Polarization parameter optimization method for full polarization imaging spectroscopy system based on genetic algorithm

Abstract

The present invention relates to a polarization parameter optimization method of a full polarization imaging spectroscopy system based on a genetic algorithm, so as to solve the technical problem that the error fluctuation of the imaging spectroscopy system measurement is large due to the value of the LCVR fast axis azimuth and phase delay. The method comprises: 1. obtaining a Mueller matrix; 2. obtaining a measurement matrix A; 3. performing error modeling according to the measurement matrix A and obtaining an optimization criterion; 4. according to the optimization criterion, using a genetic algorithm to obtain an optimal polarization parameter set; 5. obtaining the global optimal parameters of the full polarization imaging spectroscopy system. The method can effectively reduce the sensitivity of the full polarization imaging spectroscopy system to the error of the polarization device, and enhance the stability of the full polarization imaging spectroscopy system when there is an error source.

Description

Technical Field

[0001] The invention relates to a method for optimizing polarization parameters of a full polarization imaging spectrometer, and in particular to a method for optimizing polarization parameters of a full polarization imaging spectrometer system based on a genetic algorithm. Background Art

[0002] Liquid crystal variable phase retarder (LCVR) is composed of anisotropic liquid crystal molecules with uniaxial birefringence characteristics. By applying a driving voltage at both ends of the LCVR, the direction of the liquid crystal molecules is deflected with the voltage, and the deflected liquid crystal molecules can modulate the phase of the incident light wave. LCVR has the advantages of fast response, low modulation voltage, and no need for mechanical modulation, which makes it widely used in fields such as polarization imaging technology.

[0003] Figure 1 The figure shows a schematic diagram of the principle of the imaging spectroscopy system of the full polarization imaging spectrometer. The imaging spectroscopy system of the full polarization imaging spectrometer includes a first liquid crystal variable phase retarder LCVR1, a second liquid crystal variable phase retarder LCVR2, a polarizer P1, an acousto-optic tunable filter AOTF and a polarizer P2 which are sequentially arranged along the transmission direction of the optical path. Figure 2 The figure shows the working principle of the liquid crystal variable phase retarder. The liquid crystal variable phase retarder includes a spacer and an alignment layer, an ITO electrode and a quartz substrate arranged on the outside of the spacer in sequence. A voltage U is applied to the ITO electrode and the applied voltage U is compared with the threshold voltage U. th , when U≤U th When U>U th When the light is reflected by the liquid crystal molecules, they begin to rotate, causing a phase delay in the incident light.

[0004] When the imaging spectroscopy system performs full polarization measurement, various types of error sources will be coupled into the polarization measurement (PSD) system measurement matrix A, which will reduce the accuracy of the reconstruction of the imaging spectroscopy system matrix to be measured. In the imaging spectroscopy system, the error of the system measurement matrix A is closely related to the fast axis azimuth and phase delay of the two LCVRs. When the two LCVRs take different fast axis azimuths and different phase delays, the impact on the imaging spectroscopy system and the optimization results are different. In the existing literature, there is no report on the optimization analysis of the polarization parameters of the LCVR in the dual LCVRs+AOTF full polarization imaging spectroscopy system. Summary of the invention

[0005] The present invention aims to solve the technical problem that in the imaging spectral system of a full polarization imaging spectrometer, the error fluctuation of the imaging spectral system measurement is large due to the selection of the LCVR fast axis azimuth and phase delay. A polarization parameter optimization method for the full polarization imaging spectral system based on a genetic algorithm is proposed. The dual LCVR optimal fast axis azimuth and phase delay parameters obtained after optimization can effectively reduce the sensitivity of the imaging spectral system to the error of the polarization device, enhance the stability of the imaging spectral system when there is an error source, and thus improve the authenticity and reliability of the application effect.

[0006] The technical solution of the present invention is:

[0007] A method for optimizing polarization parameters of a full polarization imaging spectroscopy system based on a genetic algorithm is characterized in that it comprises the following steps:

[0008] C1. The Mueller matrix M is derived based on the full polarization imaging spectroscopy system. The formula is as follows:

[0009]

[0010] m 11 =m 21 =1;

[0011] m 12 =m 22 =(cos 2 2θ2+sin 2 2θ2cosδ2)·(cos 2 2θ1+sin 2 2θ1cosδ1)+cos2θ2sin2θ2(1-cosδ2)·cos2θ1sin2θ1(1-cosδ1)-sin2θ2sinδ2sin2θ1sinδ1;

[0012] m 13 =m 23 =(cos 2 2θ2+sinn 2 2θ2cosδ2)·cos2θ1sin2θ1(1-cosδ1)+cos2θ2sin2θ2(1-cosδ2)·(sin 2 2θ1+cos 2 2θ1cosδ1)+sin2θ2sinδ2cos2θ1sinδ1;

[0013] m 14 =m 24 = -sin2θ1sinδ1·(cos 2 2θ2+sin 22θ2cosδ2)+cos2θ2sin2θ2(1-cosδ2)·cos2θ1sinδ1-sin2θ2sinδ2cosδ1;

[0014] m 31 =m 32 =m 33 =m 34 =m 41 =m 42 =m 43 =m 44 =0;

[0015] Wherein, θ1 is the fast axis azimuth of LCVR1, δ1 is the phase delay of LCVR1; θ2 is the fast axis azimuth of LCVR2, δ2 is the phase delay of LCVR2; M LCVR2 (θ2, δ2) is the Mueller matrix of LCVR2, M LCVR1 (θ1, δ1) is the Mueller matrix of LCVR1; M P is the Mueller matrix product of polarizer P2, acousto-optic tunable filter AOTF and polarizer P1;

[0016] C2. According to the Mueller matrix M, calculate the measurement matrix A. The formula is as follows:

[0017]

[0018] In the measurement matrix A, (θ1, θ2) is a set of values, and (δ1, δ2) is four sets of values;

[0019] C3. Error modeling is performed based on the measurement matrix A. The modeling formula is as follows:

[0020]

[0021] Among them, S in For the ideal target polarization information, is the actual target polarization information, ε A is the noise of the measurement matrix A, cond(A) is the condition number; according to the modeling formula, the smaller the condition number cond(A), the smaller the error of the measurement matrix A;

[0022] C4. The two-norm condition number of the condition number cond(A) is used as the optimization criterion. The calculation formula of the two-norm condition number cond(A) is as follows:

[0023] cond(A)=||A||2·||A -1 ||2

[0024] Among them, A -1is the inverse matrix of the measurement matrix A;

[0025] The minimum result of cond(A) is Then the optimization criterion for optimizing the polarization parameters of LCVR1 and LCVR2 using the two-norm condition number cond(A) is that cond(A) is closest to The corresponding polarization parameters are the optimal polarization parameters;

[0026] C5. According to the optimization criteria determined in step C4, a genetic algorithm is used to calculate the condition number cond(A) and obtain the condition number cond(A) whose calculation result is closest to The corresponding set of polarization parameters is the optimal polarization parameters;

[0027] C6, repeat step C5, perform calculations n times, and obtain an optimal polarization parameter set formed by n groups of optimal polarization parameters, where n≥5;

[0028] C7. The optimal polarization parameters with the condition number cond(A) not greater than 3 in the optimal polarization parameter set are selected as the first screening set; from the first screening set, 2 to 4 groups of optimal polarization parameters with the least number of phase delay values ​​of LCVR1 and LCVR2 are selected as the second screening set; from the second screening set, a group of optimal polarization parameters with the least number of phase delay adjustment times is selected as the global optimal parameters of the full polarization imaging spectroscopy system.

[0029] Further, in step C1, the M P The calculation formula is as follows:

[0030]

[0031] Among them, M p2 is the Mueller matrix of polarizer P2, M p1 is the Mueller matrix of polarizer P1, M AOTF The Mueller matrix of the acousto-optic tunable filter AOTF.

[0032] Furthermore, in step C1, the Mueller matrices of LCVR1 and LCVR2 are:

[0033]

[0034] Here, θ corresponds to the fast axis azimuths θ1 and θ2 of LCVR1 and LCVR2, respectively, and δ corresponds to the phase delays δ1 and δ2 of LCVR1 and LCVR2, respectively.

[0035] Further, in step C3, the calculation formula of cond(A) is:

[0036] cond(A)=||A||·||A -1 ||

[0037] or

[0038] cond(A)=||A||2·||A -1 ||2

[0039] or

[0040] cond(A)=||A|| ∞ ·||A -1 || ∞ .

[0041] At the same time, the present invention also provides a method for optimizing polarization parameters of a full polarization imaging spectroscopy system based on a genetic algorithm, which is special in that it includes the following steps:

[0042] D1. The Mueller matrix M is derived based on the full polarization imaging spectroscopy system. The formula is as follows:

[0043]

[0044] m 11 =m 21 =1;

[0045] m 12 =m 22 =(cos 2 2θ2+sin 2 2θ2cosδ2)·(cos 2 2θ1+sin 2 2θ1cosδ1)+cos2θ2sin2θ2(1-cosδ2)·cos2θ1sin2θ1(1-cosδ1)-sin2θ2sinδ2sin2θ1sinδ1;

[0046] m 13 =m 23 =(cos 2 2θ2+sin 2 2θ2cosδ2)·cos2θ1sin2θ1(1-cosδ1)+cos2θ2sin2θ2(1-cosδ2)·(sin 2 2θ1+cos 2 2θ1cosδ1)+sin2θ2sinδ2cos2θ1sinδ1;

[0047] m 14 =m 24 = -sin2θ1sinδ1·(cos 2 2θ2+sin2 2θ2cosδ2)+cos2θ2sin2θ2(1-cosδ2)·cos2θ1sinδ1-sin2θ2sinδ2cosδ1;

[0048] m 31 =m 32 =m 33 =m 34 =m 41 =m 42 =m 43 =m 44 =0;

[0049] Wherein, θ1 is the fast axis azimuth of LCVR1, δ1 is the phase delay of LCVR1; θ2 is the fast axis azimuth of LCVR2, δ2 is the phase delay of LCVR2; M LCVR2 (θ2, δ2) is the Mueller matrix of LCVR2, M LCVR1 (θ1, δ1) is the Mueller matrix of LCVR1; M P is the Mueller matrix product of polarizer P2, acousto-optic tunable filter AOTF and polarizer P1;

[0050] θ1 and θ2 至 At least one is a known quantity;

[0051] D2. According to the Mueller matrix M, the formula for calculating the measurement matrix A is as follows:

[0052]

[0053] In the measurement matrix A, (θ1, θ2) is a set of values, and (δ1, δ2) is four sets of values;

[0054] D3. Error modeling is performed based on the measurement matrix A. The modeling formula is as follows:

[0055]

[0056] Among them, S in For the ideal target polarization information, is the actual target polarization information, ε A is the noise of the measurement matrix A, cond(A) is the condition number; according to the modeling formula, the smaller the condition number cond(A), the smaller the error of the measurement matrix A;

[0057] D4. The two-norm condition number of the condition number cond(A) is used as the optimization criterion. The calculation formula of the two-norm condition number cond(A) is as follows:

[0058] cond(A)=||A||2·||A-1 ||2

[0059] Among them, A -1 is the inverse matrix of the measurement matrix A;

[0060] The minimum result of cond(A) is Then the optimization criterion for optimizing the polarization parameters of LCVR1 and LCVR2 using the two-norm condition number cond(A) is that cond(A) is closest to The corresponding polarization parameters are the optimal polarization parameters;

[0061] D5. According to the optimization criteria determined in step D4, a genetic algorithm is used to calculate the condition number cond(A) and obtain the condition number cond(A) whose calculation result is closest to The corresponding set of polarization parameters is the optimal polarization parameters;

[0062] Using a genetic algorithm, perform n calculations to obtain n groups of optimal polarization parameters to form an optimal polarization parameter set, where n≥5;

[0063] D6. The optimal polarization parameters with the condition number cond(A) not greater than 3 in the optimal polarization parameter set are selected as the first screening set; from the first screening set, 2 to 4 groups of optimal polarization parameters with the least number of phase delay values ​​of LCVR1 and LCVR2 are selected as the second screening set; from the second screening set, a group of optimal polarization parameters with the least number of phase delay adjustment times is selected as the global optimal parameters of the full polarization imaging spectroscopy system.

[0064] Further, in step D1, the M P The calculation formula is as follows:

[0065]

[0066] The Mueller matrices of LCVR1 and LCVR2 are:

[0067]

[0068] Among them, M p2 is the Mueller matrix of polarizer P2, M p1 is the Mueller matrix of polarizer P1, M AOTF is the Mueller matrix of the acousto-optic tunable filter AOTF, θ corresponds to the fast axis azimuths θ1 and θ2 of LCVR1 and LCVR2, and δ corresponds to the phase delays δ1 and δ2 of LCVR1 and LCVR2, respectively.

[0069] Further, in step D3, the calculation formula of cond(A) is:

[0070] cond(A)=||A||·||A -1 ||

[0071] or

[0072] cond(A)=||A||2·||A -1 ||2

[0073] or

[0074] cond(A)=||A|| ∞ ·||A -1 || ∞ .

[0075] Furthermore, in step D1, the fast axis azimuth angle θ1=90° is known, and the fast axis azimuth angle θ2, the phase delay amount δ1 and the phase delay amount δ2 are to be optimized; then,

[0076] m 11 =1;

[0077] m 12 =cos 2 2θ2+sin 2 2θ2cosδ2;

[0078] m 13 =cos2θ2sin2θ2(1-cosδ2)·cosδ1-sin2θ2sinδ2sinδ1;

[0079] m 14 =-sinδ1cos2θ2sin2θ2(1-cosδ2)-sin2θ2sinδ2cosδ1.

[0080] Furthermore, in step D1, the fast axis azimuth angle θ2=45° is known, and the fast axis azimuth angle θ1, the phase delay amount δ1 and the phase delay amount δ2 are to be optimized; then,

[0081] m 11 =1;

[0082] m 12 =cosδ2·(cos 2 2θ1+sinn 2 2θ1cosδ1)-sinδ2sin2θ1sinδ1;

[0083] m 13 =cosδ2·cos2θ1sin2θ1(1-cosδ1)+sinδ2cos2θ1sinδ1;

[0084] m 14=-sin2θ1sinδ1cosδ2-sinδ2cosδ1.

[0085] Furthermore, in step D1, the fast axis azimuth angles θ1=90° and θ2=45° are known, and the phase delay amounts δ1 and δ2 are to be optimized; then,

[0086] m 11 =1;

[0087] m 12 =cosδ2;

[0088] m 13 = -sinδ2sinδ1;

[0089] m 14 =-sinδ2cosδ1.

[0090] Beneficial effects of the present invention:

[0091] 1. The method provided by the present invention uses the two-norm condition number as the optimization criterion and uses a genetic algorithm to find the condition number cond(A) whose calculation result is closest to The corresponding optimal polarization parameters are then screened out in turn through the small two-norm condition number, the small number of LCVR adjustment times, and the small number of phase delay types to obtain the global optimal parameters; according to the above calculations, the optimized polarization parameters of the full polarization imaging spectroscopy system for full polarization measurement are obtained; through the method provided by the present invention, the obtained global optimal parameters can effectively reduce the sensitivity of the full polarization imaging spectroscopy system to the polarization device error, enhance the stability of the full polarization imaging spectroscopy system when there is an error source, and improve the authenticity and reliability of the application effect.

[0092] 2. At least one of the fast-axis azimuth angles θ1 and θ2 of the two LCVRs provided by the present invention is a known quantity, which can simplify the calculation and facilitate the acquisition of the inverse matrix of the measurement matrix A. At the same time, using commonly used angles as the known fast-axis azimuth angles facilitates the calibration of the polarization parameters of the two LCVRs when performing actual full polarization measurements. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 This is a schematic diagram of the imaging spectroscopy system principle of the full polarization imaging spectrometer;

[0094] Figure 2 This is a working principle diagram of a liquid crystal variable phase retarder;

[0095] Figure 3 The flowchart of the polarization parameter optimization method of the full polarization imaging spectroscopy system based on genetic algorithm of the present invention is as follows:

[0096] Figure 4 This is a schematic diagram of the experimental results of Example 1 of the present invention;

[0097] Figure 5 Schematic diagram of polarization parameter comparison of one test result (a) of Example 1 of the present invention, two test results (b and c) of Example 2, an ideal result (d) and a non-optimized parameter result (e). DETAILED DESCRIPTION

[0098] Example 1

[0099] This embodiment provides a method for optimizing polarization parameters of a full polarization imaging spectroscopy system based on a genetic algorithm, and the Stokes full polarization measurement principle is as follows:

[0100] S in =[S0S1S2S3] T

[0101] B=A·S in

[0102] S in =A -1 ·B

[0103] Among them, S in is the ideal target polarization information, S0 is the total intensity of the incident polarized light, S1 is the intensity difference of mutually orthogonal polarized light, S2 is the intensity difference of ±45° polarized light, and S3 is the intensity difference of left-handed and right-handed circularly polarized light; B is the intensity matrix, A is the measurement matrix A, A -1 is the inverse matrix of A.

[0104] The goal of the polarization parameter optimization method of the full polarization imaging spectroscopy system is to obtain one group (θ1, θ2) and four groups (δ1, δ2) of LCVR1 and LCVR2 when performing full polarization measurement on the full polarization imaging spectroscopy system, where θ1, θ2, δ1 and δ2 are all unknown quantities, see Figure 3 , including the following steps:

[0105] C1. The Mueller matrix M is derived based on the full polarization imaging spectroscopy system. The formula is as follows:

[0106]

[0107] Where, (θ1, δ1) are the fast axis azimuth and phase delay of LCVR1; (θ2, δ2) are the fast axis azimuth and phase delay of LCVR2; M LCVR (θ2, δ2) is the Mueller matrix of LCVR2, M LCVR1 (θ1, δ1) is the Mueller matrix of LCVR1; M P is the Mueller matrix product of polarizer P2, acousto-optic tunable filter AOTF and polarizer P1;

[0108] Specifically,

[0109] M p2 is the Mueller matrix of polarizer P2, M p1 is the Mueller matrix of polarizer P1, M AOTF The Mueller matrix of the acousto-optic tunable filter AOTF.

[0110]

[0111] Here, θ corresponds to the fast axis azimuths θ1 and θ2 of LCVR1 and LCVR2, respectively, and δ corresponds to the phase delays δ1 and δ2 of LCVR1 and LCVR2, respectively.

[0112] The m in the Mueller matrix M 11 、m 12 、m 13 、m 14 It is related to the fast axis azimuth angle θ1 and phase delay amount δ1 of LCVR1, and the fast axis azimuth angle θ2 and phase delay amount δ2 of LCVR2. Specifically,

[0113] m 11 =m 21 =1;

[0114] m 12 =m 22 =(cos 2 2θ2+sin 2 2θ2cosδ2)·(cos 2 2θ1+sin 2 2θ1cosδ1)+cos2θ2sin2θ2(1-cosδ2)·cos2θ1sin2θ1(1-cosδ1)-sin2θ2sinδ2sin2θ1sinδ1;

[0115] m 13 =m 23 =(cos 2 2θ2+sin 2 2θ2cosδ2)·cos2θ1sin2θ1(1-cosδ1)+cos2θ2sin2θ2(1-cosδ2)·(sin 2 2θ1+cos 2 2θ1cosδ1)+sin2θ2sinδ2cos2θ1sinδ1;

[0116] m 14 =m 24 = -sin2θ1sinδ1·(cos2 2θ2+sin 2 2θ2cosδ2)+cos2θ2sin2θ2(1-cosδ2)·cos2θ1sinδ1-sin2θ2sinδ2cosδ1;

[0117] m 31 =m 32 =m 33 =m 34 =m 41 =m 42 =m 43 =m 44 =0.

[0118] C2. According to the Mueller matrix M, the formula for calculating the measurement matrix A is as follows:

[0119]

[0120] In the measurement matrix A, (θ1, θ2) is a set of values, and (δ1, δ2) is four sets of values;

[0121] C3. Error modeling is performed based on the measurement matrix A. The modeling formula is as follows:

[0122]

[0123] Among them, S in For the ideal target polarization information, is the actual target polarization information, ε A is the noise of the measurement matrix A, cond(A) is the condition number; according to the modeling formula, the smaller the condition number cond(A), the smaller the error of the measurement matrix A.

[0124] Specifically, the calculation formula of cond(A) is:

[0125] cond(A)=||A||·||A -1 ||

[0126] or

[0127] cond(A)=||A||2·||A -1 ||2

[0128] or

[0129] cond(A)=||A|| ∞ ·||A -1 || ∞ .

[0130] C4. The two-norm condition number of the condition number cond(A) is used as the optimization criterion. The calculation formula of the two-norm condition number cond(A) is as follows:

[0131] cond(A)=||A||2·||A -1 ||2

[0132] Among them, A is the measurement matrix A, A -1 is the inverse matrix of the measurement matrix A; according to Tyo analysis (see Tyo JS. Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error [J]. Applied Optics, 2002, 41 (4): 619-30.), the minimum value of the condition number cond (A) is N is the number of phase delay groups selected. Therefore, in this embodiment, four phase delay groups are selected, and the minimum calculation result of cond(A) is

[0133] According to the above modeling formula, it can be seen that the smaller the condition number cond(A), the smaller the error of the measurement matrix A. In this embodiment, the calculation result of cond(A) is closer to The smaller the error of the measurement matrix A is, the smaller the error is. Therefore, the optimization criterion for optimizing the polarization parameters of LCVR1 and LCVR2 using the two-norm condition number cond(A) is that cond(A) is closest to The corresponding polarization parameters are the optimal polarization parameters.

[0134] C5. According to the optimization criteria determined in step C4, a genetic algorithm is used to calculate the condition number cond(A) and obtain the condition number cond(A) whose calculation result is closest to The corresponding set of polarization parameters is the optimal polarization parameters.

[0135] C6. Repeat step C5, perform calculations n times, and obtain an optimal polarization parameter set formed by n groups of optimal polarization parameters, where n≥5.

[0136] C7. The optimal polarization parameters with the condition number cond(A) not greater than 3 in the optimal polarization parameter set are selected as the first screening set; from the first screening set, 2 to 4 sets of optimal polarization parameters with the least number of phase delay values ​​of LCVR1 and LCVR2 are selected as the second screening set; from the second screening set, a set of optimal polarization parameters with the least number of phase delay adjustment times is selected as the global optimal parameters of the full polarization imaging spectroscopy system. Figure 4, under the configuration conditions of 4 different amounts of phase delay, the optimal polarization parameters (θ1, θ2) are (18.9°, 41.9°), and (δ1, δ2) are (179.9°, 156.6°), (0.4°, 156.6°), (179.9°, 46.3°) and (0.4°, 46.3°), which are the global optimal parameters.

[0137] Taking the four groups (δ1, δ2) corresponding to the global optimal parameters as an example, the number of times the phase delay amount of LCVR1 and LCVR2 is adjusted is explained. Before the full polarization measurement starts, (δ1, δ2) is set to (179.9°, 156.6°), and δ1 and δ2 are adjusted in sequence. The first adjustment is to keep δ2 unchanged and adjust δ1 to 0.4°. The second adjustment is to adjust δ1 to 179.9°. The third adjustment is to adjust δ2 to 46.3°. The fourth adjustment is to adjust δ1 to 0.4°. Therefore, the number of times the phase delay amount is adjusted is four times.

[0138] Example 2

[0139] When the full polarization imaging spectroscopy system is subjected to full polarization measurement in this embodiment, at least one of θ1 and θ2 is a known quantity, and the remaining steps are the same as those in the first embodiment.

[0140] Specifically, when the fast axis azimuth angle θ1=90° is known, the fast axis azimuth angle θ2, the phase delay amount δ1 and the phase delay amount δ2 are to be optimized; then,

[0141] m 11 =1:

[0142] m 12 =cos 2 2θ2+sin 2 2θ2cosδ2;

[0143] m 13 =cos2θ2sin2θ2(1-cosδ2)·cosδ1-sin2θ2sinδ2sinδ1;

[0144] m 14 =-sinδ1cos2θ2sin2θ2(1-cosδ2)-sin2θ2sinδ2cosδ1.

[0145] When the fast axis azimuth angle θ2 = 45° is known, the fast axis azimuth angle θ1, phase delay δ1 and phase delay δ2 need to be optimized; then,

[0146] m 11 =1;

[0147] m 12 =cosδ2·(cos 22θ1+sin 2 2θ1cosδ1)-sinδ2sin2θ1sinδ1;

[0148] m 13 =cosδ2·cos2θ1sin2θ1(1-cosδ1)+sinδ2cos2θ1sinδ1;

[0149] m 14 =-sin2θ1sinδ1cosδ2-sinδ2cosδ1.

[0150] When the fast axis azimuth angles θ1 = 90° and θ2 = 45° are known, the phase delay δ1 and the phase delay δ2 need to be optimized; then,

[0151] m 11 =1;

[0152] m 12 =cosδ2;

[0153] m 13 = -sinδ2sinδ1;

[0154] m 14 =-sinδ2cosδ1.

[0155] See also Figure 5, by drawing a tetrahedron in the Poincare sphere, the coordinates of the tetrahedron vertices are obtained by the measurement matrix A; the parameter optimization results of the tetrahedron a are drawn in the Poincare sphere when the fast axis azimuth θ1, the fast axis azimuth θ2, the phase delay δ1 and the phase delay δ2 are all to be optimized, and its (θ1, θ2) is (18.9°, 41.9°), (δ1, δ2) is (179.9°, 156.6°), (0.4°, 156.6°), (179.9°, 46.3°) and (0.4°, 46.3°), the condition number κ2=1.742, and the volume of the tetrahedron is 0.5131; the parameter optimization results of the tetrahedron b are drawn when the fast axis azimuth θ2=45° is known, and the fast axis azimuth θ1, the phase delay δ1 and the phase delay δ2 are all to be optimized, Its (θ1, θ2) is (67.5°, 45°), (δ1, δ2) are (1.6°, 146.5°), (179.8°, 146.5°), (1.6°, 36.4°) and (179.8°, 37.4°), respectively. The condition number κ2 = 1.754, the tetrahedron volume is 0.5129; the c tetrahedron has fast axis azimuths θ1 = 90°, θ2 = 45°. , the parameter optimization results when both the phase delay δ1 and the phase delay δ2 are to be optimized, where (θ1, θ2) is (90°, 45°), (δ1, δ2) are (180°, 60°), (0°, 180°), (90°, 90°) and (0°, 60°), respectively, the condition number κ2 = 2.484, the tetrahedron volume is 0.4330; the d tetrahedron is an ideal regular tetrahedron, the condition number The volume of the tetrahedron is 0.5132; the e tetrahedron is the polarization parameter that is not optimized by the method provided by the present invention, (θ1, θ2) is (90°, 45°), (δ1, δ2) are (90°, 90°), (180°, 180°), (180°, 90°) and (90°, 60°) respectively, the condition number κ2 = 10.815, and the volume of the tetrahedron is 0.1057.

[0156] From the comparison results, it can be seen that the volume of the tetrahedron obtained by optimizing the fast-axis azimuth angle θ1, the fast-axis azimuth angle θ2, the phase delay amount δ1 and the phase delay amount δ2 at the same time is closest to the volume of the ideal regular tetrahedron, and the calculation of determining at least one fast-axis azimuth angle is simple, and based on the commonly used fast-axis azimuth angle, the optimal values ​​of other polarization parameters under the condition of determining the fast-axis azimuth angle are obtained, which is convenient for calibrating the fast-axis azimuth angle and the phase delay amount when using the full polarization imaging spectroscopy system.

Claims

1. A method for optimizing polarization parameters of a full polarization imaging spectroscopy system based on a genetic algorithm, characterized in that: The following steps are involved: C1. The Mueller matrix M is derived from the full polarization imaging spectroscopy system. The formula is as follows: m 11 =m 21 =1; m 12 =m 22 =(cos 2 2θ2+sin 2 2θ2cosδ2)·(cos 2 2θ1+sin 2 2θ1cosδ1)+cos2θ2sin2θ2(1-cosδ2)·cos2θ1sin2θ1(1-cosδ1)-sin2θ2sinδ2sin2θ1sinδ1; m 13 =m 23 =(cos 2 2θ2+sin 2 2θ2cosδ2)·cos2θ1sin2θ1(1-cosδ1)+cos2θ2sin2θ2(1-cosδ2)·(sin 2 2θ1+cos 2 2θ1cosδ1)+sin2θ2sinδ2cos2θ1sinδ1; m 14 =m 24 =-sin2θ1sinδ1·(cos 2 2θ2+sin 2 2θ2cosδ2)+cos2θ2sin2θ2(1-cosδ2)·cos2θ1sinδ1-sin2θ2sinδ2cosδ1; m 31 =m 32 =m 33 =m 34 =m 41 =m 42 =m 43 =m 44 =0; Wherein, θ1 is the fast axis azimuth of the first liquid crystal variable phase retarder, δ1 is the phase retardation amount of the first liquid crystal variable phase retarder; θ2 is the fast axis azimuth of the second liquid crystal variable phase retarder, δ2 is the phase retardation amount of the second liquid crystal variable phase retarder; M LCVR2 (θ2, δ2) is the Mueller matrix of the second liquid crystal variable phase retarder, M LCVR1 (θ1, δ1) is the Mueller matrix of the first liquid crystal variable phase retarder; M P is the Mueller matrix product of polarizer P2, acousto-optic tunable filter AOTF and polarizer P1; C2. According to the Mueller matrix M, calculate the measurement matrix A. The formula is as follows: In the measurement matrix A, (θ1, θ2) is a set of values, and (δ1, δ2) is four sets of values; C3. Error modeling is performed based on the measurement matrix A. The modeling formula is as follows: Among them, S in For the ideal target polarization information, is the actual target polarization information, ε A is the noise of the measurement matrix A, cond(A) is the condition number; according to the modeling formula, the smaller the condition number cond(A), the smaller the error of the measurement matrix A; C4. The two-norm condition number of the condition number cond(A) is used as the optimization criterion. The calculation formula of the two-norm condition number is as follows: cond(A)=||A||2·||A -1 ||2 Among them, A -1 is the inverse matrix of the measurement matrix A; The minimum result of cond(A) is Then the optimization criterion for optimizing the polarization parameters of the first liquid crystal variable phase retarder and the second liquid crystal variable phase retarder using the two-norm condition number cond(A) is that cond(A) is closest to The corresponding polarization parameters are the optimal polarization parameters; C5. According to the optimization criteria determined in step C4, a genetic algorithm is used to calculate the condition number cond(A) and obtain the condition number cond(A) whose calculation result is closest to The corresponding set of polarization parameters is the optimal polarization parameters; C6, repeat step C5, perform calculations n times, and obtain an optimal polarization parameter set formed by n groups of optimal polarization parameters, where n≥5; C7. The optimal polarization parameters with the condition number cond(A) not greater than 3 in the optimal polarization parameter set are selected as the first screening set; from the first screening set, 2 to 4 groups of optimal polarization parameters with the least number of phase delay values ​​of the first liquid crystal variable phase retarder and the second liquid crystal variable phase retarder are selected as the second screening set; from the second screening set, a group of optimal polarization parameters with the least number of phase delay adjustment times is selected as the global optimal parameters of the full polarization imaging spectroscopy system.

2. The method for optimizing polarization parameters of a full polarization imaging spectroscopy system based on a genetic algorithm according to claim 1, characterized in that: In step C1, the M P The calculation formula is as follows: Among them, M p2 is the Mueller matrix of polarizer P2, M p1 is the Mueller matrix of polarizer P1, M AOTF The Mueller matrix of the acousto-optic tunable filter AOTF.

3. The method for optimizing polarization parameters of a full polarization imaging spectroscopy system based on a genetic algorithm according to claim 2, characterized in that: In step C1, the Mueller matrices of the first liquid crystal variable phase retarder and the second liquid crystal variable phase retarder are: Wherein, θ corresponds to the fast axis azimuths θ1 and θ2 of the first liquid crystal variable phase retarder and the second liquid crystal variable phase retarder, respectively, and δ corresponds to the phase retardation amounts δ1 and δ2 of the first liquid crystal variable phase retarder and the second liquid crystal variable phase retarder, respectively.

4. The method for optimizing polarization parameters of a full polarization imaging spectroscopy system based on a genetic algorithm according to claim 3, characterized in that: In step C3, the calculation formula of cond(A) is: cond(A)=||A||·||A -1 || or cond(A)=||A||2·||A -1 ||2 or cond(A)=||A|| ∞ ·||A -1 || ∞ 。 5. The method for optimizing polarization parameters of a full polarization imaging spectroscopy system based on a genetic algorithm according to any one of claims 1 to 4, characterized in that: In step D1, the fast axis azimuth angle θ1=90° is known, and the fast axis azimuth angle θ2, the phase delay amount δ1 and the phase delay amount δ2 are to be optimized; then, m 11 ＝1； n 12 =cos 2 2θ2+sin 2 2θ2cosδ2; m 13 =cos2θ2sin2θ2(1-cosδ2)·cosδ1-sin2θ2sinδ2sinδ1; m 14 =-sinδ1cos2θ2sin2θ2(1-cosδ2)-sin2θ2sinδ2cosδ1。 6. The method for optimizing polarization parameters of a full polarization imaging spectroscopy system based on a genetic algorithm according to any one of claims 1 to 4, characterized in that: In step D1, the fast axis azimuth angle θ2 = 45° is known, and the fast axis azimuth angle θ1, the phase delay amount δ1 and the phase delay amount δ2 are to be optimized; then, m 11 ＝1； m 12 =cosδ2·(cos 2 2θ1+sin 2 2θ1cosδ1)-sinδ2sin2θ1sinδ1; m 13 =cosδ2·cos2θ1sin2θ1(1-cosδ1)+sinδ2xos2θ1sinδ1; m 14 =-sin2θ1sinδ1cosδ2-sinδ2cosδ1。 7. The method for optimizing polarization parameters of a full polarization imaging spectroscopy system based on a genetic algorithm according to any one of claims 1 to 4, characterized in that: In step D1, the fast axis azimuth angles θ1 = 90° and θ2 = 45° are known, and the phase delay amounts δ1 and δ2 are to be optimized; then, m 11 ＝1； m 12 =cosδ2; m 13 =-sinδ2sinδ1; m 14 =-sinδ2cosδ1。

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