A method for optimizing the Mueller matrix of polarization components based on liquid crystal phase retarder

Abstract

The invention discloses a Mueller matrix optimization method for a polarization component based on a liquid crystal phase retarder, belonging to the field of polarized light. Specifically, in a polarization component composed of two liquid crystal phase retarders and a polarizer, a fast axis azimuth and a phase delay that vary with temperature and voltage are introduced, the Mueller matrix of the polarization component is optimized, and the error caused by not considering the fast axis azimuth varying with temperature and voltage is eliminated.

Description

Technical Field

[0001] The invention relates to the field of polarization system optimization methods, in particular to a polarization component Mueller matrix optimization method based on a liquid crystal phase retarder. Background Art

[0002] Liquid crystal phase retarder (LCVR) is a light polarization state modulation device made by using the electro-optical birefringence characteristics of liquid crystal. By adjusting the driving voltage applied to the liquid crystal phase retarder, the phase delay of the incident light can be continuously adjusted. It can usually be regarded as a series of crystal wave plates with different phase delays. Liquid crystal phase retarder has the advantages of wide light transmission range, no need for mechanical transmission, low power consumption, fast response speed, etc., and is widely used in technical fields such as display, optical information and polarization imaging.

[0003] One-dimensional vector (S0, S1, S2, S3) T It is called the Stokes vector and is used to describe the polarization state of light. When a beam of light shines on an object, the transformation relationship between the Stokes vector of the outgoing light of the object and the Stokes vector of the incident light is called the Mueller matrix.

[0004] The polarization assembly consisting of two liquid crystal phase retarders and a linear polarizer can be combined with an illumination light source to form a polarization state generator (PSG), or it can be combined with a detector for detecting light intensity to form a polarization state detector (PSA). PSG and PSA are key components of polarization instruments such as Stokes polarimeter and Mueller polarimeter, and their performance will have a direct impact on the measurement accuracy of the polarization instrument.

[0005] The fast axis of the liquid crystal phase retarder will deflect under the influence of temperature and voltage, such as Figure 1 , Figure 2 As shown, Figure 1 A is the fast axis azimuth after the temperature changes, and B is the fast axis azimuth before the temperature changes; Figure 2 The fast axis azimuth is the correspondence between temperature and voltage. The fast axis azimuth will change when the temperature or voltage changes. There is no research on the effect of temperature on the fast axis azimuth of liquid crystal phase retarder in the existing literature, let alone the joint effect of temperature and voltage on the fast axis azimuth. Not considering the effect of temperature on the fast axis azimuth will cause the theoretical Mueller matrix model of the liquid crystal phase retarder to be different from the actual Mueller matrix, which will introduce errors when conducting polarized light research. Summary of the invention

[0006] The purpose of the present invention is to provide a Mueller matrix optimization method for a polarization component based on a liquid crystal phase retarder, so as to solve the problem in the prior art that the Mueller matrix of a polarization component composed of two liquid crystal phase retarders and a polarizer deviates from the theoretical value and produces errors due to the failure to study the change of the fast axis azimuth angle of the liquid crystal phase retarder with temperature and voltage.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is:

[0008] A method for optimizing the Mueller matrix of a polarization component based on a liquid crystal phase retarder, wherein a fast axis azimuth that varies with temperature is introduced into the Mueller matrix of the polarization component, thereby obtaining the Mueller matrix optimized for the polarization component, comprising the following steps:

[0009] Step 1, measuring the fast axis azimuths of two liquid crystal phase retarders at different temperatures and voltages, and fitting the corresponding relationship θ(T, U) of the fast axis azimuth of each liquid crystal phase retarder with respect to temperature and voltage based on the measurement results, where θ represents the fast axis azimuth of each liquid crystal phase retarder, T represents the temperature of each liquid crystal phase retarder, and U represents the driving voltage of each liquid crystal phase retarder;

[0010] Step 2: Based on the calibrated fast axis azimuth, measure the phase delay of two liquid crystal phase retarders at different temperatures and voltages, and fit the measured data into the corresponding relationship δ(T, U) of the phase delay of each liquid crystal phase retarder with respect to temperature and voltage, where δ represents the phase delay of each liquid crystal phase retarder.

[0011] Step 3: Substitute the calibrated fast axis azimuth angle of each liquid crystal phase retarder with respect to temperature and voltage θ(T, U) and the phase delay with respect to temperature and voltage δ(T, U) into the Mueller matrix theoretical model M(θ, δ), and obtain the rewritten Mueller matrix M(T, U) of the corresponding liquid crystal phase retarder as shown in formula (1):

[0012] M(T,U)=M(θ(T,U), δ(T,U)) (1);

[0013] Step 4: According to the Stokes vector relationship of the incident light and the outgoing light of the polarization state generator PSG and the polarization state detector PSA, the following formulas are obtained:

[0014] S out =M i (T, U1)×M2(T, U2)×M P ×S in =M PSG (T, U1, U2)×S in (2)

[0015] Sout =M P ×M2(T,U2)×M1(T,U1)×S in =M PSA (T, U1, U2)×S in (3)

[0016] In formulas (2) and (3), M1 and M2 are the Mueller matrices of the two liquid crystal phase retarders, U1 and U2 are the driving voltages of the two liquid crystal phase retarders, and M P is the Mueller matrix of the linear polarizer that constitutes the polarization assembly, M PSG and M PSA are the Mueller matrices of the polarization state generator PSG and the polarization state detector PSA, respectively. in and S ou t are the Stokes vectors of the incident and outgoing light, respectively;

[0017] In formula (2) and formula (3), if the temperature T is determined, for any voltage combination (U1, U2) of the polarization state generator PSG, PSG will generate a light beam with a specific polarization state. If this light beam is irradiated on the polarization state detector PSA with the same voltage combination (U1, U2), the detected light intensity will be the maximum. Except for the light source part of the polarization state generator PSG and the light intensity detector part of the polarization state detector PSA, the remaining components have exactly the same structure, that is, the polarization components to be optimized. The Mueller matrix M can be used G (T, U1, U2) is used to describe this polarization component, as shown in formula (4):

[0018] S out =M2(T,U2)×M1(T,U1)×M P ×S in =M G (T, U1, U2)×S in (4)

[0019] Among them, the outgoing light S out The first component S out0 Represents brightness, the first component S out is the incident light S in The linear function of is shown in formula (5):

[0020] S out0 =αS in0 +βS in1 +γS in2 +εS in3 (5)

[0021] In formula (5), α, β, γ, ε are the matrix M G(T, U1, U2) Element m in the first row 11 (T, U1, U2), m 12 (T, U1, U2), m 13 (T, U1, U2), m 14 (T, U1, U2), S in0 , S in1 , S in2 , S in3 is the incident light S in The four Stokes components of ;

[0022] For formula (4), if the temperature T is known, different voltage combinations can be used to obtain different M G Matrix. For a given incident light S in , assuming there are 4 temporarily unknown voltage combinations (U 11 , U 12 )、(U 21 , U 22 )、(U 31 , U 32 )、(U 41 , U 42 ), then there are 4 Mueller matrices M G1 (T,U 11 , U 12 )、M G2 (T,U 21 , U 22 )、M G3 (T,U 31 , U 32 )、M G4 (T,U 41 , U 42 ), combined with formula (5), a linear equation system is established as shown in formula (6):

[0023]

[0024] In formula (6), α1, β1, γ1, ε1 are the matrix M G1 (T,U 11 , U 12 ) The first row of elements, α2, β2, γ2, ε2 are the matrix M G2 (T,U 21 , U 22 ) The first row of elements, α3, β3, γ3, ε3 are the elements of the matrix M G3 (T,U 31 , U 32 ) The first row of elements, α4, β4, γ4, ε4 are the matrix M G4 (T,U 41 , U 42) The first row of elements, I1, I2, I3, I4 represent brightness, I1 is equal to α1S in0 +β1S in1 +γ1S in2 +ε1S in3 , I2 equals α2S in0 +β2S in1 +γ2S in2 +ε2S in3 , I3 equals α3S in0 +β3S in1 +γ3S in2 +ε3S in3 , I4 equals α4S in0 +β4S in1 +γ4S in +ε4S in , the matrix M L yes I am

[0025] For the linear equation system shown in formula (6), use the matrix M L The condition number is used to characterize S in The matrix M is sensitive to the error and uncertainty of its brightness I. L The condition number CN(M L ) is defined as the matrix M L The ratio of the maximum singular value to the minimum singular value is shown in formula (7):

[0026]

[0027] In formula (7), σ max and σ min They are the matrices M L The largest and smallest non-zero singular values ​​of the matrix M L The smaller the condition number, the more incident light S in The less sensitive it is to errors or uncertainties in brightness I;

[0028] Step 5: Calculate the matrix M L The condition number reaches the theoretical minimum When the driving voltage of the two liquid crystal phase retarders (U 11 , U 12 )、(U 21 , U 22 )、(U 31 , U 32 )、(U 41 , U 42 ), substitute the calculated driving voltage into the Mueller matrix M used to describe the polarization component G(T, U1, U2), get the optimized Mueller matrix M G1 (T,U 11 , U 12 )、M G2 (T,U 21 , U 22 )、M G3 (T,U 31 , U 32 )、M G4 (T,U 41 , U 42 ), the process is as follows:

[0029] The theoretical minimum value of the condition number of the matrix ML is If and only if the four Stokes vectors (α1, β1, γ1, ε1) T 、(α2,β2,γ2,ε2) T 、(α3,β3,γ3,ε3) T 、(α4,β4,γ4,ε4) T It is established when the tetrahedron formed by the corresponding four points on the Poincaré sphere after normalization is a regular tetrahedron;

[0030] In order to make the matrix M L The condition number is minimized. Take any inscribed regular tetrahedron on the Poincaré sphere and calculate the four vertices of the regular tetrahedron as D1(S 11 , S 12 , S 13 )、D2(S 21 , S 22 , S 23 )、D3(S 31 , S 32 , S 33 )、D4(S 41 , S 42 , S 43 ); Let the matrix equal At this time, the matrix M L The condition number can reach the theoretical minimum

[0031] As mentioned above, α1, β1, γ1, ε1 are the matrix M G1 (T,U 11 , U 12 ) The first row of array elements, while M G1 (T,U 11 , U 12 ) The first row of array elements can also be represented as m 111 (U 11 , U 12 )、m 112(U 11 , U 12 )、m 113 (U 11 , U 12 )、m 114 (U 11 , U 12 ). Let α1 = m 111 (U 11 , U 12 ),β1=m 112 (U 11 , U 12 ),γ1=m 113 (U 11 , U 12 ),ε1=m 114 (U 11 , U 12 ), the corresponding unknown voltage (U 11 , U 12 ). Similarly, we can calculate (U 21 , U 22 )、(U 31 , U 32 ) and (U 41 , U 42 ).

[0032] The calculated driving voltage (U 11 , U 12 )、(U 21 , U 22 )、(U 31 , U 32 )、(U 41 , U 42 ) is substituted into the Mueller matrix M G (T, U1, U2), get the optimized Mueller matrix M G1 (T,U 11 , U 12 )、M G2 (T,U 21 , U 22 )、M G3 (T,U 31 , U 32 )、M G4 (T,U 41 , U 42 ).

[0033] The present invention takes into account the combined effects of temperature and voltage on the fast-axis azimuth of a liquid crystal phase retarder, optimizes the Mueller matrix theoretical model of a polarization component consisting of two liquid crystal phase retarders and a polarizer, eliminates the error caused by not considering the changes in the fast-axis azimuth with temperature and voltage, and improves the accuracy of the overall Mueller matrix of the polarization component. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of the fast-axis azimuth angle deflection of the liquid crystal phase retarder.

[0035] Figure 2 Schematic diagram of the fast axis azimuth changing with temperature and voltage.

[0036] Figure 3 Schematic diagram of phase delay changing with temperature and voltage.

[0037] Figure 4 It is a schematic diagram of the structure of the polarization state generator PSG and the polarization state detector PSA. DETAILED DESCRIPTION

[0038] The specific implementation of the present invention is further described in detail below with reference to the accompanying drawings and examples:

[0039] like Figure 4 As shown, Figure 4 (a) is a schematic diagram of the optical path of PSG, in which two liquid crystal phase retarders 1 and 2 and a linear polarizer 3 form a polarization component, which then cooperates with a light source 4 to form PSG. Figure 4 (b) is a schematic diagram of the optical path of PSA, in which two liquid crystal phase retarders 1 and 2 and a linear polarizer 3 form a polarization component, which is then combined with a light intensity detector 5 to form PSA. This embodiment is described by taking the polarization state generator PSG as an example, and the analysis method of the polarization state detector PSA is similar.

[0040] In this embodiment, the initial fast axis azimuth of the first liquid crystal retarder 1 is 45° to the vertical direction, the initial fast axis azimuth of the second liquid crystal retarder 2 is 22.5° to the vertical direction, and the polarization direction of the linear polarizer 3 is the vertical direction.

[0041] First, the extinction method is used to measure the corresponding relationship between temperature and voltage and the fast axis azimuth of the two liquid crystal phase retarders 1 and 2. The liquid crystal phase retarder is placed between two linear polarizers with mutually perpendicular polarization directions, the liquid crystal phase retarder is rotated to find the extinction position, the fast axis azimuth of the liquid crystal phase retarder is recorded, and the measured data is fitted into the corresponding relationship of the fast axis azimuth with respect to temperature and voltage θ1(T, U1) and θ2(T, U2). Figure 2 Schematic diagram of the relationship between the fast axis azimuth and temperature and voltage. In the figure, the X-axis is voltage, the Y-axis is temperature, and the Z-axis is the fast axis azimuth.

[0042] Based on the calibrated correspondence between the fast axis azimuth and temperature and voltage, the brightness method is used to measure the correspondence between temperature and voltage and the phase delay of the two liquid crystal phase retarders 1 and 2. a and voltage Ua When the liquid crystal phase retarder is rotated to the same position as θ a (T a , U a ) at a 45° angle, rotate the second linear polarizer and record the brightness of the light beam behind the polarizer, calculate and record as a , voltage is U a The measured data are fitted into the corresponding relationship of phase delay with respect to temperature and voltage δ1(T, U1) and δ2(T, U2). Figure 3 The figure is a schematic diagram of the corresponding relationship between phase delay and temperature and voltage. In the figure, the X-axis is voltage, the Y-axis is temperature, and the Z-axis is phase delay.

[0043] According to the calibrated correspondence between the fast-axis azimuth angles and temperature and the phase delay and temperature and voltage of the two liquid crystal phase retarders, their Mueller matrices can be rewritten as M1(T, U1) = M1(θ1(T, U1), δ1(T, U1)) and M2(T, U2) = M2(θ2(T, U2), δ2(T, U2)) respectively.

[0044] When the ambient temperature T is known, the equation for the incident light after it enters the polarization component is:

[0045] S out =M2(U2)×M1(U1)×M P ×S in =M G (U1, U2)×S in (1)

[0046] Where M P is the linear polarizer that constitutes the polarization component, M1 and M2 are the Mueller matrices of the two liquid crystal phase retarders, U1 and U2 are the driving voltages of the two liquid crystal phase retarders, and the outgoing light Stokes vector S out The first component S out represents brightness, which is the incident light S in The linear function of is:

[0047] S out0 =αS in0 +βS in1 +γS in2 +εS in3 (2)

[0048] Where α, β, γ, ε are matrix M G (U1, U2) Element m in the first row 11 (U1, U2), m 12 (U1, U2), m 13(U1, U2), m 14 (U1, U2), S in0 , S in1 , S in2 , S in3 is the incident light S in The four Stokes components of .

[0049] For a given incident light S in , by using multiple voltage combinations, a linear equation system can be established. Taking 4 voltage groups as an example, the linear equation system can be expressed as:

[0050]

[0051] In formula (3), α1, β1, γ1, ε1 are matrix M G1 (T,U 11 , U 12 ) The first row of elements, α2, β2, γ2, ε2 are the matrix M G2 (T,U 21 , U 22 ) The first row of elements, α3, β3, γ3, ε3 are the elements of the matrix M G3 (T,U 31 , U 32 ) The first row of elements, α4, β4, γ4, ε4 are the matrix M G4 (T,U 41 , U 42 ) The first row of elements, I1, I2, I3, I4 represent brightness, I1 is equal to α1S in0 +β1S in1 +γ1S in2 +ε1S in3 , I2 equals α2S in0 +β2S in1 +γ2S in2 +ε2S in3 , I3 equals α3S in0 +β3S in1 +γ3S in2 +ε3S in3 , I4 equals α4S in0 +β4S in1 +γ4S in2 +ε4S in3 , the matrix M L yes I am

[0052] In order to make the matrix M LThe condition number is minimized. Take an inscribed regular tetrahedron on the Poincare sphere at random. Its four vertices are D1(0.5776, 0.5776, -0.5776), D2(-0.5776, 0.5776, 0.5776), D3(-0.5776, -0.5776, -0.5776) and D4(0.5776, -0.5776, 0.5776). The matrix M can be obtained from the coordinates of the four vertices. L for:

[0053]

[0054] As mentioned above, α1, β1, γ1, ε1 are the matrix M G1 (U 11 , U 12 ) The first row of array elements, while M G1 (U 11 , U 12 ) The first row of array elements can also be represented as m 111 (U 11 , U 12 )、m 112 (U 11 , U 12 )、m 113 (U 11 , U 12 )、m 114 (U 11 , U 12 ). Let α1=0.5=m 111 (U 11 , U 12 ), β1=0.2887=m 112 (U 11 , U 12 ),γ1=0.2887=m 113 (U 11 , U 12 ),ε1=-0.2887=m 114 (U 11 , U 12 ), the corresponding unknown voltage (U 11 , U 12 ). Similarly, we can calculate (U 21 , U 22 )、(U 31 , U 32 ) and (U 41 , U 42 ).

[0055] M G1 (T,U 11 , U 12 )、MG2 (T,U 21 , U 22 )、M G3 (T,U 31 , U 32 )、M G4 (T,U 41 , U 42 ) is the Mueller matrix corrected by the polarization component.

[0056] The present invention takes into account the combined effects of temperature and voltage on the fast-axis azimuth of a liquid crystal phase retarder, optimizes the Mueller matrix theoretical model of a polarization component consisting of two liquid crystal phase retarders and a polarizer, eliminates the error caused by not considering the changes in the fast-axis azimuth with temperature and voltage, and improves the accuracy of the overall Mueller matrix of the polarization component.

[0057] The specific implementation methods described above are only used to further explain the purpose and technical solutions of the present invention in detail, and are not used to limit the scope of protection of the present invention. Modifications to the specific implementation methods of the present invention or equivalent replacement of some technical features without departing from the spirit of the present invention should be included in the scope of the technical solutions claimed for protection by the present invention.

Claims

1. A Mueller matrix optimization method for a polarization component based on a liquid crystal phase retarder, which is used for a polarization component composed of two liquid crystal phase retarders and a linear polarizer, wherein the polarization component forms a polarization state generator PSG when used with an illumination light source, and forms a polarization state detector PSA when used with a light intensity detector, and is characterized in that: Introducing a fast axis azimuth that varies with temperature into the Mueller matrix of the polarization component, thereby obtaining an optimized Mueller matrix of the polarization component, comprises the following steps: Step 1, obtaining the corresponding relationship θ(T, U) between the fast axis azimuth of two liquid crystal phase retarders and the temperature and voltage, wherein θ represents the fast axis azimuth of each liquid crystal phase retarder, T represents the temperature of each liquid crystal phase retarder, and U represents the driving voltage of each liquid crystal phase retarder; Step 2, obtaining a corresponding relationship δ(T, U) between the phase delay of two liquid crystal phase retarders with respect to temperature and voltage, wherein δ represents the phase delay of each liquid crystal phase retarder; Step 3: Substitute the calibrated fast axis azimuth angle of each liquid crystal phase retarder with respect to temperature and voltage θ(T, U) and the phase delay with respect to temperature and voltage δ(T, U) into the Mueller matrix theoretical model M(θ, δ), and obtain the rewritten Mueller matrix M(T, U) of the corresponding liquid crystal phase retarder as shown in formula (1): M(T,U)=M(θ(T,U), δ(T,U)) (1); Step 4: According to the Stokes vector relationship of the incident light and the outgoing light of the polarization state generator PSG and the polarization state detector PSA, the following formulas are obtained: S out =M1(T,U1)×M2(T,U2)×M P ×S in =M PSG (T,U1,U2)×S in (2), S out =M P ×M2(T,U2)×M1(T,U1)×S in =M PSA (T,U1,U2)×S in (3), In formulas (2) and (3), M1 and M2 are the Mueller matrices of the two liquid crystal phase retarders, U1 and U2 are the driving voltages of the two liquid crystal phase retarders, and M P is the Mueller matrix of the linear polarizer that constitutes the polarization assembly, M PSG and M PSA are the Mueller matrices of the polarization state generator PSG and the polarization state detector PSA, respectively. in and S out are the Stokes vectors of the incident and outgoing light, respectively; In formula (2) and formula (3), if the temperature T is determined, for any set of voltage combinations (U1, U2) of the polarization state generator PSG, PSG will generate a light beam with a specific polarization state. If this light beam is irradiated onto the polarization state detector PSA with the same voltage combination (U1, U2), the detected light intensity will be the maximum. Except for the light source part of the polarization state generator PSG and the light intensity detector part of the polarization state detector PSA, the remaining components have exactly the same structure, that is, the polarization components to be optimized. The Mueller matrix M can be used G (T, U1, U2) is used to describe this polarization component, as shown in formula (4): S out =M2(T,U2)×M1(T,U1)×M P ×S in =M G (T,U1,U2)×S in (4), Among them, the outgoing light S out The first component S out0 Represents brightness, the first component S out0 is the incident light S in The linear function of is shown in formula (5): I=S out0 =αS in0 +βS in1 +γS in2 +εS in3 (5), In formula (5), I represents brightness, α, β, γ, and ε are matrices M G (T, U1, U2) Element m in the first row 11 (T, U1, U2), m 12 (T, U1, U2), m 13 (T, U1, U2), m 14 (T, U1, U2)S in0 , S in1 , S in2 , S in3 is the incident light S in The four Stokes components of ; For formula (4), if the temperature T is known, different voltage combinations can be used to obtain different M G Matrix; for a given incident light S in , assuming there are 4 temporarily unknown voltage combinations (U 11 , U 12 )、(U 21 , U 22 )、(U 31 , U 32 )、(U 41 , U 42 ), then there are 4 Mueller matrices M G1 (T,U 11 , U 12 )、M G2 (T,U 21 , U 22 )、M G3 (T,U 31 , U 32 )、M G4 (T,U 41 , U 42 ), combined with formula (5), a linear equation system is established as shown in formula (6): In formula (6), α1, β1, γ1, ε1 are the matrix M G1 (T,U 11 , U 12 ) The first row of elements, α2, β2, γ2, ε2 are the matrix M G2 (T,U 21 , U 22 ) The first row of elements, α3, β3, γ3, ε3 are the elements of the matrix M G3 (T,U 31 , U 32 ) The first row of elements, α4, β4, γ4, ε4 are the matrix M G4 (T,U 41 , U 42 ) The first row of elements, I1, I2, I3, I4 represent brightness, I1 is equal to α1S in0 +β1S in1 +γ1S in2 +ε1S in3 , I2 equals α2S in0 +β2S in1 +γ2S in2 +ε2S in3 , I3 equals α3S in0 +β3S in1 +γ3S in2 +ε3S in3 , I4 equals α4S in0 +β4S in1 +γ4S in2 +ε4S in3 , the matrix M L yes For the linear equation system shown in formula (6), use the matrix M L The condition number is used to characterize S in The matrix M is sensitive to the error and uncertainty of its brightness I. L The condition number CN(M L ) is defined as the matrix M L The ratio of the maximum singular value to the minimum singular value is shown in formula (7): In formula (7), σ max and σ min They are the matrices M L The largest and smallest non-zero singular values ​​of the matrix M L The smaller the condition number, the more incident light S in The less sensitive it is to errors or uncertainties in brightness I; Step 5: Calculate the matrix M L When the condition number reaches the theoretical minimum, the driving voltage (U 11 , U 12 )、(U 21 , U 22 )、(U 31 , U 32 )、(U 41 , U 42 ), substitute the calculated driving voltage into the Mueller matrix M used to describe the polarization component G (T, U1, U2), get the optimized Mueller matrix M G1 (T,U 11 , U 12 )、M G2 (T,U 21 , U 22 )、M G3 (T,U 31 , U 32 )、M G4 (T,U 41 , U 42 ).

2. The method for optimizing the Mueller matrix of a polarization component based on a liquid crystal phase retarder according to claim 1, characterized in that: In step 1, the fast axis azimuths of two liquid crystal phase retarders are measured at different temperatures and voltages, and the corresponding relationship θ(T, U) of the fast axis azimuth of each liquid crystal phase retarder with respect to temperature and voltage is fitted based on the measurement results.

3. The method for optimizing the Mueller matrix of a polarization component based on a liquid crystal phase retarder according to claim 1, characterized in that: In step 2, based on the calibrated fast axis azimuth, the phase retardation of two liquid crystal phase retarders at different temperatures and voltages is measured, and the measured data is fitted into the corresponding relationship δ(T, U) of the phase retardation of each liquid crystal phase retarder with respect to temperature and voltage.

4. The method for optimizing the Mueller matrix of a polarization component based on a liquid crystal phase retarder according to claim 1, characterized in that: In step 5, the matrix M L The theoretical minimum value of the condition number that can be achieved is 5. A method for optimizing the Mueller matrix of a polarization component based on a liquid crystal phase retarder according to claim 1 or 4, characterized in that: Step 5: Matrix M L The theoretical minimum condition number that can be achieved is If and only if the four Stokes vectors (α1, β1, γ1, ε1) T 、(α2,β2,γ2,ε2) T 、(α3,β3,γ3,ε3) T 、(α4,β4,γ4,ε4) T It is established when the tetrahedron formed by the corresponding four points on the Poincaré sphere after normalization is a regular tetrahedron; In order to make the matrix M L The condition number is minimized. Take any inscribed regular tetrahedron on the Poincaré sphere and calculate the four vertices of the regular tetrahedron as D1(S 11 , S 12 , S 13 )、D2(S 21 , S 22 , S 23 )、D3(S 31 , S 32 , S 33 )、D4(S 41 , S 42 , S 43 ); Let the matrix equal At this time, the matrix M L The condition number can reach the theoretical minimum As mentioned above, α1, β1, γ1, ε1 are the matrix M G1 (T,U 11 , U 12 ) The first row of array elements, while M G1 (T,U 11 , U 12 ) The first row of array elements can also be represented as m 111 (U 11 , U 12 )、m 112 (U 11 , U 12 )、m 113 (U 11 , U 12 )、m 114 (U 11 , U 12 ); let α1 = m 111 (U 11 , U 12 ),β1=m 112 (U 11 , U 12 ),γ1=m 113 (U 11 , U 12 ),ε1=m 114 (U 11 , U 12 ), the corresponding unknown voltage (U 11 , U 12 ); Similarly, we can calculate (U 21 , U 22 )、(U 31 , U 32 ) and (U 41 , U 42 ); The calculated driving voltage (U 11 , U 12 )、(U 21 , U 22 )、(U 31 , U 32 )、(U 41 , U 42 ) is substituted into the Mueller matrix M G (T, U1, U2), get the optimized Mueller matrix M G1 (T,U 11 , U 12 )、M G2 (T,U 21 , U 22 )、M G3 (T,U 31 , U 32 )、M G4 (T,U 41 , U 42 ).

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