonlinear regression method;

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

[0063] The parameter calibration method provided in the embodiment does not need to establish a strictly accurate model, does not need a lock-in amplifier to extract a specific frequency component, and has no hard pre-requirements for system parameters. By introducing two basis vectors, all dynamic system parameters of the system are contained in the basis vectors, the continuously modulated light intensity signal is projected into a light intensity projection matrix, and the parameters in the basis vectors are obtained through a nonlinear regression method, that is, the acquisition and calibration of the system dynamic parameters are realized.

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

[0065] The analysis matrix of the analyzer and the modulation matrix of the polarizer are introduced, and a calculation model of the light intensity projection matrix about the analysis matrix of the analyzer, the sample Mueller matrix and the modulation matrix of the polarizer is established;

[0066] The light intensity projection matrix corresponding to each of the plurality of calibration samples is calibrated through a nonlinear regression method;

[0067] Based on the calculation model of the light intensity projection matrix, the analysis matrix of the analyzer and the modulation matrix of the polarizer are obtained by solving the light intensity projection matrix of the plurality of calibration samples using an eigenvalue calibration method, and the calibration of the static system parameters of the system is completed.

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

[0069] The light intensity projection matrix constructed in the embodiment contains all the static system parameters of the system and the Mueller matrix information of the sample. Through the measurement of a series of calibration samples and the eigenvalue calibration method, the calibrated modulation matrix of the polarizer and the analysis matrix of the analyzer are obtained, and the calibration of the static system parameters of the system is completed.

[0070] The parameters to be calibrated include: (1) azimuth angles of the polarizer, the analyzer and the four photoelastic modulators; (2) peak retardation, modulation frequency, initial phase and static retardation of each photoelastic modulator. According to the properties of the system parameters, the parameters are divided into dynamic system parameters and static system parameters. The dynamic system parameters are the parameters that may change in each measurement, including the peak retardation, the modulation frequency and the initial phase of each photoelastic modulator. The static system parameters are the parameters that remain stable in each measurement, including the azimuth angle information of the polarization elements and the static retardation of each photoelastic modulator. In the four photoelastic modulator Mueller matrix polarimeter, each polarization element is fixed, and the static retardation of the photoelastic modulator is only related to the material and the geometric shape.

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

[0072] Specifically, the parameters to be measured are divided into two parts for calibration. In the first step, the dynamic system parameters in the basis vector and the light intensity projection matrix are calibrated by a nonlinear regression method. In the second step, the modulation matrix W of the polarizing arm and the analysis matrix A of the analyzing arm are calibrated by the eigenvalue calibration method. The technical solutions of the present application are further described below through specific embodiments.

[0073] In the embodiment, the multiple 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 reflection system, the calibration samples include air, a polarizer with an azimuth angle of 0° and an isotropic film. The calibration process is as shown in Figure 3

[0074] In step one, the four calibration samples are placed in the sample site 106 in sequence, the light path is aligned, and the data acquisition of the light intensity signal is completed. In the straight-through system, the light intensity signal result of the reference sample is denoted 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°, respectively. Under oblique incidence, the light intensity signal results of the reference sample are recorded as where i = 1, 2, 3, corresponding to air, polarizer with azimuth angle of 0° and isotropic film, respectively.

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

[0076]

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

[0078] In step three, a suitable basis vector should be selected, where the polarizing arm basis vector is S W (t), and the analyzer arm basis vector is S A (t). The analyzer arm basis vector and the polarizing arm basis vector are specifically established on the basis of the system model of the polarizing arm and the analyzer arm, i.e. formula 1, by selecting the sine and cosine functions of the dynamic retardation part of the phase retardation of the photoelastic modulator and their products. For each time t, S W (t) is a 9 × 1 vector, and S A (t) is a 1 × 9 vector. A 9 × 9 light intensity projection matrix B is obtained from the time-domain continuous modulation light intensity signal:

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

[0080]

[0081]

[0082] wherein, represents a dynamic delay part in the phase delay of the photoelastic modulator, the subscripts 1-4 of the base vector represent the labels of the photoelastic modulators; the base vector contains all the dynamic system parameters in the system, A and W are the analysis matrix of the detection arm and the modulation matrix of the polarizing arm respectively, and B is the light intensity projection matrix. A is a 9x4 matrix, W is a 4x9 matrix, and B is a 9x9 matrix. The modulation matrix W of the polarizing arm contains the azimuth angle parameters of the polarization elements in the polarizing arm and the static delay parameters of the photoelastic modulator; the analysis matrix A of the detection arm contains the azimuth angle parameters of the polarization elements in the detection arm and the static delay parameters of the photoelastic modulator. The above formula 1 is a system model of a general four-photoelastic-modulation-type Mueller matrix polarimeter, which can be written in the form of formula 2 by introducing the base vector.

[0083] In step three, the dynamic system parameters in the base vector are calibrated by a nonlinear regression method, and the light intensity projection matrix B is obtained simultaneously. This process requires finding appropriate initial values. There is an approximate linear relationship between the peak delay and the control voltage, and the peak delay initial value close to the true value can be obtained by the control voltage, that is, according to the control voltage of each photoelastic modulator in the polarization experiment, the peak delay initial value of each photoelastic modulator is determined. The initial value of the photoelastic frequency and the initial phase can be obtained from the reference signal of the photoelastic control, which is the signal output by the controller of the photoelastic modulator, together with the signal output by the photodetector of the detected light intensity, which can be obtained by a multi-channel data 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 the initial phase initial value of each photoelastic modulator are determined. As the projection of the light intensity signal on the selected base vector, B has good identification, so a randomly generated 9x9 matrix can be selected as its initial value, that is, the light intensity projection matrix initial value is determined by a random generation method, for example, a 9x9 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 polarization system dynamic parameters in the detection arm base vector and the polarizing arm base vector are calibrated by a nonlinear regression method, and the light intensity projection matrix is also calibrated by a nonlinear regression method, which specifically includes:

[0085] determining the initial value of the polarization system dynamic parameters and the light intensity projection matrix;

[0086] The parameters in the calculation model of the light intensity signal are optimized 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, and finally the parameters in the calculation model of the light intensity signal, including the polarization system dynamic parameters and the light intensity projection matrix, are calibrated.

[0087] In step four, 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 a unit matrix, the light intensity projection matrix of air 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 five, the transition matrix is obtained by processing the light intensity projection matrices of multiple calibration samples, and the construction of the transition matrix is shown as follows:

[0091]

[0092] where + 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, and C A is the transition matrix corresponding to the analyzing arm. By constructing the transition matrix, the analyzing matrix A of the analyzing arm and the modulating matrix W of the polarizing arm are constructed into different equations, which facilitates 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 eigenvalues of the transition matrix are consistent with the eigenvalues of the calibration sample. However, the transition matrix C is a 9x9 matrix, and it is difficult to find accurate eigenvalues due to errors. Therefore, when calculating the eigenvalues of the calibration sample, a 4x4 submatrix of the light intensity projection matrix is selected to calculate the transition matrix, or a 4x4 submatrix of the transition matrix is selected to calculate the eigenvalues of the calibration sample, and then the Mueller matrix elements of the calibration sample are accurately calibrated based on the eigenvalues of the calibration sample.

[0094] Any one of the above two transition matrices can be selected here, and specifically when selecting a 4x4 sub-matrix from a 9x9 matrix, the element in the first row and the first column of the 9x9 matrix needs to be selected, and further considering that the static delay of the photoelastic modulator is generally small, the elements in the second row and the second column are avoided to be selected, and in addition, when the elements in one row of the 9x9 matrix are selected, the same number of elements in the corresponding column should be selected. According to this, the elements in the 9x9 matrix are selected to form a 4x4 sub-matrix, and the eigenvalues of the sub-matrix are the eigenvalues of the calibration sample, and the calculation accuracy is higher.

[0095] In step seven, the transition matrix is vectorized to construct the linear equation group matrix of each non-air sample. Further, when the non-air sample includes a polarizer and a wave plate, solving the obtained analysis matrix of the analyzing polarizer arm and the modulation matrix of the polarizing arm further includes: based on the linear equation group matrix of each non-air sample, the azimuth angle of the non-air sample is calibrated and obtained.

[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, and do not include the azimuth angle information; the calibration azimuth angle needs to be solved based on the linear equation group to obtain the complete Mueller matrix, and then the analysis matrix of the analyzing polarizer arm and the modulation matrix of the polarizing arm are solved based on the complete Mueller matrix. Take the through system as an example, the selected calibration sample includes a polarizer and a wave plate, and the complete Mueller matrix contains the azimuth angle information and the characteristic information thereof, and here the azimuth angle of the 0° polarizer is taken as the reference, and the azimuth angles of the 90° polarizer and the 30° wave plate may deviate due to installation errors, and therefore also need to be accurately solved. That is, the Mueller matrix M S,1 of the 0° polarizer, P the Mueller matrix M S,2 of the 90° polarizer is R(-θ S2 )·M P ·R(θ S2 ), and the Mueller matrix M S,3 of the 30° wave plate is R(-θ S3 )·M C (δ)·R(θ S3 ), wherein θ S2 and θ S3 are the accurate azimuth angles of the 90° polarizer and the 30° wave plate, respectively.

[0097] When the azimuth angle of the calibration sample is solved by the traversal method, the above transition matrix needs to be vectorized to construct the linear equation group, as shown in formulas (7.1)-(7.2); then the linear equation group matrices corresponding to the same to-be-solved matrix of all non-air samples are assembled to obtain the linear equation group matrix K W corresponding to the matrix W of all non-air samples and the linear equation group matrix KA Taking a 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 descending order of λ1>…λ2. 35 >λ 36 Choose the matrix K of the linear equation system. A Or K W The ratio λ of the two smallest eigenvalues 36 / λ 35 The minimum value is used as the evaluation criterion to optimize the acquisition of the optimal azimuth angle for the non-air sample.

[0098]

[0099] in, E represents the Kronecker product of two matrices, and vec(·) represents the vectorization of the matrix. i Let represent the identity matrix of order i, eig(·) represents solving for the eigenvalues ​​of the matrix, and argmin{·} represents solving for the minimum value. The optimal value of the azimuth angle θ represents the azimuth angle calibration value for all non-air calibration samples, H. W H is the matrix of the system of linear equations corresponding to a single non-air reference sample with respect to matrix W. A K is the matrix of the system of linear equations corresponding to a single non-air reference sample with respect to matrix A. W K is the matrix of the system of linear equations corresponding to all non-air reference samples with respect to matrix W. A It is the matrix of the linear equations corresponding to matrix A for all non-air reference samples.

[0100] This invention solves the modulation matrix and analysis matrix by using the eigenvalue calibration method, and calibrates the azimuth information or error of the polarization element in the system. This eliminates the need for further feedback adjustment of the azimuth error, reducing the difficulty and complexity of system implementation.

[0101] This invention can be used not only in a through-type four-photonic Mueller matrix polarization system but also in an oblique-incidence four-photonic Mueller matrix polarization system. It only requires measuring an isotropic thin film sample to complete the calibration based on the through-type measurement of air and a 0-degree polarizer, and at the same time calibrating the system's incident angle.

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

[0103] What needs to be solved is the eigenvalue corresponding to the zero eigenvalue of the K matrix by using the complete light intensity projection matrix or the transition matrix. Specifically, the solution of A is K A The solution of W is K W The solution of W is K

[0104] The present application provides a four-optical-polarimetry-modulator-type Mueller matrix polarimeter system calibration and measurement method, and all system parameters are calibrated in two steps. In the first step, the dynamic system parameters of the system are calibrated by a nonlinear regression method, and the light intensity projection matrix is obtained. In the second step, the static system parameters are calibrated by an eigenvalue calibration method. This method uses two novel basis vectors to project the continuous modulation spectrum in the time domain into a light intensity projection matrix independent of time by a nonlinear regression method. By measuring a series of samples, the matrix containing system configuration information is obtained based on the eigenvalue, the eigenvector and the matrix correlation theory, and the system calibration is realized. Compared with existing calibration methods, this method does not depend on an accurate system model, can calibrate all system parameters in the system under any effective azimuth angle configuration, and has the advantages of simple calibration operation, high calibration precision, strong noise resistance, wide adaptability and the like.

[0105] The method comprises the following steps:

[0106] A series of calibration samples are measured, and sufficient light intensity information of the plurality of calibration samples is collected.

[0107] A new model is constructed by introducing a basis vector containing dynamic system parameters and a light intensity projection matrix containing static system parameters and sample information, and the dynamic system parameters in the basis vector are calibrated by a nonlinear regression method, and a discrete light intensity projection matrix is obtained.

[0108] The light intensity projection matrix of the calibration sample is processed by using an eigenvalue calibration method, the modulation matrix of the polarizer arm and the analysis matrix of the analyser arm are solved and obtained, and the calibration of the static system parameters of the system is completed.

[0109] Further, in another embodiment, a parameter calibration system of 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 the computer program to perform the parameter calibration method of the four photoelastic modulator type Mueller matrix polarization system according to any one of the preceding embodiments.

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

[0111] In the transmission type calibration, the zero degree of the 0° azimuth polarizer can be taken as the reference zero degree, and the azimuth angles of the calibration in the embodiment are all relative to the relative azimuth angle of the 0° azimuth polarizer, which can be used as absolute angles in the transmission system. In the following, the azimuth angles of the devices obtained by the calibration are not described as relative azimuth angles, and the system configuration is shown in Table 1.

[0112] Table 1 System configuration table

[0113]

[0114] Open the four photoelastic modulators, and measure the air, the polarizer with an azimuth angle of 0°, the polarizer with an azimuth angle of about 90°, and the 1 / 4 wave plate with an azimuth angle of about 30°, respectively.

[0115] Introduce the basis vectors as shown in formulas (3) and (4), wherein the initial value of the peak retardation is selected as the reference value on the photoelastic modulator controller, which is obtained by the applied control voltage based on the approximate linear relationship between the peak retardation and the control voltage, the initial values of the frequency and the initial phase are obtained by the reference signal, and the initial value of the light intensity projection matrix is a randomly generated 9×9 real number matrix. Then, the dynamic system parameters in the basis vectors and the light intensity projection matrix can be obtained by fitting the measured frequency domain light intensity according to formula (2), Figure 4 For the light intensity fitting effect of this step, the light intensity can still be accurately fitted under the interference of 27 dB random noise.

[0116] According to the obtained light intensity projection matrix, the modulation matrix and the analysis matrix are obtained by using the eigenvalue calibration method, that is, the calibration of the static system parameters is realized. In order to verify the accuracy of the calibration result, the polarizer with multiple azimuth angles and the 1 / 3 wave plate are selected as the to-be-measured samples for simulation verification. Similarly, the light intensity projection matrix of the to-be-measured sample is obtained by the nonlinear regression method, and the Mueller matrix of the to-be-measured sample is solved in an analytical way under the condition that the modulation matrix and the analysis matrix have been calibrated. Figure 5 is the comparison between the Mueller matrix of the to-be-measured sample measured based on the calibration method of the present application and the reference value, Figure 6 is the error of the Mueller matrix of the to-be-measured sample measured based on the calibration method of the present application. Under the interference of 27 dB noise, the measurement error is within six thousandths.

[0117] It is to be understood that the above description is intended to be illustrative and not restrictive. Many other embodiments will be apparent to those of skill in the art upon reading and understanding the above description. The scope of the application should, therefore, be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.

Claims

1. A method of parameter calibration of a Mueller matrix polarimetry system of the four photoelastic modulator type, wherein, The polarization system comprises, sequentially along an optical path, a light source module, a polarizing arm, a sample site, an analyzing arm, a collection lens and a detector, the polarizing arm comprises, sequentially, a polarizer, a first photoelastic modulator and a second photoelastic modulator, the analyzing arm comprises, sequentially, a third photoelastic modulator, a fourth photoelastic modulator and an analyzer; characterized in that the parameter calibration method comprises: performing a polarization experiment based on the polarization system and collecting an experimental light intensity signal; introducing an analyzing arm basis vector and a polarizing arm basis vector containing dynamic parameters of the polarization system, and establishing a calculation model of the light intensity signal with respect to the analyzing arm basis vector, a light intensity projection matrix and the polarizing arm basis vector; based on the polarization experiment and the calculation model of the light intensity signal, calibrating the dynamic parameters of the polarization system in the analyzing arm basis vector and the polarizing arm basis vector by a nonlinear regression method; wherein the dynamic parameters of the polarization system include peak retardation, modulation frequency and initial phase of each photoelastic modulator; 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 retardation of the contained photoelastic modulators and the product thereof.

2. The method of claim 1, wherein the four-beam polarimetric modulator type Mueller matrix polarization system is a four-beam polarimetric modulator type Mueller matrix polarization system. said depolarizing arm base vector S A and said polarizing arm base vector S W as follows: ； ； wherein represents a dynamic delay portion in the phase delay amount of the photoelastic modulator, subscripts 1 to 4 of the photoelastic modulator; F , , are the peak delay amount, the frequency, and the initial phase of the photoelastic modulator, respectively.

3. The method of claim 1, wherein the four-beam polarimetric modulator type Mueller matrix polarization system is a four-beam polarimetric modulator type Mueller matrix polarization system. based on the polarization experiment and the calculation model of the light intensity signal, calibrating the dynamic parameters of the polarization system in the analyzing arm basis vector and the polarizing arm basis vector by a nonlinear regression method, further comprising calibrating the light intensity projection matrix by a nonlinear regression method, specifically comprising: determining initial values of the dynamic parameters of the polarization system and the light intensity projection matrix; starting from the initial values, optimizing the parameters in the calculation model of the light intensity signal with the purpose of minimizing the error between the calculation value of the light intensity signal and the experimental value in the polarization experiment, and finally calibrating the parameters in the calculation model of the light intensity signal, including the dynamic parameters of the polarization system and the light intensity projection matrix.

4. The method of claim 3, wherein the four-beam polarimetric modulator type Mueller matrix polarization system is a four-beam polarimetric modulator type Mueller matrix polarization system. determining the initial values of the dynamic parameters of the polarization system and the light intensity projection matrix specifically comprises: determining the initial values of the peak retardation of each photoelastic modulator according to the control voltages of each photoelastic modulator in the polarization experiment; determining the initial values of the modulation frequency and the initial phase of each photoelastic modulator according to the control signals and the experimental light intensity signal of each photoelastic modulator in the polarization experiment; determining the initial value of the light intensity projection matrix by a random generation method.

5. The method of claim 3, wherein the four-beam polarimetric modulator type Mueller matrix polarization system is a four-beam polarimetric modulator type Mueller matrix polarization system. performing a polarization experiment based on the polarization system and collecting an experimental light intensity signal, specifically comprising: selecting a plurality of calibration samples and performing polarization experiments respectively; correspondingly, the parameter calibration method further comprises: introducing an analyzing arm analysis matrix and a polarizing arm modulation matrix containing static parameters of the polarization system, and establishing a calculation model of the light intensity projection matrix with respect to the analyzing arm analysis matrix, a sample Mueller matrix and the polarizing arm modulation matrix; calibrating the light intensity projection matrix corresponding to each of the plurality of calibration samples by a nonlinear regression method; based on the calculation model of the light intensity projection matrix, using an eigenvalue calibration method to solve the light intensity projection matrix of the plurality of calibration samples to obtain the analyzing arm analysis matrix and the polarizing arm modulation matrix, and completing the calibration of the static system parameters of the system; wherein the static system parameters of the system include the azimuth angle of the polarizer, the azimuth angle of the analyzer, the azimuth angle of each photoelastic modulator and the static retardation of each photoelastic modulator.

6. The method of claim 5, wherein the four-beam polarimetric modulator type Mueller matrix polarization system is a four-beam polarimetric modulator type Mueller matrix polarization system. The calculation model of the light intensity signal and the calculation model of the light intensity projection matrix are as follows: ； wherein is the light intensity signal; S A is the analyser arm basis vector; S W is the polariser arm basis vector; B is the light intensity projection matrix; M S is the Mueller matrix of the sample; A is the analyser arm analysis matrix; W is the polariser arm modulation matrix.

7. The method of claim 6, wherein the four-beam polarimetric modulator type Mueller matrix polarization system is a four-beam polarimetric modulator type Mueller matrix polarization system. The plurality of calibration samples include air and at least two non-air samples; Solving the obtained analyzing matrix of the polarizing prism and the modulating matrix of the polarizer specifically includes: Processing the light intensity projection matrix of the plurality of calibration samples to obtain a transition matrix, and the transition matrix is constructed as follows: ； ； Where + represents the Moore-Penrose generalized inverse, the Mueller matrix element of air is the identity matrix, the light intensity projection matrix of air is B0, and the light intensity projection matrices of other samples are... ; Representing the j The Mueller matrix of a non-air sample, C W It is the transition matrix corresponding to the starting arm, C A It is the transition matrix corresponding to the bias detection arm; Based on the transition matrix, the Mueller matrix elements of each non-air sample are determined by the eigenvalue calibration method; Vectorizing the transition matrix to construct a linear equation group matrix of each non-air sample; Based on the Mueller matrix elements of each non-air sample and the linear equation group matrix of all non-air samples, the analyzing matrix of the polarizing prism and the modulating matrix of the polarizer are determined by the eigenvalue calibration method.

8. The method of claim 7, wherein the four-beam polarimetric modulator type Mueller matrix polarization system is a four-beam polarimetric modulator type Mueller matrix polarization system. Based on the linear equation group matrix of all non-air samples, the analyzing matrix of the polarizing prism and the modulating matrix of the polarizer are determined by the eigenvalue calibration method, specifically including: Based on the linear equation group matrix corresponding to the matrix A of all non-air samples, the eigenvector corresponding to the zero eigenvalue is solved, and the analyzing matrix A of the polarizing prism is determined based on the eigenvector; Based on the linear equation group matrix corresponding to the matrix W of all non-air samples, the eigenvector corresponding to the zero eigenvalue is solved, and the modulating matrix W of the polarizer is determined based on the eigenvector.

9. A system for calibrating parameters of a Mueller matrix polarimetry system of the four photoelastic modulator type, characterized in that, The system includes a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the parameter calibration method of the four photoelastic modulator type Mueller matrix polarization system according to any one of claims 1-8.

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