High-stability and high-precision Stokes-Mueller imager instrument matrix integrated optimization method

Abstract

The invention discloses a high-stability and high-precision Stokes-Mueller imager instrument matrix integrated optimization method, relates to the technical field of polarization detection, and can realize in-situ integrated optimization of instrument matrixes of Stokes-Mueller imaging polarizers configured by different polarization state generators (PSGs) and polarization state analyzers (PSAs). According to the method, the polarization characteristics of the non-polarization elements are considered, the instrument matrix of the Stokes-Mueller imager is optimized again, and the optimal instrument measurement parameters are obtained. And the anti-noise capability of the whole instrument is improved, so that the stability is improved, and the measurement precision of the instrument is improved. The method is not only suitable for the optimization of a reflection type Stokes-Mueller imager, but also suitable for the optimization of a transmission type Stokes-Mueller imager.

Description

Technical Field

[0001] The invention relates to the technical field of polarization detection, and in particular to an integrated optimization method for a high-stability and high-precision Stokes-Mueller imager instrument matrix. Background Art

[0002] The Stokes-Mueller imaging polarimeter can obtain the image information of the sample while detecting all the polarization information of the sample. Due to its non-invasive, non-contact and highly sensitive characteristics, it has attracted widespread attention in the fields of biomedicine, materials science, quantum, etc. The key to the Stokes-Mueller imaging polarimeter's ability to detect the polarization information of the sample is that the polarization state generator PSG can generate a variety of specific incident polarization states by changing the device parameters, and the polarization state analyzer PSA can generate a variety of specific detection polarization states by changing the device parameters. The matrix composed of all incident polarization states is the instrument matrix of PSG, and the matrix composed of all detection polarization states is the instrument matrix of PSA.

[0003] The instrument matrices used in the current Stokes-Mueller imaging polarimeter PSA and PSG only consider the polarization characteristics of the polarization modulation devices in PSA and PSG, thereby optimizing the obtained results.

[0004] For example, in the double rotating wave plate method, both PSA and PSG consist of a polarizer with an azimuth angle of 0° and a quarter-wave plate with adjustable azimuth angle. After the instrument matrix is ​​optimized, the optimal azimuth angles are ±15° and ±50.3°.

[0005] Liquid crystal modulation method, PSA and PSG are composed of a polarizer with an azimuth angle of 0°, two fixed azimuth angles of 27.4° and 72.4° respectively, and a liquid crystal variable phase retarder with adjustable phase retardation. After the instrument matrix is ​​optimized, the optimal phase retardation of the two liquid crystals is 135° and 315° respectively.

[0006] The polarization state analyzer based on the polarization camera is used as a PSA with a liquid crystal variable phase retarder with variable azimuth angle and variable delay amount in front. After the instrument matrix is ​​optimized, the azimuth angle of the liquid crystal variable phase retarder is arbitrary, and the phase delay amount is 90° and 0°.

[0007] All of the above instrument matrices ignore the polarization characteristics of the non-polarizing elements in the instrument and their influence on the incident polarization state and the detected polarization state. This will result in the instrument matrix not being in the optimal configuration during the actual measurement process, thereby reducing the instrument's anti-noise capability and further reducing the instrument's measurement accuracy. There is currently no solution to this problem. Summary of the invention

[0008] In view of this, the present invention provides a high-stability and high-precision Stokes-Mueller imager instrument matrix integrated optimization method, which can realize in-situ integrated optimization of the instrument matrix of Stokes-Mueller imaging polarimeter configured with different polarization state generators PSG and polarization state analyzers PSA, thereby improving the overall anti-noise ability of the instrument, thereby improving the stability and improving the measurement accuracy of the instrument.

[0009] To achieve the above object, the technical solution of the present invention is: the Stokes-Mueller imager is a coaxial reflection-type Stokes-Mueller imaging polarimeter or a transmission-type Stokes-Mueller imaging polarimeter, and the following steps are used to perform integrated optimization of the instrument matrix:

[0010] Step 1: Set the calibration elements, at least three elements, two polarizers, the azimuth angle difference of the polarizers is 90 degrees and a wave plate.

[0011] Step 2: Select three positions, position 1 is the detection sample position of the Stokes-Mueller imager instrument, position 2 is the light input position of the polarization state analyzer PSA, and position 3 is the light output position of the polarization state generator PSG.

[0012] Step 3: Calibrate two instrument matrices at the three selected positions respectively, including the instrument matrix of all devices before the light reaches the calibration element and the instrument matrix of all devices after leaving the calibration element; the two matrices obtained at position 1 are A and G; the two instrument matrices obtained at position 2 are A1 and G1; the two instrument matrices obtained at position 3 are A2 and G2.

[0013] Step 4: Use the instrument matrix calibrated in step 3 to calculate the forward propagation Mueller matrix NPO of the non-polarized element f and the backward pass Mueller matrix NPO b .

[0014] Step 5: Substitute the forward and backward transferred Mueller matrices of the non-polarizing element into the ideal polarization state generator PSG and polarization state analyzer PSA instrument matrices for correction, and re-optimize the measurement parameters of the Stokes-Mueller imager instrument using the optimization objective of minimizing the instrument matrix condition number.

[0015] Furthermore, in step one, the calibration elements are set to be an eighth wave plate with an azimuth angle of 30°, a quarter wave plate with an azimuth angle of 30°, a polarizer with an azimuth angle of 0°, and a polarizer with an azimuth angle of 90°.

[0016] Furthermore, when the Stokes-Mueller imager is a coaxial reflection Stokes-Mueller imaging polarimeter, the basic structure includes a reflector, an objective lens module, a beam splitter module, a polarization state analyzer PSA and a polarization state generator PSG.

[0017] Then in step 2, the selected position 1 is between the reflector and the objective lens module.

[0018] The selected position 2 is between the beam splitter module and the polarization state analyzer PSA.

[0019] The selected position 3 is between the polarization state generator PSG and the beam splitter module.

[0020] Furthermore, the process of obtaining two matrices A and G at position 1 is specifically as follows:

[0021] Sa1, firstly, an eighth wave plate with an azimuth angle of 30°, a polarizer with an azimuth angle of 0°, and a polarizer with an azimuth angle of 90° are placed between the reflector and the objective lens module, and Stokes-Mueller imaging is performed to obtain four groups of light intensities, namely, I mirror ,I1,I2,I3; among them, I mirror is the light intensity matrix without sample, I1 and I2 are the light intensity matrices measured by polarizers with azimuth angles of 0° and 90°, and I3 is the light intensity matrix measured by an eighth wave plate with an azimuth angle of 30°.

[0022] Sa2, constructs the intermediate matrices C1, C2, C3 using the measured light intensity:

[0023]

[0024]

[0025] Sa3, further obtained:

[0026] M m M1G-GC1=0

[0027] M m M2G-GC2 = 0

[0028] M m M3G-GC3=0

[0029] Where M1, M2, and M3 are the Mueller matrices of different calibration elements;

[0030] Sa4, solve M1, M2, and M3 based on the model of the calibration component and the eigenvalues ​​of C1, C2, and C3.

[0031] Sa5, construct the equation:

[0032]

[0033] Where E is a 4×4 unit matrix, vec is a matrix straightening operator, is the Kronecker product operator.

[0034] H1vec(G)=0;

[0035] Further deformation, Similarly, construct

[0036]

[0037] This gives us the L matrix:

[0038]

[0039] L·vec(G)=0

[0040] The solution of the L matrix composed of different calibration elements with an eigenvalue of 0 must be unique. G is the solution vector when the eigenvalue of the L matrix is ​​0. Then according to I mirror =A·M m ·G can be used to obtain the A matrix. So far, the two matrices A and G corresponding to position 1 have been obtained.

[0041] Furthermore, position 2 uses the following steps to obtain two matrices A1 and G1:

[0042] Sb1, firstly, a quarter wave plate with an azimuth angle of 30°, a polarizer with an azimuth angle of 0°, and a polarizer with an azimuth angle of 90° are placed between the beam splitter module and the polarization state analyzer PSA, and Stokes-Mueller imaging is performed to obtain four groups of light intensities, namely, I air ,I A1 ,I A2 ,I A3 ; where I air is the light intensity matrix when there is no sample at position 2; I A1 ,I A2 is the light intensity matrix measured by polarizers with azimuth angles of 0° and 90°, I A3 This is the light intensity matrix measured for a quarter-wave plate with an azimuth angle of 30°.

[0043] Sb2, construct the intermediate matrix C using the measured light intensity A1 , C A2 , C A3 :

[0044]

[0045]

[0046] Sb3, thus we get:

[0047] M A1 G1-G1C A1 =0

[0048] M A2 G1-G1C A2 =0

[0049] M A3 G1-G1C A3 =0

[0050] Among them, M A1 ,M A2 ,M A3 Here we show the Mueller matrices of the 0° and 90° polarizers and the 30° quarter-wave plate respectively.

[0051] Sb4, according to the calibration component model and C A1 , C A2 , C A3 The eigenvalue solution is M A1 ,M A2 ,M A3 .

[0052] Sb5, construct the equation:

[0053]

[0054] Where E is a 4×4 unit matrix, vec is a matrix straightening operator, is the Kronecker product operator.

[0055] Simplified expression:

[0056] H A1 vec(G1)=0

[0057] Further transformed into:

[0058]

[0059] Similarly, construct

[0060]

[0061] From this we get L A matrix:

[0062]

[0063] L A vec(G1)=0

[0064] Where G1 is LA The solution vector when the matrix eigenvalue is 0, and then according to I air =A1·G1, then we get the A1 matrix.

[0065] Furthermore, position 3 uses the following steps to obtain two matrices A2 and G2:

[0066] Sc1: First, a quarter wave plate with an azimuth angle of 30°, a polarizer with an azimuth angle of 0°, and a polarizer with an azimuth angle of 90° are placed between the polarization state generator PSG and the spectroscope module. The instrument matrix of all devices before reaching the calibration element is represented by G2, and the instrument matrix of all devices after leaving the calibration element is represented by A2; Stokes-Mueller imaging is performed, and four groups of light intensities are obtained, namely, I air1 ,I G1 ,I G2 ,I G3 ; where I air1 is the light intensity matrix when there is no sample at position 2; I G1 ,I G2 is the light intensity matrix measured by polarizers with azimuth angles of 0° and 90°, I G3 This is the light intensity matrix measured for a quarter-wave plate with an azimuth angle of 30°.

[0067] Sc2: Construct the intermediate matrix C using the measured light intensity G1 , C G2 , C G3 :

[0068]

[0069]

[0070] Sc3, thus we get:

[0071] M G1 G2-G2C G1 =0

[0072] M G2 G2-G2C G2 =0

[0073] M G3 G2-G2C G3 =0

[0074] Among them, M G1 ,M G2 ,M G3 Here we show the Mueller matrices of the 0° and 90° polarizers and the 30° quarter-wave plate respectively.

[0075] Sc4, according to the model of the calibration component and C G1 , CG2 , C G3 The eigenvalue solution is M G1 ,M G2 ,M G3 .

[0076] Sc5, construct the equation:

[0077]

[0078] Where E is a 4×4 unit matrix, vec is a matrix straightening operator, is the Kronecker product operator.

[0079] Simplified expression:

[0080] H G1 vec(G2)=0

[0081] Further transformed into:

[0082]

[0083] Similarly, construct

[0084]

[0085] From this we get L G matrix:

[0086]

[0087] L G vec(G2)=0

[0088] Where G2 is L G The solution vector when the matrix eigenvalue is 0, and then according to I air1 =A2·G2, then we get the A2 matrix.

[0089] Furthermore, the Stokes-Mueller imager is a transmission-type Stokes-Mueller imaging polarimeter, and its basic structure includes a light source, a polarization state generator PSG, a condenser, an objective lens and a polarization state analyzer PSA.

[0090] Then in step 2, the selected position 1 is between the condenser and the objective lens.

[0091] The selected position 2 is between the objective lens and the polarization state analyzer PSA.

[0092] The selected position 3 is between the polarization state generator PSG and the condenser.

[0093] Furthermore, the Stokes-Mueller imager is a transmission-type Stokes-Mueller imaging polarimeter, and the instrument matrices obtained by calibration at three positions are A and G, A1 and G1, and A2 and G2 respectively; the calibration at the three positions adopts the following process:

[0094] A' refers to A, A1 or A2, and G' refers to G, G1 or G2.

[0095] Sd1, first place a quarter wave plate with an azimuth angle of 30°, a polarizer with an azimuth angle of 0°, and a polarizer with an azimuth angle of 90° at positions n, where n is 1, 2, or 3, and perform Stokes-Mueller imaging to obtain four groups of light intensities, I air ',I A1 ',I A2 ',I A3 '; where I air ' is the light intensity matrix when there is no sample at position 2; I A1 ',I A2 ' is the light intensity matrix measured by polarizers with azimuth angles of 0° and 90°, I A3 ' is the light intensity matrix measured by a quarter wave plate with an azimuth angle of 30°.

[0096] Sd2, constructing the intermediate matrix C using the measured light intensity A1 '、C A2 '、C A3 ':

[0097] C A1 '=(I air ') -1 I A1 '

[0098] C A2 '=(I air ') -1 I A2 '

[0099] C A3 '=(I air ') -1 I A3 '

[0100] Sd3, thus we get:

[0101] M A1 'G1'-G1'C A1 '=0

[0102] M A2 'G1'-G1'C A2 '=0

[0103] M A3 'G1'-G1'C A3 '=0

[0104] Among them, M A1 '、M A2 '、M A3 Here, ' represents the Mueller matrix of the 0° and 90° polarizers and the 30° quarter-wave plate respectively.

[0105] Sd4, according to the model of the calibration component and C A1 '、C A2 '、C A3 'Eigenvalue solution M A1 '、M A2 '、M A3 '.

[0106] Sd5, construct the equation:

[0107]

[0108] Where E is a 4×4 unit matrix, vec is a matrix straightening operator, is the Kronecker product operator.

[0109] Simplified expression:

[0110] H A1 'vec(G1')=0

[0111] Further transformed into:

[0112] (H A1 ') T ·H A1 'vec(G1')=0

[0113] Similarly, construct

[0114]

[0115]

[0116] From this we get L A 'The matrix is:

[0117] L A '=(H A1 ') T ·H A1 +(H A2 ') T ·H A2 +(H A3 ') T ·H A3

[0118] LA '·vec(G1')=0

[0119] Where G' is L A 'The solution vector when the matrix eigenvalue is 0, and then according to I air '=A'·G', then we get the A' matrix.

[0120] Furthermore, step five: substitute the forward and backward propagation Mueller matrices of the non-polarizing element into the ideal polarization state generator PSG and polarization state analyzer PSA instrument matrices for correction, and re-optimize the measurement parameters of the Stokes-Mueller imager instrument using the optimization objective of minimizing the instrument matrix condition number, specifically:

[0121] After obtaining the instrument matrix at the three positions, calculate the polarization characteristics of the non-polarizing optical element. The specific method is:

[0122] Forward Mueller Matrix of Non-Polarizing Optics NPO f :

[0123] NPO f =G·G2 -1

[0124] Backward Mueller Matrix of Non-Polarizing Optical Components NPO b :

[0125] NPO b =A1 -1 ·A

[0126] The forward and backward matrices of the obtained non-polarized optical element are respectively introduced into the ideal instrument matrix optimization model:

[0127] Modified PSA instrument matrix A * :

[0128] A * =A Ideal NPO b

[0129] Corrected PSG instrument matrix G * :

[0130] G * =NPO f ·G Ideal

[0131] A Ideal and G Ideal It is an ideal instrument matrix model.

[0132] Beneficial effects:

[0133] 1. The present invention provides a high-stability and high-precision Stokes-Mueller imager instrument matrix integrated optimization method, which can realize in-situ integrated optimization of the instrument matrix of the Stokes-Mueller imaging polarimeter configured with different polarization state generators PSG and polarization state analyzers PSA, takes into account the polarization characteristics of non-polarizing elements, realizes the re-optimization of the Stokes-Mueller imager instrument matrix, and obtains the best instrument measurement parameters. The overall anti-noise ability of the instrument is improved, thereby improving the stability and the measurement accuracy of the instrument. This method is not only applicable to the optimization of reflective Stokes-Mueller imagers, but also to the optimization of transmissive Stokes-Mueller imagers.

[0134] 2. This method is applicable to the optimization of Stokes-Mueller imagers with various polarization modulation methods, such as the double rotating wave plate method, liquid crystal modulation method, and polarization modulation based on polarization cameras.

[0135] 3. This method requires step-by-step calibration at three locations: the light output of the polarization state generator, the sample, and the light input of the polarization state analyzer to obtain the polarization parameters of the non-polarizing element.

[0136] 4. The optimization process of this optimization method does not change the optical path of the Stokes-Mueller imager, and takes into account the polarization characteristics of all non-polarizing components in the instrument, thus achieving online integrated optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0137] Figure 1 . Schematic diagram of the basic structure of the coaxial reflection Stokes-Mueller imager; reflector 101, objective lens module 102, spectroscope module 103, polarization state analyzer 104, polarization state generator 105, light source 106;

[0138] Figure 2 . Schematic diagram of the basic structure of a transmission Stokes-Mueller imager; light source 201, polarization state generator 201, condenser 203, objective lens 204, polarization state analyzer 205. DETAILED DESCRIPTION

[0139] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0140] The present invention provides a high-stability and high-precision Stokes-Mueller imager instrument matrix integrated optimization method, characterized in that the Stokes-Mueller imager is a coaxial reflection Stokes-Mueller imaging polarimeter or a transmission Stokes-Mueller imaging polarimeter, and the instrument matrix is ​​integratedly optimized by the following steps:

[0141] Step 1: Set the calibration elements, at least three elements, two polarizers, the azimuth angle difference of the polarizers is 90 degrees and a wave plate;

[0142] Step 2: Select three positions, position 1 is the detection sample of the Stokes-Mueller imager, position 2 is the light input position of the polarization state analyzer PSA, and position 3 is the light output position of the polarization state generator PSG;

[0143] Step 3: calibrate two instrument matrices at the three selected positions respectively, including the instrument matrices of all devices before the light reaches the calibration element and the instrument matrices of all devices after leaving the calibration element; the two matrices obtained at position 1 are A and G; the two instrument matrices obtained at position 2 are A1 and G1; the two instrument matrices obtained at position 3 are A2 and G2;

[0144] Step 4: Use the instrument matrix calibrated in step 3 to calculate the forward propagation Mueller matrix NPO of the non-polarized element f and the backward pass Mueller matrix NPO b ;

[0145] Step 5: Substitute the forward and backward transferred Mueller matrices of the non-polarizing element into the ideal polarization state generator PSG and polarization state analyzer PSA instrument matrices for correction, and re-optimize the measurement parameters of the Stokes-Mueller imager instrument using the optimization objective of minimizing the instrument matrix condition number.

[0146] In the embodiment of the present invention, in step one, the calibration elements are set to be an eighth wave plate with an azimuth angle of 30°, a quarter wave plate with an azimuth angle of 30°, a polarizer with an azimuth angle of 0°, and a polarizer with an azimuth angle of 90°.

[0147] In the embodiment of the present invention, when the Stokes-Mueller imager is a coaxial reflection Stokes-Mueller imaging polarimeter, the basic structure includes a reflector 101, an objective lens module 102, a beam splitter module 103, a polarization state analyzer PSA104 and a polarization state generator PSG105;

[0148] Then in step 2, the selected position 1 is between the reflector 101 and the objective lens module 102;

[0149] The selected position 2 is between the beam splitter module 103 and the polarization state analyzer PSA 104;

[0150] The selected position 3 is between the polarization state generator PSG 105 and the beam splitter module 103 .

[0151] Then the process of obtaining two matrices A and G for position 1 is as follows:

[0152] Sa1, firstly, an eighth wave plate with an azimuth angle of 30°, a polarizer with an azimuth angle of 0°, and a polarizer with an azimuth angle of 90° are placed between the reflector 101 and the objective lens module 102, respectively, and Stokes-Mueller imaging is performed to obtain four groups of light intensities, namely, I mirror ,I1,I2,I3; among them, I mirror is the light intensity matrix without sample, I1 and I2 are the light intensity matrices measured by polarizers with azimuth angles of 0° and 90°, and I3 is the light intensity matrix measured by an eighth wave plate with an azimuth angle of 30°;

[0153] Sa2, constructs the intermediate matrices C1, C2, C3 using the measured light intensity:

[0154]

[0155]

[0156] Sa3, further obtained:

[0157] M m M1G-GC1=0

[0158] M m M2G-GC2 = 0

[0159] M m M3G-GC3=0

[0160] Where M1, M2, and M3 are the Mueller matrices of different calibration elements;

[0161] Sa4, solve M1, M2, M3 according to the model of the calibration component and the eigenvalues ​​of C1, C2, C3;

[0162] Sa5, construct the equation:

[0163]

[0164] Where E is a 4×4 unit matrix, vec is a matrix straightening operator, is the Kronecker product operator;

[0165] H1vec(G)=0;

[0166] Further deformation, Similarly, construct

[0167]

[0168]

[0169] This gives us the L matrix:

[0170]

[0171] L·vec(G)=0

[0172] The solution of the L matrix composed of different calibration elements with an eigenvalue of 0 must be unique. G is the solution vector when the eigenvalue of the L matrix is ​​0. Then according to I mirror =A·M m ·G can be used to obtain the A matrix. So far, the two matrices A and G corresponding to position 1 have been obtained.

[0173] For position 2, the following steps are used to obtain two matrices A1 and G1:

[0174] Sb1, firstly, a quarter wave plate with an azimuth angle of 30°, a polarizer with an azimuth angle of 0°, and a polarizer with an azimuth angle of 90° are placed between the beam splitter module 103 and the polarization state analyzer PSA104, and Stokes-Mueller imaging is performed to obtain four groups of light intensities, namely, I air ,I A1 ,I A2 ,I A3 ; where I air is the light intensity matrix when there is no sample at position 2; I A1 ,I A2 is the light intensity matrix measured by polarizers with azimuth angles of 0° and 90°, I A3 The light intensity matrix measured by a quarter-wave plate with an azimuth angle of 30°;

[0175] Sb2, construct the intermediate matrix C using the measured light intensity A1 , C A2 , C A3 :

[0176]

[0177]

[0178] Sb3, thus we get:

[0179] M A1 G1-G1C A1 =0

[0180] M A2 G1-G1C A2 =0

[0181] M A3 G1-G1C A3 =0

[0182] Among them, M A1 ,M A2 ,M A3 Here we represent the Mueller matrices of the 0° and 90° polarizers, and the 30° quarter-wave plate;

[0183] Sb4, according to the calibration component model and C A1 , C A2 , C A3 The eigenvalue solution is M A1 ,M A2 ,M A3 ;

[0184] Sb5, construct the equation:

[0185]

[0186] Where E is a 4×4 unit matrix, vec is a matrix straightening operator, is the Kronecker product operator;

[0187] Simplified expression:

[0188] H A1 vec(G1)=0;

[0189] Further transformed into:

[0190]

[0191] Similarly, construct

[0192]

[0193] From this we get L A matrix:

[0194]

[0195] L A vec(G1)=0

[0196] Where G1 is L A The solution vector when the matrix eigenvalue is 0, and then according to I air =A1·G1, then we get the A1 matrix.

[0197] For position 3, the following steps are used to obtain two matrices A2 and G2:

[0198] Sc1: First, a quarter wave plate with an azimuth angle of 30°, a polarizer with an azimuth angle of 0°, and a polarizer with an azimuth angle of 90° are placed between the polarization state generator PSG105 and the spectroscope module 103, respectively. The instrument matrix of all devices before reaching the calibration element is represented by G2, and the instrument matrix of all devices after leaving the calibration element is represented by A2; Stokes-Mueller imaging is performed, and four groups of light intensities are obtained, namely, I air1 ,I G1 ,I G2 ,I G3 ; where I air1 is the light intensity matrix when there is no sample at position 2; I G1 ,I G2 is the light intensity matrix measured by polarizers with azimuth angles of 0° and 90°, I G3 The light intensity matrix measured by a quarter-wave plate with an azimuth angle of 30°;

[0199] Sc2: Construct the intermediate matrix C using the measured light intensity G1 , C G2 , C G3 :

[0200]

[0201]

[0202] Sc3, thus we get:

[0203] M G1 G2-G2C G1 =0

[0204] M G2 G2-G2C G2 =0

[0205] M G3 G2-G2C G3 =0

[0206] Among them, M G1 ,M G2 ,M G3 Here we represent the Mueller matrices of the 0° and 90° polarizers, and the 30° quarter-wave plate;

[0207] Sc4, according to the model of the calibration component and C G1 , C G2 , C G3 The eigenvalue solution is M G1 ,M G2 ,M G3;

[0208] Sc 5, construct the equation:

[0209]

[0210] Where E is a 4×4 unit matrix, vec is a matrix straightening operator, is the Kronecker product operator;

[0211] Simplified expression:

[0212] H G1 vec(G2)=0;

[0213] Further transformed into:

[0214]

[0215] Similarly, construct

[0216]

[0217] From this we get L G matrix:

[0218]

[0219] L G vec(G2)=0

[0220] Where G2 is L G The solution vector when the matrix eigenvalue is 0, and then according to I air1 =A2·G2, then we get the A2 matrix.

[0221] In the embodiment of the present invention, when the Stokes-Mueller imager is a transmission-type Stokes-Mueller imaging polarimeter, its basic structure includes a light source 201, a polarization state generator PSG202, a condenser 203, an objective lens 204 and a polarization state analyzer PSA205;

[0222] Then in step 2, the selected position 1 is between the condenser lens 203 and the objective lens 204;

[0223] The selected position 2 is between the objective lens 204 and the polarization state analyzer PSA 205;

[0224] The selected position 3 is between the polarization state generator PSG202 and the focusing mirror 203 .

[0225] In the embodiment of the present invention, when the Stokes-Mueller imager is a transmissive Stokes-Mueller imaging polarimeter, the instrument matrices obtained by calibration at three positions are also A and G, A1 and G1, A2 and G2 respectively; then the calibration at the three positions adopts the following process:

[0226] A' refers to A, A1 or A2, and G' refers to G, G1 or G2;

[0227] Sd1, first place a quarter wave plate with an azimuth angle of 30°, a polarizer with an azimuth angle of 0°, and a polarizer with an azimuth angle of 90° at positions n, where n is 1, 2, or 3, and perform Stokes-Mueller imaging to obtain four groups of light intensities, I air ',I A1 ',I A2 ',I A3 '; where I air ' is the light intensity matrix when there is no sample at position 2; I A1 ',I A2 ' is the light intensity matrix measured by polarizers with azimuth angles of 0° and 90°, I A3 ' is the light intensity matrix measured by a quarter wave plate with an azimuth angle of 30°;

[0228] Sd2, constructing the intermediate matrix C using the measured light intensity A1 '、C A2 '、C A3 ':

[0229] C A1 '=(I air ') -1 I A1 '

[0230] C A2 '=(I air ') -1 I A2 '

[0231] C A3 '=(I air ') -1 I A3 '

[0232] Sd3, thus we get:

[0233] M A1 'G1'-G1'C A1 '=0

[0234] M A2 'G1'-G1'C A2 '=0

[0235] M A3 'G1'-G1'C A3 '=0

[0236] Among them, M A1 ', M A2 ', M A3 'Here are the Mueller matrices of the 0° and 90° polarizers and the 30° quarter-wave plate;

[0237] Sd4, according to the model of the calibration component and C A1 '、C A2 '、C A3 'Eigenvalue solution M A1 ', M A2 ', M A3 ';

[0238] Sd5, construct the equation:

[0239]

[0240] Where E is a 4×4 unit matrix, vec is a matrix straightening operator, is the Kronecker product operator;

[0241] Simplified expression:

[0242] H A1 'vec(G1')=0;

[0243] Further transformed into:

[0244] (H A1 ') T ·H A1 'vec(G1')=0

[0245] Similarly, construct

[0246]

[0247]

[0248] From this we get L A 'The matrix is:

[0249] L A '=(H A1 ') T ·H A1 +(H A2 ') T ·H A2 +(H A3 ') T ·H A3

[0250] L A '·vec(G1')=0

[0251] Where G' is L A 'The solution vector when the matrix eigenvalue is 0, and then according to I air '=A'·G', then we get the A' matrix.

[0252] In the embodiment of the present invention, in step 5, for the instrument optimization of the Stokes-Mueller imaging polarimeter, after obtaining the instrument matrix at three positions, the polarization characteristics of the non-polarizing optical element are calculated. The specific method is:

[0253] Forward Mueller Matrix of Non-Polarizing Optics NPO f :

[0254] NPO f =G·G2 -1

[0255] Backward Mueller Matrix of Non-Polarizing Optical Components NPO b :

[0256] NPO b =A1 -1 ·A

[0257] The forward and backward matrices of the obtained non-polarized optical element are respectively introduced into the ideal instrument matrix optimization model:

[0258] Modified PSA instrument matrix A * :

[0259] A * =A Ideal NPO b

[0260] Corrected PSG instrument matrix G * :

[0261] G * =NPO f ·G Ideal

[0262] A Ideal and G Ideal It is an ideal instrument matrix model.

[0263] The instrument configurations included in the model include but are not limited to the dual rotating wave plate method, liquid crystal modulation method and polarization state analyzer based on polarization camera.

[0264] The specific method is as follows:

[0265] 1. PSA instrument matrix optimization. In theory, the ideal PSA instrument matrix without considering the polarization characteristics of non-polarizing components consists of at least four detection polarization states. The mathematical expression of the detection polarization state is: A q =[a q，0 a q，1 a q,2 a q，3 ], depending on the composition of the polarization state analyzer, such as the double rotating wave plate method, liquid crystal modulation method and polarization state analysis based on polarization camera, the polarization state A is detected q The optimizable parameters include, but are not limited to, the phase retarder azimuth angle and the phase retarder phase delay amount.

[0266] Ideal PSA instrument matrix A Ideal The model is:

[0267]

[0268] Where M is the number of detected polarization states.

[0269] The actual polarization state analyzer instrument matrix A' considering the polarization characteristics of non-polarizing optical elements is modeled as:

[0270]

[0271] Next, A' is optimized to obtain the best instrument measurement parameters. The optimization objectives include but are not limited to the minimum condition number of the matrix A' and the minimum equal weighted variance. The optimization algorithms include but are not limited to global optimization, gradient optimization, and genetic algorithm.

[0272] 2.PSG instrument matrix optimization, theoretically, the ideal PSG instrument matrix without considering the polarization characteristics of non-polarizing components consists of at least four incident polarization states. The mathematical representation of the incident polarization state is: G q =[g 0,q g 1,q g 2,q g 3,q ] T , depending on the composition of the polarization state generator, such as the double rotating wave plate method and the liquid crystal modulation method, the incident polarization state G q The optimizable parameters include, but are not limited to, the phase retarder azimuth angle and the phase retarder phase delay amount.

[0273] Ideal PSG instrument matrix G Ideal The model is:

[0274]

[0275] Where N is the number of incident polarization states;

[0276] The actual polarization state generator instrument matrix considering the polarization characteristics of non-polarizing optical elements is G', and the model is:

[0277]

[0278] Next, G' is optimized to obtain the best instrument measurement parameters. The optimization objectives include but are not limited to the minimum condition number of the matrix G' and the minimum equal weighted variance. The optimization algorithms include but are not limited to global optimization, gradient optimization, and genetic algorithm.

[0279] Simulation calculation as NPO f =NPO b When the dichroisms are 0.1, 0.2, and 0.3 respectively, the actual instrument matrix condition number κ(W) = κ(A)·κ(G) is measured using an ideal instrument matrix. The condition number is used to evaluate the stability of the instrument. The smaller the condition number, the higher the stability of the instrument. NPO is taken into account. f and NPO b After re-optimizing the instrument measurement parameters, the condition number κ(W) of the actual instrument matrix.

[0280] Table 1 Condition numbers of the instrument matrix before and after considering the polarization characteristics of non-polarized devices

[0281] Dichroism 0.1 0.2 0.3 Condition number not considered 9.37 8.44 7.97 Considering the condition number 8.68 7.35 6.54

[0282] To verify the consideration of NPO f and NPO b After re-optimizing the instrument measurement parameters, the effect of improving the measurement accuracy of the instrument matrix. The instrument matrix before and after simulation optimization changes the measurement accuracy of the Mueller matrix of polarizers and quarter-wave plates with different azimuth angles of 0-180 degrees and 10 degrees step when there is Gaussian noise with a standard deviation of 5% in the light intensity signal detected by the detector. The evaluation index is the average root mean square error

[0283]

[0284] Among them, M sample is the Mueller matrix calculated based on the measured light intensity value of the sample, is the theoretical Mueller matrix of the sample, and n is the number of elements in the Mueller matrix.

[0285] Table 2 The influence of the polarization characteristics of non-polarized devices on the measurement accuracy of the instrument before and after considering

[0286]

[0287] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A high stability and high precision Stokes-Mueller imager instrument matrix integrated optimization method, characterized in that: The Stokes-Mueller imager is a coaxial reflection-type Stokes-Mueller imaging polarimeter or a transmission-type Stokes-Mueller imaging polarimeter, and the following steps are used to perform integrated optimization of the instrument matrix: Step 1: Set the calibration elements, at least three elements, two polarizers, the azimuth angle difference of the polarizers is 90 degrees and a wave plate; Step 2: Select three positions, position 1 is the detection sample of the Stokes-Mueller imager, position 2 is the light input position of the polarization state analyzer PSA, and position 3 is the light output position of the polarization state generator PSG; Step 3: calibrating two instrument matrices at the three selected positions respectively, including the instrument matrix of all devices before the light reaches the calibration element and the instrument matrix of all devices after the light leaves the calibration element; The two matrices obtained at position 1 are A and G; the two instrument matrices obtained at position 2 are A1 and G1; the two instrument matrices obtained at position 3 are A2 and G2; Step 4: Use the instrument matrix calibrated in step 3 to calculate the forward propagation Mueller matrix NPO of the non-polarized element f and the backward pass Mueller matrix NPO b ; Step 5: Substitute the forward and backward transferred Mueller matrices of the non-polarizing element into the ideal polarization state generator PSG and polarization state analyzer PSA instrument matrices for correction, and re-optimize the measurement parameters of the Stokes-Mueller imager instrument using the optimization goal of minimizing the instrument matrix condition number.

2. The high stability and high precision Stokes-Mueller imager instrument matrix integrated optimization method as described in claim 1, characterized in that: In the step 1, the calibration elements are set to be an eighth wave plate with an azimuth angle of 30°, a quarter wave plate with an azimuth angle of 30°, a polarizer with an azimuth angle of 0°, and a polarizer with an azimuth angle of 90°.

3. The high stability and high precision Stokes-Mueller imager instrument matrix integrated optimization method as described in claim 2, characterized in that: When the Stokes-Mueller imager is a coaxial reflection type Stokes-Mueller imaging polarimeter, the basic structure comprises a reflector (101), an objective lens module (102), a spectroscope module (103), a polarization state analyzer PSA (104) and a polarization state generator PSG (105); Then in the step 2, the selected position 1 is between the reflector (101) and the objective lens module (102); The selected position 2 is between the beam splitter module (103) and the polarization state analyzer PSA (104); The selected position 3 is between the polarization state generator PSG (105) and the beam splitter module (103).

4. The high stability and high precision Stokes-Mueller imager instrument matrix integrated optimization method as described in claim 3, characterized in that: The process of obtaining two matrices A and G at position 1 is specifically as follows: Sa1, firstly, an eighth wave plate with an azimuth angle of 30°, a polarizer with an azimuth angle of 0°, and a polarizer with an azimuth angle of 90° are placed between the reflector (101) and the objective lens module (102), and Stokes-Mueller imaging is performed to obtain four groups of light intensities, namely, I mirror ,I1,I2,I3; among them, I mirror is the light intensity matrix without sample, I1 and I2 are the light intensity matrices measured by polarizers with azimuth angles of 0° and 90°, and I3 is the light intensity matrix measured by an eighth wave plate with an azimuth angle of 30°; Sa2, constructs the intermediate matrices C1, C2, C3 using the measured light intensity: Sa3, further obtained: M m ·M1G-GC1=0 M m ·M2G-GC2=0 M m ·M3G-GC3=0 Where M1, M2, and M3 are the Mueller matrices of different calibration elements; Sa4, solve M1, M2, M3 according to the model of the calibration component and the eigenvalues ​​of C1, C2, C3; Sa5, construct the equation: Where E is a 4×4 unit matrix, vec is a matrix straightening operator, is the Kronecker product operator; H1vec(G)=0; Further deformation, Similarly, construct This gives us the L matrix: L·vec(G)=0 The solution of the L matrix composed of different calibration elements with an eigenvalue of 0 must be unique. G is the solution vector when the eigenvalue of the L matrix is ​​0. Then according to I mirror =A·M m ·G can be used to obtain the A matrix. So far, the two matrices A and G corresponding to position 1 have been obtained.

5. The high stability and high precision Stokes-Mueller imager instrument matrix integrated optimization method as described in claim 3, characterized in that: The position 2 uses the following steps to obtain two matrices A1 and G1: Sb1, firstly, a quarter wave plate with an azimuth angle of 30°, a polarizer with an azimuth angle of 0°, and a polarizer with an azimuth angle of 90° are placed between the beam splitter module (103) and the polarization state analyzer PSA (104), and Stokes-Mueller imaging is performed to obtain four groups of light intensities, namely, I air ,I A1 ,I A2 ,I A3 ; where I air is the light intensity matrix when there is no sample at position 2; I A1 ,I A2 is the light intensity matrix measured by polarizers with azimuth angles of 0° and 90°, I A3 The light intensity matrix measured by a quarter-wave plate with an azimuth angle of 30°; Sb2, construct the intermediate matrix C using the measured light intensity A1 , C A2 , C A3 : Sb3, thus we get: M A1 G1-G1C A1 =0 M A2 G1-G1C A2 =0 M A3 G1-G1C A3 =0 Among them, M A1 ,M A2 ,M A3 Here we represent the Mueller matrices of the 0° and 90° polarizers, and the 30° quarter-wave plate; Sb4, according to the calibration component model and C A1 , C A2 , C A3 The eigenvalue solution is M A1 ,M A2 ,M A3 ; Sb5, construct the equation: Where E is a 4×4 unit matrix, vec is a matrix straightening operator, is the Kronecker product operator; Simplified expression: H A1 thing(G1)=0; Further transformed into: Similarly, construct From this we get L A matrix: L A ·thing(G1)=0 Where G1 is L A The solution vector when the matrix eigenvalue is 0, and then according to I air =A1·G1, then we get the A1 matrix.

6. The high stability and high precision Stokes-Mueller imager instrument matrix integrated optimization method as described in claim 3, characterized in that: The position 3 obtains two matrices A2 and G2 by the following steps: Sc1: First, a quarter wave plate with an azimuth angle of 30°, a polarizer with an azimuth angle of 0°, and a polarizer with an azimuth angle of 90° are placed between the polarization state generator PSG (105) and the spectroscope module (103), respectively. The instrument matrix of all devices before reaching the calibration element is represented by G2, and the instrument matrix of all devices after leaving the calibration element is represented by A2; Stokes-Mueller imaging is performed, and four groups of light intensities are obtained, namely, I air1 ,I G1 ,I G2 ,I G3 ; where I air1 is the light intensity matrix when there is no sample at position 2; I G1 ,I G2 is the light intensity matrix measured by polarizers with azimuth angles of 0° and 90°, I G3 The light intensity matrix measured by a quarter-wave plate with an azimuth angle of 30°; Sc2: Construct the intermediate matrix C using the measured light intensity G1 , C G2 , C G3 : Sc3, thus we get: M G1 G2-G2C G1 =0 M G2 G2-G2C G2 =0 M G3 G2-G2C G3 =0 Among them, M G1 ,M G2 ,M G3 Here we represent the Mueller matrices of the 0° and 90° polarizers, and the 30° quarter-wave plate; Sc4, according to the model of the calibration component and C G1 , C G2 , C G3 The eigenvalue solution is M G1 ,M G2 ,M G3 ; Sc5, construct the equation: Where E is a 4×4 unit matrix, vec is a matrix straightening operator, is the Kronecker product operator; Simplified expression: H G1 vec(G2)=0; Further transformed into: Similarly, construct From this we get L G matrix: L G ·vec(G2)=0 Where G2 is L G The solution vector when the matrix eigenvalue is 0, and then according to I air1 =A2·G2, then we get the A2 matrix.

7. The high stability and high precision Stokes-Mueller imager instrument matrix integrated optimization method as claimed in claim 1, characterized in that: The Stokes-Mueller imager is a transmission-type Stokes-Mueller imaging polarimeter, and its basic structure comprises a light source (201), a polarization state generator PSG (202), a condenser (203), an objective lens (204) and a polarization state analyzer PSA (205); Then in the step 2, the selected position 1 is between the condenser lens (203) and the objective lens (204); The selected position 2 is between the objective lens (204) and the polarization state analyzer PSA (205); The selected position 3 is between the polarization state generator PSG (202) and the focusing mirror (203).

8. The high stability and high precision Stokes-Mueller imager instrument matrix integrated optimization method as claimed in claim 7, characterized in that: The Stokes-Mueller imager is a transmission-type Stokes-Mueller imaging polarimeter. The instrument matrices obtained by calibration at three positions are A and G, A1 and G1, and A2 and G2. The calibration at the three positions adopts the following process: A' refers to A, A1 or A2, and G' refers to G, G1 or G2; Sd1, first place a quarter wave plate with an azimuth angle of 30°, a polarizer with an azimuth angle of 0°, and a polarizer with an azimuth angle of 90° at positions n, where n is 1, 2, or 3, and perform Stokes-Mueller imaging to obtain four groups of light intensities, I air ',I A1 ',I A2 ',I A3 '; where I air ' is the light intensity matrix when there is no sample at position 2; I A1 ',I A2 ' is the light intensity matrix measured by polarizers with azimuth angles of 0° and 90°, I A3 ' is the light intensity matrix measured by a quarter wave plate with an azimuth angle of 30°; Sd2, constructing the intermediate matrix C using the measured light intensity A1 '、C A2 '、C A3 ': C A1 ’=(I air ’) -1 ·I A1 ’ C A2 ’=(I air ’) -1 ·I A2 ’ C A3 ’=(I air ’) -1 ·I A3 ’ Sd3, thus we get: M A1 ’G1’-G1’C A1 ’=0 M A2 ’G1’-G1’C A2 ’=0 M A3 ’G1’-G1’C A3 ’=0 Among them, M A1 '、M A2 '、M A3 'Here are the Mueller matrices of the 0° and 90° polarizers and the 30° quarter-wave plate; Sd4, according to the model of the calibration component and C A1 '、C A2 '、C A3 'Eigenvalue solution M A1 '、M A2 '、M A3 '; Sd5, construct the equation: Where E is a 4×4 unit matrix, vec is a matrix straightening operator, is the Kronecker product operator; Simplified expression: H A1 'thing(G1')=0; Further transformed into: (H A1 ') T ·H A1 'thing(G1')=0 Similarly, construct From this we get L A 'The matrix is: L A ’=(H A1 ’) T ·H A1 +(H A2 ’) T ·H A2 +(H A3 ’) T ·H A3 L A '·vec(G1')=0 Where G' is L A 'The solution vector when the matrix eigenvalue is 0, and then according to I air '=A'·G', then we get the A' matrix.

9. The high stability and high precision Stokes-Mueller imager instrument matrix integrated optimization method according to any one of claims 1 to 8, characterized in that: The step 5: Substitute the forward and backward transfer Mueller matrices of the non-polarizing element into the ideal polarization state generator PSG and polarization state analyzer PSA instrument matrices for correction, and re-optimize the measurement parameters of the Stokes-Mueller imager instrument using the optimization goal of minimizing the instrument matrix condition number, specifically: After obtaining the instrument matrix at the three positions, calculate the polarization characteristics of the non-polarizing optical element. The specific method is: Forward Mueller Matrix of Non-Polarizing Optics NPO f : NPO f =G·G2 -1 Backward Mueller Matrix of Non-Polarizing Optical Components NPO b : NPO b =A1 -1 A The forward and backward matrices of the obtained non-polarized optical element are respectively introduced into the ideal instrument matrix optimization model: Modified PSA instrument matrix A * : A * =A Ideal ·NPO b Corrected PSG instrument matrix G * : G * =NPO f ·G Ideal A Ideal and G Ideal It is an ideal instrument matrix model.

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