CN115200713A - Polarization parameter optimization method of full-polarization imaging spectrum system based on genetic algorithm - Google Patents
Polarization parameter optimization method of full-polarization imaging spectrum system based on genetic algorithm Download PDFInfo
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- G—PHYSICS
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- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
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Abstract
The invention relates to a polarization parameter optimization method of a full-polarization imaging spectrum system based on a genetic algorithm, which aims to solve the technical problem that the error fluctuation of the measurement of the imaging spectrum system is large due to the values of the azimuth angle and the phase delay of the fast axis of LCVR. The method comprises the following steps: 1. acquiring a Mueller matrix; 2. acquiring a measurement matrix A; 3. error modeling is carried out according to the measurement matrix A and an optimization criterion is obtained; 4. acquiring an optimal polarization parameter set by adopting a genetic algorithm according to an optimization criterion; 5. and acquiring global optimal parameters of the full-polarization imaging spectrum system. The method can effectively reduce the sensitivity of the full-polarization imaging spectrum system to errors of the polarization device and enhance the stability of the full-polarization imaging spectrum system in the presence of error sources.
Description
Technical Field
The invention relates to a method for optimizing polarization parameters of a full-polarization imaging spectrometer, in particular to a method for optimizing polarization parameters of a full-polarization imaging spectrum system based on a genetic algorithm.
Background
The liquid crystal variable phase retarder (LCVR) is composed of anisotropic liquid crystal molecules with uniaxial birefringence, and the directions of the liquid crystal molecules are deflected along with voltage by applying driving voltage at two ends of the LCVR, so that the deflected liquid crystal molecules can realize the modulation of the phase of incident light waves; the LCVR has the advantages of fast response, low modulation voltage, no need of mechanical modulation and the like, so that the LCVR is widely applied to the fields of polarization imaging technology and the like.
Fig. 1 is a schematic diagram of an imaging spectrum system of a full-polarization imaging spectrometer, where the imaging spectrum 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 a light path transmission direction. FIG. 2 is a schematic diagram showing the operation of a liquid crystal variable phase retarder including a spacer, and an alignment layer, an ITO electrode and a quartz substrate sequentially disposed outside the spacer, wherein a voltage U is applied to the ITO electrode, and the applied voltage U is compared with a threshold voltage U th When U is less than or equal to U th When the alignment direction of the liquid crystal molecules in the spacer is parallel to the quartz substrate, when U > U th At this time, the liquid crystal molecules start to rotate, and the incident light is phase-delayed.
When the imaging spectrum system carries out full-polarization measurement, various types of error sources can be coupled into a measurement matrix A of a polarization measurement (PSD) system, so that the accuracy of matrix reconstruction of the imaging spectrum system to be measured can be reduced. In an imaging spectrum system, the error of a system measurement matrix A is closely related to the fast axis azimuth angle and the phase delay amount of two LCVRs, and the influence and the optimization result of the two LCVRs on the imaging spectrum system are different when the two LCVRs adopt different fast axis azimuth angles and different phase delay amounts. In the existing literature, no report on optimization analysis research on polarization parameters of LCVRs in a dual LCVRs + AOTF full-polarization imaging spectroscopic system is found.
Disclosure of Invention
The invention aims to solve the technical problem that the measurement error fluctuation of an imaging spectrum system is larger due to the values of LCVR fast axis azimuth angles and phase delay amounts in the imaging spectrum system of a full-polarization imaging spectrometer, and provides a polarization parameter optimization method of the full-polarization imaging spectrum system based on a genetic algorithm.
The technical scheme of the invention is as follows:
a method for optimizing polarization parameters of a full-polarization imaging spectrum system based on a genetic algorithm is characterized by comprising the following steps:
c1, deducing a Mueller matrix M according to a full-polarization imaging spectrum system, wherein the formula is as follows,
m 11 ＝m 21 ＝1；
m 12 ＝m 22 ＝(cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 )·(cos 2 2θ 1 +sin 2 2θ 1 cosδ 1 )+cos2θ 2 sin2θ 2 (1-cosδ 2 )·cos2θ 1 sin2θ 1 (1-cosδ 1 )-sin2θ 2 sinδ 2 sin2θ 1 sinδ 1 ；
m 13 ＝m 23 ＝(cos 2 2θ 2 +sinn 2 2θ 2 cosδ 2 )·cos2θ 1 sin2θ 1 (1-cosδ 1 )+cos2θ 2 sin2θ 2 (1-cosδ 2 )·(sin 2 2θ 1 +cos 2 2θ 1 cosδ 1 )+sin2θ 2 sinδ 2 cos2θ 1 sinδ 1 ；
m 14 ＝m 24 ＝-sin2θ 1 sinδ 1 ·(cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 )+cos2θ 2 sin2θ 2 (1-cosδ 2 )·cos2θ 1 sinδ 1 -sin2θ 2 sinδ 2 cosδ 1 ；
m 31 ＝m 32 ＝m 33 ＝m 34 ＝m 41 ＝m 42 ＝m 43 ＝m 44 ＝0；
wherein, theta 1 Is the fast axis azimuth angle, delta, of LCVR1 1 Is the phase delay amount of LCVR 1; theta 2 Is the fast axis azimuth angle, δ, of LCVR2 2 Is the phase delay amount of LCVR 2; m LCVR2 (θ 2 ，δ 2 ) Mueller matrix, M, for LCVR2 LCVR1 (θ 1 ，δ 1 ) A Mueller matrix of LCVR 1; m P The product of Mueller matrix of the polaroid P2, the AOTF and the polaroid P1;
c2, calculating a measurement matrix A according to the Mueller matrix M, wherein the formula is as follows,
in measurement matrix A, (θ) 1 ，θ 2 ) Is a group of values, (delta) 1 ，δ 2 ) Taking values from four groups;
c3, carrying out error modeling according to the measurement matrix A, wherein a modeling formula is as follows,
wherein S is in For the desired polarization information of the object,
for actual target polarization information,. Epsilon A To measure the noise of matrix A, cond (A) is a condition number; the smaller the condition number cond (A) obtained according to a modeling formula is, the smaller the error of the measurement matrix A is;
and C4, taking the two-norm condition number of the condition number cond (A) as an optimization criterion, wherein the calculation formula of the two-norm condition number cond (A) is as follows:
cond(A)＝||A|| 2 ·||A -1 || 2
wherein A is -1 Is the inverse of the measurement matrix a;
the calculated result of cond (A) is at least
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 parameter is the optimal polarization parameter;
c5, calculating the condition number cond (A) by adopting a genetic algorithm according to the optimization criterion determined in the step C4, and obtaining the condition number cond (A) with the calculation result closest to the condition number cond (A)
The corresponding group of polarization parameters are optimal polarization parameters;
c6, repeating the step C5, and carrying out n-time calculation to obtain an optimal polarization parameter set formed by n groups of optimal polarization parameters, wherein n is more than or equal to 5;
c7, taking the optimal polarization parameter with the condition number cond (A) in the optimal polarization parameter set not more than 3 as a first screening set; selecting 2-4 groups of optimal polarization parameters with the least phase delay amount of LCVR1 and LCVR2 from the first screening set as a second screening set; and selecting a group of optimal polarization parameters with the minimum phase delay adjustment times from the second screening set as global optimal parameters of the full-polarization imaging spectrum system.
Further, in step C1, said M P The calculation formula of (a) is as follows:
wherein M is p2 Mueller matrix, M, being a polarizer P2 p1 Mueller matrix, M, of polarizer P1 AOTF For acousto-optically tunable filters AOTFA Mueller matrix.
Further, in step C1, the Mueller matrix of the LCVR1 and the LCVR2 is,
wherein theta respectively corresponds to fast axis azimuth theta of LCVR1 and LCVR2 1 、θ 2 δ corresponds to the phase delay δ of LCVR1 and LCVR2, respectively 1 、δ 2 。
Further, 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 || ∞ 。
Meanwhile, the invention also provides a method for optimizing the polarization parameters of the full-polarization imaging spectrum system based on the genetic algorithm, which is characterized by comprising the following steps of:
d1, deducing a Mueller matrix M according to a full-polarization imaging spectrum system, wherein the formula is as follows,
m 11 ＝m 21 ＝1；
m 12 ＝m 22 ＝(cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 )·(cos 2 2θ 1 +sin 2 2θ 1 cosδ 1 )+cos2θ 2 sin2θ 2 (1-cosδ 2 )·cos2θ 1 sin2θ 1 (1-cosδ 1 )-sin2θ 2 sinδ 2 sin2θ 1 sinδ 1 ；
m 13 ＝m 23 ＝(cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 )·cos2θ 1 sin2θ 1 (1-cosδ 1 )+cos2θ 2 sin2θ 2 (1-cosδ 2 )·(sin 2 2θ 1 +cos 2 2θ 1 cosδ 1 )+sin2θ 2 sinδ 2 cos2θ 1 sinδ 1 ；
m 14 ＝m 24 ＝-sin2θ 1 sinδ 1 ·(cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 )+cos2θ 2 sin2θ 2 (1-cosδ 2 )·cos2θ 1 sinδ 1 -sin2θ 2 sinδ 2 cosδ 1 ；
m 31 ＝m 32 ＝m 33 ＝m 34 ＝m 41 ＝m 42 ＝m 43 ＝m 44 ＝0；
wherein, theta 1 Is the fast axis azimuth angle, δ, of LCVR1 1 Is the phase delay amount of LCVR 1; theta 2 Is the fast axis azimuth angle, δ, of LCVR2 2 Is the phase delay amount of LCVR 2; m LCVR2 (θ 2 ，δ 2 ) Mueller matrix, M, for LCVR2 LCVR1 (θ 1 ，δ 1 ) A Mueller matrix of LCVR 1; m P The product of Mueller matrix of the polaroid P2, the AOTF and the polaroid P1;
θ 1 and theta 2 To One less is a known amount;
d2, according to the Mueller matrix M, calculating the measurement matrix A according to the following formula,
in measurement matrix A, (θ) 1 ，θ 2 ) Is a group of values, (delta) 1 ，δ 2 ) Four groups of values are taken;
d3, carrying out error modeling according to the measurement matrix A, wherein a modeling formula is as follows,
wherein S is in For the desired polarization information of the target,
for actual target polarization information, ∈ A To measure the noise of matrix A, cond (A) is a condition number; obtaining the smaller the condition number cond (A) is obtained according to a modeling formula, the smaller the error of the measurement matrix A is;
d4, using the two-norm condition number of the condition number cond (a) as an optimization criterion, wherein the calculation formula of the two-norm condition number cond (a) is as follows:
cond(A)＝||A|| 2 ·||A -1 || 2
wherein, A -1 Is the inverse of the measurement matrix a;
the calculated result of cond (A) is at least
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 parameter is the optimal polarization parameter;
d5, calculating the condition number cond (A) by adopting a genetic algorithm according to the optimization criterion determined in the step D4, and obtaining the condition number cond (A) with the calculation result closest to the condition number cond (A)
The corresponding group of polarization parameters are optimal polarization parameters;
calculating for n times by adopting a genetic algorithm, and acquiring n groups of optimal polarization parameters to form an optimal polarization parameter set, wherein n is more than or equal to 5;
d6, taking the optimal polarization parameter with the condition number cond (A) in the optimal polarization parameter set not more than 3 as a first screening set; selecting 2-4 groups of optimal polarization parameters with the least phase delay amount of LCVR1 and LCVR2 from the first screening set as a second screening set; and selecting a group of optimal polarization parameters with the minimum phase delay adjustment times from the second screening set as global optimal parameters of the full-polarization imaging spectrum system.
Further, in step D1, M is P The calculation formula of (a) is as follows:
the Mueller matrix of the LCVR1 and the LCVR2 is,
wherein M is p2 Mueller matrix, M, being a polarizer P2 p1 Mueller matrix, M, of polarizer P1 AOTF The Mueller matrix of the AOTF of the acousto-optic tunable filter is that theta respectively corresponds to the fast axis azimuth angle theta of the LCVR1 and the LCVR2 1 、θ 2 δ corresponds to the phase delay δ of LCVR1 and LCVR2, respectively 1 、δ 2 。
Further, in step D3, 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 || ∞ 。
Further, in step D1, the fast axis azimuth angle θ 1 Known by =90 °, fast axis azimuth angle θ 2 Phase retardation amount delta 1 And phase retardation δ 2 Optimizing; then the user can use the device to make a visual display,
m 11 ＝1；
m 12 ＝cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 ；
m 13 ＝cos2θ 2 sin2θ 2 (1-cosδ 2 )·cosδ 1 -sin2θ 2 sinδ 2 sinδ 1 ；
m 14 ＝-sinδ 1 cos2θ 2 sin2θ 2 (1-cosδ 2 )-sin2θ 2 sinδ 2 cosδ 1 。
further, in step D1, the fast axis azimuth angle θ 2 =45 ° known fast axis azimuth θ 1 Phase retardation amount delta 1 And the phase retardation amount delta 2 To be optimized; then the process of the first step is carried out,
m 11 ＝1；
m 12 ＝cosδ 2 ·(cos 2 2θ 1 +sinn 2 2θ 1 cosδ 1 )-sinδ 2 sin2θ 1 sinδ 1 ；
m 13 ＝cosδ 2 ·cos2θ 1 sin2θ 1 (1-cosδ 1 )+sinδ 2 cos2θ 1 sinδ 1 ；
m 14 ＝-sin2θ 1 sinδ 1 cosδ 2 -sinδ 2 cosδ 1 。
further, in step D1, the fast axis azimuth angle θ 1 ＝90°，θ 2 With known phase delay δ of 45 ° = known 1 And the phase delay amount δ 2 To be optimized; then the process of the first step is carried out,
m 11 ＝1；
m 12 ＝cosδ 2 ；
m 13 ＝-sinδ 2 sinδ 1 ；
m 14 ＝-sinδ 2 cosδ 1 。
the invention has the beneficial effects that:
1. the method provided by the invention uses the two-norm condition number as the optimization criterion, and adopts the genetic algorithm to seek the condition number cond (A) with the calculation result closest to the condition number cond (A)
Corresponding optimal polarization parameters are sequentially subjected to the two-norm conditionThe number is small, the LCVR adjusting times are few, and the phase delay quantity is few in variety, so that the global optimal parameters are screened out; obtaining optimized polarization parameters for full polarization measurement of the full polarization imaging spectrum system according to the calculation; by the method provided by the invention, the obtained global optimal parameters can effectively reduce the sensitivity of the full-polarization imaging spectrum system to errors of the polarization device, enhance the stability of the full-polarization imaging spectrum system when an error source exists, and improve the authenticity and reliability of the application effect.
2. At least one of the fast axis azimuth angles theta 1 and theta 2 of the two LCVRs is a known quantity, so that the operation can be simplified, and the inverse matrix of the measurement matrix A can be conveniently obtained; meanwhile, a common angle is used as a known fast axis azimuth angle, and the polarization parameters of the two LCVRs are conveniently calibrated when actual full-polarization measurement is carried out.
Drawings
FIG. 1 is a schematic diagram of an imaging spectroscopy system of a full-polarization imaging spectrometer;
FIG. 2 is a schematic diagram of the operation of a liquid crystal variable phase retarder;
FIG. 3 is a flow chart of the method for optimizing polarization parameters of a full-polarization imaging spectrum system based on a genetic algorithm, which comprises the following steps:
FIG. 4 is a graph showing the experimental results of example 1 of the present invention;
fig. 5 is a schematic diagram showing the comparison of the polarization parameters of one test result (a) of example 1, two test results (b and c) of example 2, an ideal result (d), and an unoptimized value parameter result (e) according to the present invention.
Detailed Description
Example 1
The embodiment provides a polarization parameter optimization method of a full-polarization imaging spectrum system based on a genetic algorithm, and the Stokes full-polarization measurement principle of the method is as follows:
S in ＝[S 0 S 1 S 2 S 3 ] T
B＝A·S in
S in ＝A -1 ·B
wherein S is in For ideal target polarization information, S 0 Is the total intensity of the incident polarized light, S 1 Is the difference in intensity of mutually orthogonally polarized light, S 2 Intensity difference of polarized light of +/-45 degrees, S 3 The light intensity difference of the left-handed circularly polarized light and the right-handed circularly polarized light; b is a light intensity matrix, A is a measurement matrix A, A -1 Is the inverse matrix of a.
The method for optimizing the polarization parameters of the full-polarization imaging spectrum system aims to: obtaining a set of (θ) of LCVR1, LCVR2 for full-polarization measurements of a full-polarization imaging spectroscopy system 1 ，θ 2 ) And four groups (delta) 1 ，δ 2 ) Wherein θ 1 、θ 2 、δ 1 And delta 2 All are unknown, see fig. 3, comprising the steps of:
c1, deducing a Mueller matrix M according to a full-polarization imaging spectrum system, wherein the formula is as follows,
wherein (theta) 1 ，δ 1 ) Respectively a fast axis azimuth angle and a phase delay amount of the LCVR 1; (theta) 2 ，δ 2 ) Fast axis azimuth and phase retardation of the LCVR2 are respectively; m LCVR (θ 2 ，δ 2 ) Mueller matrix, M, for LCVR2 LCVR1 (θ 1 ，δ 1 ) A Mueller matrix of LCVR 1; m is a group of P The product of Mueller matrix of the polaroid P2, the AOTF and the polaroid P1;
in particular, the method comprises the following steps of,
M p2 mueller matrix, M, being a polarizer P2 p1 Mueller matrix, M, of polarizer P1 AOTF Is a Mueller matrix of the AOTF of the acousto-optic tunable filter.
Wherein, θ is respectivelyFast axis azimuth angle theta corresponding to LCVR1 and LCVR2 1 、θ 2 δ corresponds to the phase delay δ of LCVR1 and LCVR2, respectively 1 、δ 2 。
M in Mueller matrix M 11 、m 12 、m 13 、m 14 Is the fast axis azimuth angle θ from the LCVR1 1 And the phase retardation δ 1 Fast axis azimuth θ of LCVR2 2 And the phase retardation δ 2 In connection with, in particular,
m 11 ＝m 21 ＝1；
m 12 ＝m 22 ＝(cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 )·(cos 2 2θ 1 +sin 2 2θ 1 cosδ 1 )+cos2θ 2 sin2θ 2 (1-cosδ 2 )·cos2θ 1 sin2θ 1 (1-cosδ 1 )-sin2θ 2 sinδ 2 sin2θ 1 sinδ 1 ；
m 13 ＝m 23 ＝(cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 )·cos2θ 1 sin2θ 1 (1-cosδ 1 )+cos2θ 2 sin2θ 2 (1-cosδ 2 )·(sin 2 2θ 1 +cos 2 2θ 1 cosδ 1 )+sin2θ 2 sinδ 2 cos2θ 1 sinδ 1 ；
m 14 ＝m 24 ＝-sin2θ 1 sinδ 1 ·(cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 )+cos2θ 2 sin2θ 2 (1-cosδ 2 )·cos2θ 1 sinδ 1 -sin2θ 2 sinδ 2 cosδ 1 ；
m 31 ＝m 32 ＝m 33 ＝m 34 ＝m 41 ＝m 42 ＝m 43 ＝m 44 ＝0。
c2, according to the Mueller matrix M, calculating the measurement matrix A according to the following formula,
in measurement matrix A, (θ) 1 ，θ 2 ) Is a group of values, (delta) 1 ，δ 2 ) Four groups of values are taken;
c3, carrying out error modeling according to the measurement matrix A, wherein a modeling formula is as follows,
wherein S is in For the desired polarization information of the object,
for actual target polarization information, ∈ A To measure the noise of matrix A, cond (A) is the condition number; the smaller the condition number cond (A) obtained from the modeling formula, the smaller the error of the measurement matrix A.
Specifically, 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 || ∞ 。
And C4, taking the two-norm condition number of the condition number cond (A) as an optimization criterion, wherein the calculation formula of the two-norm condition number cond (A) is as follows:
cond(A)＝||A|| 2 ·||A -1 || 2
wherein A is a measurement matrix A, A -1 Is the inverse of the measurement matrix a; according to type analysis (see type JS. Design of optimal polarimeters: knowledge of signal-to-noise ratio and knowledge of systematic error [ J ]]Applied Optics,2002, 41 (4): 619-30.) minimum value of the condition number cond (A)
N is the number of groups selected for the phase delay, therefore, in this embodiment, four groups are selected for the phase delay, and the calculation result of cond (A) is the minimum
As can be seen from the modeling formula, the smaller the condition number cond (A), the smaller the error of the measurement matrix A, and in this embodiment, the closer the calculation result of cond (A) is to the calculation result of cond (A)
The smaller the error of the measurement matrix A 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 parameter is the optimal polarization parameter.
C5, calculating the condition number cond (A) by adopting a genetic algorithm according to the optimization criterion determined in the step C4, and obtaining the condition number cond (A) with the calculation result closest to the condition number cond (A)
The corresponding set of polarization parameters is the optimal polarization parameter.
And C6, repeating the step C5, and calculating for n times to obtain an optimal polarization parameter set formed by n groups of optimal polarization parameters, wherein n is more than or equal to 5.
C7, taking the optimal polarization parameter with the condition number cond (A) not more than 3 in the optimal polarization parameter set as a first screening set; selecting 2-4 groups of optimal polarization parameters with the least phase delay amount of LCVR1 and LCVR2 from the first screening set as a second screening set; and selecting a group of optimal polarization parameters with the minimum phase delay adjustment times from the second screening set as global optimal parameters of the full-polarization imaging spectrum system. Referring to fig. 4, the preferred polarization parameters (θ) obtained under the configuration conditions that the phase retardation amounts to 4 different numbers are obtained 1 ，θ 2 ) Is (18.9 degree, 41.9 degree), (delta) 1 ，δ 2 ) Are respectively (179.9 °)156.6 °), (0.4 °,156.6 °), (179.9 °,46.3 °) and (0.4 °,46.3 °) are globally optimal parameters.
4 groups (delta) corresponding to global optimum parameters 1 ，δ 2 ) For example, the number of phase retardation adjustment times of LCVR1 and LCVR2 is explained, and (δ) is set before the start of full polarization measurement 1 ，δ 2 ) Is (179.9 degrees, 156.6 degrees), and delta is sequentially adjusted according to the sequence 1 、δ 2 First adjustment to δ 2 Without change, will delta 1 Is adjusted to 0.4 DEG, and is adjusted to delta for the second time 1 Is adjusted to 179.9 DEG, and is adjusted to delta for the third time 2 Is adjusted to 46.3 degrees, and the fourth adjustment is to adjust delta 1 The adjustment is made to 0.4 °, and therefore, the number of phase delay amount adjustments is four.
Example 2
When the embodiment carries out full-polarization measurement on the full-polarization imaging spectrum system, theta 1 And theta 2 At least one was a known amount and the remaining steps were the same as in example 1.
In particular, the current fast axis azimuth angle theta 1 =90 ° known fast axis azimuth angle θ 2, phase retardation amount δ 1 And the phase retardation amount delta 2 Optimizing; then the process of the first step is carried out,
m 11 ＝1：
m 12 ＝cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 ；
m 13 ＝cos2θ 2 sin2θ 2 (1-cosδ 2 )·cosδ 1 -sin2θ 2 sinδ 2 sinδ 1 ；
m 14 ＝-sinδ 1 cos2θ 2 sin2θ 2 (1-cosδ 2 )-sin2θ 2 sinδ 2 cosδ 1 。
when fast axis azimuth angle theta 2 Known by 45 degrees, fast axis azimuth angle θ 1 Phase retardation amount δ 1 And phase retardation δ 2 Optimizing; then the process of the first step is carried out,
m 11 ＝1；
m 12 ＝cosδ 2 ·(cos 2 2θ 1 +sin 2 2θ 1 cosδ 1 )-sinδ 2 sin2θ 1 sinδ 1 ；
m 13 ＝cosδ 2 ·cos2θ 1 sin2θ 1 (1-cosδ 1 )+sinδ 2 cos2θ 1 sinδ 1 ；
m 14 ＝-sin2θ 1 sinδ 1 cosδ 2 -sinδ 2 cosδ 1 。
when fast axis azimuth angle theta 1 ＝90°，θ 2 =45 ° known, phase delay amount δ 1 And the phase delay amount δ 2 To be optimized; then the process of the first step is carried out,
m 11 ＝1；
m 12 ＝cosδ 2 ；
m 13 ＝-sinδ 2 sinδ 1 ；
m 14 ＝-sinδ 2 cosδ 1 。
referring to fig. 5, by drawing a tetrahedron within the Poincare sphere, the tetrahedron vertex coordinates are found from the measurement matrix a; respectively drawing a tetrahedron in the Poincare sphere as a fast axis azimuth angle theta 1 Fast axis azimuth angle theta 2 Phase retardation amount delta 1 And the phase retardation amount delta 2 The result of the optimization of the parameters in the case of each waiting to be optimized, which is (theta) 1 ，θ 2 ) Is (18.9 degree, 41.9 degree), (delta) 1 ，δ 2 ) (179.9 °,156.6 °), (0.4 °,156.6 °), (179.9 °,46.3 °) and (0.4 °,46.3 °), respectively, the condition number κ 2=1.742, the tetrahedral volume being 0.5131; b tetrahedron is fast axis azimuth angle theta 2 Known by 45 degrees, fast axis azimuth angle θ 1 Phase retardation amount delta 1 And the phase retardation amount delta 2 Parameter optimization results in case of all-to-be-optimized, which is (θ) 1 ，θ 2 ) Is (67.5 degrees, 45 degrees), (delta) 1 ，δ 2 ) Respectively (1.6 °,146.5 °), (179.8 °,146.5 °), (1.6 °,36.4 °) and (179.8 °,37.4 °), the condition number κ 2=1.754, the tetrahedral volume is 0.5129; c tetrahedron is fast axis azimuth angle theta 1 ＝90°，θ 2 With known phase delay δ of 45 ° = known 1 And the phase delay amount δ 2 Parameter optimization results in case of all-to-be-optimized, which is (θ) 1 ，θ 2 ) Is (90 degrees, 45 degrees), (delta) 1 ，δ 2 ) Respectively (180 °,60 °), (0 °,180 °), (90 ° ) and (0 °,60 °), a condition number κ 2=2.484, and a tetrahedral volume of 0.4330; d tetrahedron is ideal regular tetrahedron, condition number
Tetrahedral volume 0.5132; the e tetrahedron is the polarization parameter (theta) not optimized by the method provided by the invention 1 ，θ 2 ) Is (90 degrees, 45 degrees), (delta) 1 ，δ 2 ) Respectively (90 ° ), (180 °,180 °), (180 °,90 °) and (90 °,60 °), condition number κ 2=10.815, tetrahedral volume is 0.1057.
From the comparison results, it can be seen that the fast axis azimuth angle θ is simultaneously matched 1 Fast axis azimuth angle theta 2 Phase retardation amount delta 1 And the phase retardation amount delta 2 The volume of the tetrahedron obtained by optimization is closest to that of an ideal regular tetrahedron, the operation of determining at least one fast axis azimuth angle is simple, the optimal values of other polarization parameters under the condition of determining the fast axis azimuth angle are obtained according to the commonly used fast axis azimuth angle, and the fast axis azimuth angle and the phase retardation can be conveniently calibrated when the full-polarization imaging spectrum system is used.
Claims (10)
1. A method for optimizing polarization parameters of a full-polarization imaging spectrum system based on a genetic algorithm is characterized by comprising the following steps:
c1, deducing a Mueller matrix M according to a full-polarization imaging spectrum system, wherein the formula is as follows,
m 11 ＝m 21 ＝1；
m 12 ＝m 22 ＝(cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 )·(cos 2 2θ 1 +sin 2 2θ 1 cosδ 1 )+cos2θ 2 sin2θ 2 (1-cosδ 2 )·cos2θ 1 sin2θ 1 (1-cosδ 1 )-sin2θ 2 sinδ 2 sin2θ 1 sinδ 1 ；
m 13 ＝m 23 ＝(cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 )·cos2θ 1 sin2θ 1 (1-cosδ 1 )+cos2θ 2 sin2θ 2 (1-cosδ 2 )·(sin 2 2θ 1 +cos 2 2θ 1 cosδ 1 )+sin2θ 2 sinδ 2 cos2θ 1 sinδ 1 ；
m 14 ＝m 24 ＝-sin2θ 1 sinδ 1 ·(cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 )+cos2θ 2 sin2θ 2 (1-cosδ 2 )·cos2θ 1 sinδ 1 -sin2θ 2 sinδ 2 cosδ 1 ；
m 31 ＝m 32 ＝m 33 ＝m 34 ＝m 41 ＝m 42 ＝m 43 ＝m 44 ＝0；
wherein, theta 1 Is the fast axis azimuth angle, δ, of LCVR1 1 Is the phase delay amount of LCVR 1; theta 2 Is the fast axis azimuth angle, δ, of LCVR2 2 Is the phase delay amount of LCVR 2; m LCVR (θ 2 ，δ 2 ) Mueller matrix, M, for LCVR2 LCVR1 (θ 1 ，δ 1 ) A Mueller matrix of LCVR 1; m P The product of Mueller matrix of the polaroid P2, the AOTF and the polaroid P1;
c2, calculating a measurement matrix A according to the Mueller matrix M, wherein the formula is as follows,
in the measurement matrix A，(θ 1 ，θ 2 ) Is a group of values, (delta) 1 ，δ 2 ) Four groups of values are taken;
c3, carrying out error modeling according to the measurement matrix A, wherein a modeling formula is as follows,
wherein S is in For the desired polarization information of the object,
for actual target polarization information,. Epsilon A To measure the noise of matrix A, cond (A) is a condition number; the smaller the condition number cond (A) obtained according to the modeling formula is, the smaller the error of the measurement matrix A is:
c4, taking the two-norm condition number of the condition number cond (A) as an optimization criterion, wherein the calculation formula of the two-norm condition number is as follows:
cond(A)＝||A|| 2 ·||A -1 || 2
wherein A is -1 Is the inverse of the measurement matrix a;
the calculated result of cond (A) is at least
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 parameter is the optimal polarization parameter;
c5, calculating the condition number cond (A) by adopting a genetic algorithm according to the optimization criterion determined in the step C4, and obtaining the condition number cond (A) with the calculation result closest to the condition number cond (A)
The corresponding group of polarization parameters are optimal polarization parameters;
c6, repeating the step C5, and carrying out n-time calculation to obtain an optimal polarization parameter set formed by n groups of optimal polarization parameters, wherein n is more than or equal to 5;
c7, taking the optimal polarization parameter with the condition number cond (A) in the optimal polarization parameter set not more than 3 as a first screening set; selecting 2-4 groups of optimal polarization parameters with the least phase delay amount of LCVR1 and LCVR2 from the first screening set as a second screening set; and selecting a group of optimal polarization parameters with the minimum phase delay adjustment times from the second screening set as global optimal parameters of the full-polarization imaging spectrum system.
2. The method for optimizing polarization parameters of a full-polarization imaging spectroscopy system based on genetic algorithm according to claim 1, wherein:
in step C1, M is P The calculation formula of (c) is as follows:
wherein M is p2 Mueller matrix, M, of polarizer P2 p1 Mueller matrix, M, of polarizer P1 AOTF Is a Mueller matrix of an acousto-optic tunable filter AOTF.
3. The method for optimizing polarization parameters of a full-polarization imaging spectroscopy system based on genetic algorithm as claimed in claim 2, wherein:
in step C1, the Mueller matrix of LCVR1 and LCVR2 is,
wherein theta corresponds to the fast axis azimuth theta of the LCVR1 and the LCVR2 respectively 1 、θ 2 δ corresponds to the phase delay δ of LCVR1 and LCVR2, respectively 1 、δ 2 。
4. The method for optimizing polarization parameters of a full-polarization imaging spectroscopy system based on genetic algorithm as claimed in claim 3, wherein:
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. A method for optimizing polarization parameters of a full-polarization imaging spectrum system based on a genetic algorithm is characterized by comprising the following steps:
d1, deducing a Mueller matrix M according to a full-polarization imaging spectrum system, wherein the formula is as follows,
m 11 ＝m 21 ＝1；
m 12 ＝m 22 ＝(cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 )·(cos 2 2θ 1 +sin 2 2θ 1 cosδ 1 )+cos2θ 2 sin2θ 2 (1-cosδ 2 )·cos2θ 1 sin2θ 1 (1-cosδ 1 )-sin2θ 2 sinδ 2 sin2θ 1 sinδ 1 ；
m 13 ＝m 23 ＝(cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 )·cos2θ 1 sin2θ 1 (1-cosδ 1 )+cos2θ 2 sin2θ 2 (1-cosδ 2 )·(sin 2 2θ 1 +cos 2 2θ 1 cosδ 1 )+sin2θ 2 sinδ 2 cos2θ 1 sinδ 1 ；
m 14 ＝m 24 ＝-sin2θ 1 sinδ 1 ·(cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 )+cos2θ 2 sin2θ 2 (1-cosδ 2 )·cos2θ 1 sinδ 1 -sin2θ 2 sinδ 2 cosδ 1 ；
m 31 ＝m 32 ＝m 33 ＝m 34 ＝m 41 ＝m 42 ＝m 43 ＝m 44 ＝0；
wherein, theta 1 Is the fast axis azimuth angle, δ, of LCVR1 1 Is the phase delay amount of LCVR 1; theta 2 Is the fast axis azimuth angle, δ, of LCVR2 2 Is the phase delay amount of LCVR 2; m LCVR (θ 2 ，δ 2 ) Mueller matrix, M, for LCVR2 LCV (θ 1 ，δ 1 ) A Mueller matrix of LCVR 1; m P The product of Mueller matrix of the polaroid P2, the AOTF and the polaroid P1;
θ 1 and theta 2 At least one is a known amount;
d2, according to the Mueller matrix M, calculating the measurement matrix A according to the following formula,
in measurement matrix A, (θ) 1 ，θ 2 ) Is a group of values, (delta) 1 ，δ 2 ) Taking values from four groups;
d3, carrying out error modeling according to the measurement matrix A, wherein a modeling formula is as follows,
wherein S is in For the desired polarization information of the object,
for actual target polarization information, ∈ A To measureNoise of matrix A, cond (A) is a condition number; obtaining the smaller the condition number cond (A) is obtained according to a modeling formula, the smaller the error of the measurement matrix A is;
d4, using the two-norm condition number of the condition number cond (a) as an optimization criterion, wherein the calculation formula of the two-norm condition number cond (a) is as follows:
cond(A)＝||A|| 2 ·||A -1 || 2
wherein, A -1 Is the inverse of the measurement matrix a;
the calculated result of cond (A) is at least
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 parameter is the optimal polarization parameter;
d5, calculating the condition number cond (A) by adopting a genetic algorithm according to the optimization criterion determined in the step D4, and obtaining the condition number cond (A) with the calculation result closest to that of the condition number cond (A)
The corresponding group of polarization parameters are optimal polarization parameters;
d6, repeating the step D5, performing n-time calculation, and obtaining n groups of optimal polarization parameters to form an optimal polarization parameter set, wherein n is more than or equal to 5;
d7, taking the optimal polarization parameter with the condition number cond (A) not more than 3 in the optimal polarization parameter set as a first screening set; selecting 2-4 groups of optimal polarization parameters with the least phase delay amount of LCVR1 and LCVR2 from the first screening set as a second screening set; and selecting a group of optimal polarization parameters with the minimum phase delay adjustment times from the second screening set as global optimal parameters of the full-polarization imaging spectrum system.
6. The method for optimizing polarization parameters of a full-polarization imaging spectroscopy system based on genetic algorithm as claimed in claim 5, wherein:
in step D1, M is P The calculation formula of (a) is as follows:
the Mueller matrix of the LCVR1 and the LCVR2 is,
wherein, M p2 Mueller matrix, M, being a polarizer P2 p1 Mueller matrix, M, of polarizer P1 AOTF The Mueller matrix of the AOTF of the acousto-optic tunable filter is that theta respectively corresponds to fast axis azimuth angles theta of LCVR1 and LCVR2 1 、θ 2 δ corresponds to the phase delay δ of LCVR1 and LCVR2 1 、δ 2 。
7. The method for optimizing polarization parameters of a full-polarization imaging spectroscopy system based on genetic algorithm according to claim 6, wherein:
in step D3, 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 || ∞ 。
8. The method for optimizing polarization parameters of a full-polarization imaging spectroscopy system based on genetic algorithm according to any one of claims 5 to 7, wherein:
in step D1, the azimuth angle theta of the fast axis 1 Known by =90 °, fast axis azimuth angle θ 2 Phase retardation amount δ 1 And phase retardation δ 2 To be optimized; then the user can use the device to make a visual display,
m 11 ＝1；
m 12 ＝cos 2 2θ 2 +sin 2 2θ 2 cosδ 2 ；
m 13 ＝cos2θ 2 sin2θ 2 (1-cosδ 2 )·cosδ 1 -sin2θ 2 sinδ 2 sinδ 1 ；
m 14 ＝-sinδ 1 cos2θ 2 sin2θ 2 (1-cosδ 2 )-sin2θ 2 sinδ 2 cosδ 1 。
9. the method for optimizing polarization parameters of a full-polarization imaging spectroscopy system based on a genetic algorithm as claimed in any one of claims 5 to 7, wherein:
in step D1, the fast axis azimuth angle theta 2 Known by 45 degrees, fast axis azimuth angle θ 1 Phase retardation amount delta 1 And the phase retardation amount delta 2 To be optimized; then the process of the first step is carried out,
m 11 ＝1；
m 12 ＝cosδ 2 ·(cos 2 2θ 1 +sin 2 2θ 1 cosδ 1 )-sinδ 2 sin2θ 1 sinδ 1 ；
m 13 ＝cosδ 2 ·cos2θ 1 sin2θ 1 (1-cosδ 1 )+sinδ 2 cos2θ 1 sinδ 1 ；
m 14 ＝-sin2θ 1 sinδ 1 cosδ 2 -sinδ 2 cosδ 1 。
10. the method for optimizing polarization parameters of a full-polarization imaging spectroscopy system based on genetic algorithm according to any one of claims 5 to 7, wherein:
in step D1, the fast axis azimuth angle theta 1 ＝90°，θ 2 =45 ° known, phase delay amount δ 1 And the phase delay amount δ 2 To be optimized; then the user can use the device to make a visual display,
m 11 ＝1；
m 12 ＝cosδ 2 ；
m 13 ＝-sinδ 2 sinδ 1 ；
m 14 ＝-sinδ 2 cosδ 1 。
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