Low-sensitivity-oblique incidence double Stokes-Mueller polarization measurement optimization method

Abstract

The invention provides a low-sensitivity-oblique incidence double Stokes-Mueller polarization measurement optimization method, which comprises the following steps of: firstly, introducing the sum of two angles representing three-dimensional rotation of an element, so that a Mueller matrix can describe the condition of three-dimensional rotation of a polarization element, and further describe the effect of the polarization element on oblique incidence light; then, a polarization element Mueller matrix containing three-dimensional rotation is used for representing an instrument matrix of DSMP, the DSMP is optimized by using the matrix in combination with a minimum condition number and a genetic algorithm, the PSG rotation angle low in sensitivity to light oblique incidence is optimized, and high stability can be kept in actual measurement; therefore, the method can describe the effect of the polarization element on the oblique incident light or the effect of the polarization element in three-dimensional rotation on the normal incident light, but the existing method cannot describe the two conditions and only can describe the effect of the polarization element on the normal incident light; according to the method, the random error caused by oblique incidence of light in polarization measurement can be optimized, and the random error caused by oblique incidence of light is neglected in an existing optimization method.

Description

Technical Field

[0001] This invention belongs to the field of polarization measurement technology, and in particular relates to an optimized method for low-sensitivity oblique-incidence dual Stokes-Mueller polarization measurement. Background Technology

[0002] Barzda et al. from the University of Toronto studied the Double Stokes-Mueller Polarimetry (DSMP) technique. This technique can characterize the nonlinear optical properties of noncentrosymmetric materials and provide molecular structural information for substances such as collagen and myosin. Due to its high specificity, high penetration, sensitivity to molecular structure, and ability to acquire both linear and nonlinear information, it has been used to observe and study the microstructure of pathological tissues such as thyroid cancer, breast cancer, and non-small cell lung cancer.

[0003] In DSMP, the interpretation of sample microstructure depends on measurement stability. However, measurement stability is affected by random errors, including random fluctuations in light intensity and random errors inherent in the instrument itself. Therefore, it is necessary to optimize random errors. Optimization can be achieved by reducing the condition number (CN) of the instrument matrix or by using equal weighted variance (EWV). Xiaobo Li from the Chinese University of Hong Kong and Jinxian Wu from Beijing Institute of Technology optimized nonlinear polarimeters with different structures. Xiaobo Li optimized the polarization state generator (PSG) of the nonlinear polarimeter using the Pareto polyhedron method and the minimum EWV method, with the Pareto polyhedron method showing poor results and the minimum EWV method showing better results. Jinxian Wu optimized the PSG of the nonlinear polarimeter using the minimum condition number method and a genetic algorithm, achieving a configuration with higher stability.

[0004] Currently, such as Figure 1The minimum condition number method shown aims to minimize the condition number of the instrument matrix and combines it with a genetic algorithm to optimize the rotation angles of multiple iterative PSG waveplates. Xiaobo Li and Jinxian Wu optimized the DSMP. Xiaobo Li optimized the PSG rotation angle of the nonlinear polarimeter using the Pareto polyhedron method and the minimum EWV method. The Pareto polyhedron method performed poorly, while the minimum EWV method performed better, suppressing random errors introduced by light intensity fluctuations and instrument instability. However, both methods neglected the random errors introduced by oblique incidence. Jinxian Wu optimized the PSG rotation angle of the nonlinear polarimeter during sum and difference frequency processes using the minimum condition number method and a genetic algorithm. Its advantage is that the phase delay difference of the waveplate caused by different wavelengths of incidence can be suppressed, but it also neglects the random errors introduced by oblique incidence.

[0005] In actual measurements, factors such as system assembly errors or experimental platform vibrations can cause light to be incident obliquely into the polarimeter, affecting measurement stability. Current optimization methods neglect the random errors introduced by oblique light incidence and fail to analyze and optimize them. Summary of the Invention

[0006] To address the aforementioned issues, this invention provides an optimization method for low-sensitivity oblique-incidence dual Stokes-Mueller polarization measurement. The Jones and Mueller matrices of the polarization element under oblique incidence are derived, the instrument matrix of the DSMP under oblique incidence is constructed, and these matrices are combined with the minimum condition number and a genetic algorithm to optimize the DSMP. This optimizes the PSG rotation angle, which is less sensitive to oblique incidence, ensuring high stability in actual measurements under oblique incidence.

[0007] An optimized method for low-sensitivity oblique-incidence dual Stokes-Mueller polarization measurements includes the following steps: S1: Construct the instrument matrix of the polarization state generator PSG, which consists of the polarization elements to be optimized in the polarization measurement system DSMP. ;in, , , These represent the fast axis azimuth angles set for each polarization element to be optimized during the 9th modulation by the polarization state generator PSG, and the rotation axis azimuth and elevation angles, which are considered as unknown random errors in polarization measurement. , , , , N The total number of polarization elements to be optimized. Indicates the first The modulation is the first The fast axis azimuth angle set for each polarization element to be optimized; simultaneously... and The resulting combination is randomly assigned to R groups of values; S2: For Randomly set P different initial values, and assign P different values ​​to... As P individuals, ; S3: Use P different values Traversal and The R sets of values ​​form P×R possible combinations of values; S4: Obtain P×R instrument matrices under P×R possible value combinations. Then, based on each individual The corresponding R instrument matrices Obtain the fitness of each individual ; S5: Determine whether the set number of iterations has been reached. If yes, select the individual with the minimum fitness value from all iterations as the final optimization result. If no, proceed to step 6. S6: Select some individuals from the P individuals in the current iteration using the roulette wheel algorithm for crossover and mutation until a new set of P individuals is obtained. The lower the fitness, the higher the probability of being selected. Then, repeat steps S3 to S5 using the new set of P individuals.

[0008] Furthermore, any individual Corresponding fitness The method to obtain it is as follows: Obtain each The corresponding R instrument matrices Average condition number Standard deviation of all condition numbers and the range of all condition numbers ; according to , , Obtain each body separately Corresponding fitness , These are the corresponding weights.

[0009] Furthermore, weight The values ​​for the rotation axis azimuth angle are set according to actual needs, and P is greater than 1. The range of values ​​for the pitch angle of the rotation axis is: .

[0010] Furthermore, the constructed instrument matrix Each column These are the two Stokes vectors of the PSG after each modulation of the incident light. Among them, instrument matrix Any of the first The corresponding double Stokes vector Used to characterize incident light After the first The two-photon polarization state and dual Stokes vector of the submodulated PSG Depend on Seeking, Indicates incident light After the first The linear polarization state of the PSG after submodulation. The value is the first The product of the Mueller matrix of each polarization element to be optimized after modulation and the incident light.

[0011] Furthermore, when the polarization state generator PSG is composed of a quarter-wave plate, a half-wave plate, and a polarizer, the instrument matrix... The List The incident light passes through the first The dual Stokes vector of the submodulated PSG as follows:

[0012] in, , , , Incident light After the first The linear polarization state of the submodulated PSG The four components; superscript It represents a second-order nonlinear effect; T represents the transpose.

[0013] Furthermore, incident light After the first polarization state of the submodulated PSG The calculation method is as follows:

[0014] in, The two-dimensional Muller matrix of a quarter-wave plate. The two-dimensional Mueller matrix of a half-wave plate. The two-dimensional Mueller matrix of the polarizer. , , , They are respectively , , , product The four components.

[0015] Furthermore, the method for calculating the two-dimensional Mueller matrix of any polarization element to be optimized is as follows: Construct four linearly independent two-dimensional Jones vectors, the first of which is... Two-dimensional Jones vector Represented as:

[0016] in, , They represent the incident light at... and Vibration in the direction; simultaneously, construct the corresponding two-dimensional Stokes vector. and three-dimensional Jones vector as follows:

[0017]

[0018] Among them, the three-dimensional Jones vector As the incident polarization state, and the three-dimensional Jones matrix of the polarization element to be optimized. The action yields four corresponding outgoing three-dimensional Jones vectors, where the first... One outgoing three-dimensional Jones vector Represented as:

[0019] in, , , They represent the emitted light at... , and Vibration in the direction of movement; Extract the outgoing 3D Jones vector The component perpendicular to the direction of light propagation yields the corresponding two-dimensional Jones vector. :

[0020] According to the two-dimensional Jones vector Obtain the corresponding two-dimensional Stokes vector :

[0021] According to the two-dimensional Stokes vector and two-dimensional Stokes vector Determine the two-dimensional Mueller matrix of the polarization element to be optimized. :

[0022] in, This represents the set of four Stokes vectors.

[0023] Furthermore, assuming the incident light propagates along the Z-axis, the rotation axis Located in the XY plane, and the axis of rotation The angle with the Y-axis is The angle between the normal of the polarization element to be optimized and the Z-axis is currently... ; The three-dimensional Jones matrix of the polarization element to be optimized The calculation method is as follows:

[0024] in, This indicates the polarization element to be optimized around the rotation axis. Rotation The three-dimensional rotation matrix, This indicates the polarization element to be optimized around the rotation axis. Rotation The three-dimensional rotation matrix, Indicates the azimuth angle of the fast axis as The rotation matrix at time, Indicates the azimuth angle of the fast axis as Rotation matrix at time; The intrinsic Jones matrix representing the polarization element; for The third-order extended form, express The third-order extended form.

[0025] Beneficial effects: This invention provides an optimized method for low-sensitivity oblique-incidence dual Stokes-Mueller polarization measurement, which first introduces two angles representing the three-dimensional rotation of the element. and This invention enables the Mueller matrix to describe the three-dimensional rotation of the polarization element, and thus the effect of the polarization element on obliquely incident light. Then, the Mueller matrix of the polarization element with three-dimensional rotation is used to characterize the instrument matrix of the DSMP (Digital Subtraction Angiography) instrument. This matrix, combined with the minimum condition number and a genetic algorithm, optimizes the DSMP, improving the PSG (Polarization Sequencing Gear) rotation angle, which is less sensitive to oblique incidence, and maintaining high stability in actual measurements. Therefore, this invention can describe the effect of the polarization element on obliquely incident light, or the effect of a three-dimensionally rotated polarization element on normally incident light, whereas existing methods cannot describe these two cases and can only describe the effect of the polarization element on normally incident light. This invention can optimize the random error caused by oblique incidence in polarization measurements, while existing optimization methods ignore this random error. Attached Figure Description

[0026] Figure 1 The DSMP flowchart is optimized using a genetic algorithm to address the existing minimum condition number. Figure 2 The flowchart for optimizing DSMP with minimum condition number and genetic algorithm under oblique light incidence provided by this invention; Figure 3 This is a schematic diagram of the three-dimensional rotation of the polarization element provided by the present invention; Figure 4 A schematic diagram illustrating the change in the propagation phase of incident light during three-dimensional rotation of the waveplate provided by the present invention; Figure 5 A flowchart illustrating the calculation of the two-dimensional Mueller matrix for the polarization element provided by this invention. Detailed Implementation

[0027] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.

[0028] This invention primarily combines the Mueller matrix of the polarization element under oblique incidence with the minimum condition number and a genetic algorithm to achieve simulation and stability optimization of DSMP under oblique incidence. Based on this, as... Figure 2 As shown, this invention provides an optimized method for low-sensitivity oblique-incidence dual Stokes-Mueller polarization measurement, comprising the following steps: S1: Construct the instrument matrix of the polarization state generator PSG, which consists of the polarization elements to be optimized in the polarization measurement system DSMP. ;in, , , These represent the fast axis azimuth angles set for each polarization element to be optimized during the 9th modulation by the polarization state generator PSG, and the rotation axis azimuth and elevation angles, which are considered as unknown random errors in polarization measurement. , , , , N The total number of polarization elements to be optimized. Indicates the first The modulation is the first The fast axis azimuth angle set for each polarization element to be optimized; simultaneously... and The resulting combination is randomly assigned to R groups of values; It should be noted that the constructed instrument matrix Each column These are the two Stokes vectors of the PSG after each modulation of the incident light. Among them, instrument matrix Any of the first The corresponding double Stokes vector Used to characterize incident light After the first The two-photon polarization state and dual Stokes vector of the submodulated PSG Depend on Seeking, Indicates incident light After the first The linear polarization state of the PSG after submodulation. The value is the first The product of the Mueller matrix of each polarization element to be optimized after modulation and the incident light.

[0029] When the polarization state generator PSG consists of a quarter-wave plate, a half-wave plate, and a polarizer, the instrument matrix... The List The incident light passes through the first The dual Stokes vector of the submodulated PSG as follows:

[0030] in, , , , Incident light After the first The linear polarization state of the submodulated PSG The four components; superscript It represents a second-order nonlinear effect; T represents the transpose.

[0031] Incident light After the first polarization state of the submodulated PSG The calculation method is as follows:

[0032] in, The two-dimensional Muller matrix of a quarter-wave plate. The two-dimensional Mueller matrix of a half-wave plate. The two-dimensional Mueller matrix of the polarizer. , , , They are respectively , , , product The four components.

[0033] S2: For Randomly set P different initial values, and assign P different values ​​to... As P individuals, ; S3: Use P different values Traversal and The R sets of values ​​form P×R possible combinations of values; S4: Obtain P×R instrument matrices under P×R possible value combinations. Then, based on each individual The corresponding R instrument matrices Obtain the fitness of each individual ; any individual Corresponding fitness The method to obtain it is as follows: Obtain each The corresponding R instrument matrices Average condition number Standard deviation of all condition numbers and the range of all condition numbers ; according to , , Obtain each body separately Corresponding fitness , These are the corresponding weights. Wherein, the weights... The values ​​for the rotation axis azimuth angle are set according to actual needs, and P is greater than 1. The range of values ​​for the pitch angle of the rotation axis is: .

[0034] S5: Determine whether the set number of iterations has been reached. If yes, select the individual with the minimum fitness value from all iterations as the final optimization result. If no, proceed to step 6. S6: Select some individuals from the P individuals in the current iteration using the roulette wheel algorithm for crossover and mutation until a new set of P individuals is obtained. The lower the fitness, the higher the probability of being selected. Then, repeat steps S3 to S5 using the new set of P individuals.

[0035] The following section details how to obtain the Mueller matrix of the polarization element when light is obliquely incident.

[0036] Step 1: First, obtain the three-dimensional Jones matrix of the polarization element when the light is obliquely incident. When light is incident obliquely on the surface of a polarizing element, it is equivalent to the polarizing element rotating at a specific angle in three-dimensional space when the light is incident normally. In other words, the effect of the polarizing element on obliquely incident light is equivalent to the effect of a polarizing element with three-dimensional rotation on normally incident light. Therefore, we will focus on the three-dimensional rotation of the element and theoretically analyze the changes in its polarization modulation effect.

[0037] like Figure 3 As shown, light propagates along the Z-axis, and the polarizing element undergoes a certain rotation in three-dimensional space. That is, the rotation of the element is no longer confined to the XY plane, but rather forms an angle with it. For an element with three-dimensional rotation, a rotation axis located within the XY plane can always be found. The angle between the Y-axis and the Y-axis is Its direction cosine is . The normal to the component surface makes an angle of θ with the Z-axis. This patent will and Defined as the azimuth and pitch angles of the rotation axis respectively, the three-dimensional rotation of the component can be determined by the angle around the axis. Rotation get.

[0038] As previously stated, when light is incident obliquely on the surface of a component, it is equivalent to the component undergoing a three-dimensional rotation when the light is incident normally. Therefore, the polarization modulation effect of the polarization element on obliquely incident light is transformed into the polarization modulation effect of a polarization element with three-dimensional rotation on normally incident light. The Jones method or the Stokes-Muller method is typically used to describe the polarization transfer process. Since the Jones method is an expression for the optical field components, it is more intuitive and easier to understand. Furthermore, its matrix dimension is smaller than that of the Stokes-Muller method, facilitating calculation. Therefore, this invention uses the Jones method to describe the behavior of the polarization element when it has a three-dimensional rotation.

[0039] Their Jones matrices are not considered when the three-dimensional rotation of the polarization elements is neglected. Represented as: (1) in Indicates the azimuth angle of the fast axis as The rotation matrix at time, Indicates counter-rotation; This represents the eigenJones matrix of the polarization element. Here, the rotation matrix... The in-plane rotation is represented by the SO(2) group and has the following form: (2) This expression can be written in exponential form: (3) in For the generators of the SO(2) group: (4) When the polarization element undergoes three-dimensional rotation, simply add a matrix representing the three-dimensional rotation to equation (1) above. Then, the Jones matrix of the polarization element when three-dimensional rotation exists... Represented as: (5) Indicates rotation around the axis Rotation The three-dimensional rotation matrix, This indicates inverse rotation. Similar to rotation along the fast axis, it's a three-dimensional rotation matrix. Represented by the SO(3) group: (6) in For the generators of the SO(3) group: (7) The 3D rotation matrix is ​​a 3×3 matrix. To ensure the dimensions of the matrix match during the operation, the fast-axis rotation matrix is ​​used. The eigenJones matrices of both elements should be extended to third order. Since fast-axis rotation is a special case of three-dimensional rotation, i.e., rotation about the Z-axis (direction cosine)... Rotation Then the third-order extended form of the fast-axis rotation matrix for: (8) When the top left 2×2 portion is truncated, the form is the same as before expansion.

[0040] The polarization elements in DSMP are polarizers, half-wave plates, and quarter-wave plates. The eigenvalues ​​of polarizers and wave plates are... and Traditionally they are: (9) in and respectively waveplate at and The phase delay in the direction. When the eigenJones matrices of the polarization element are extended by a third order, they become describable to the phase delay in the polarization element. , , The three-dimensional Jones matrix of the light under the influence of the three incident components. For a linear polarizer, light of any polarization state can only vibrate in the transmission direction, while vibrations in other directions are absorbed. Therefore, its Jones matrix must satisfy the Hermitian property, i.e. Then the three-dimensional Jones matrix of the polarizer is: (10) in This represents the conjugate transpose. For a waveplate, it produces a phase delay only between the vibrations of light in two specific directions. The components have no effect, and its Jones matrix must satisfy unitary property, i.e. Then the three-dimensional Jones matrix of the waveplate is: (11) in This is the identity matrix. For half-wave plates and quarter-wave plates, their normalized three-dimensional Jones matrices are as follows: (12) in and These represent a half-wave plate and a quarter-wave plate, respectively. When the wave plate undergoes three-dimensional rotation, the phase of the incident light propagating within the wave plate also changes accordingly, such as... Figure 4 As shown; at this time Defined as: (13) in For wavelength, Let be the ordinary refractive index of the wave plate. The thickness of the waveplate.

[0041] Substituting equations (6)~(8) and (10)~(11) into equation (5), we can obtain the three-dimensional Jones matrix of the polarization element when three-dimensional rotation exists. : (14) in, This indicates the polarization element to be optimized around the rotation axis. Rotation The three-dimensional rotation matrix, This indicates the polarization element to be optimized around the rotation axis. Rotation The three-dimensional rotation matrix, Indicates the azimuth angle of the fast axis as The rotation matrix at time, Indicates the azimuth angle of the fast axis as Rotation matrix at time; The intrinsic Jones matrix representing the polarization element; for The third-order extended form, express The third-order extended form.

[0042] In other words, when the polarization element undergoes three-dimensional rotation, its Jones matrix is ​​determined by the fast axis azimuth angle. Rotation axis azimuth angle and pitch angle A joint decision.

[0043] Step 2: Obtain the two-dimensional Mueller matrix of the polarization element when light is obliquely incident, based on the three-dimensional Mueller matrix. In DSMP, polarization propagation is usually described using the double Stokes-Muller form, and only the two-dimensional polarization information perpendicular to the direction of light propagation is of concern. In order to quantitatively analyze the error introduced by oblique incidence of light in this process, the three-dimensional Jones matrix derived above needs to be transformed into a two-dimensional Muller matrix.

[0044] This invention uses the Jones method for transformation, and the transformation process is as follows: Figure 5 As shown, it includes the following steps: Construct four linearly independent two-dimensional Jones vectors, the first of which is... Two-dimensional Jones vector Represented as: (16) in, , They represent the incident light at... and Vibration in the direction; simultaneously, construct the corresponding two-dimensional Stokes vector. and three-dimensional Jones vector as follows: (17) (18) 3D Jones Vector As the incident polarization state, and the three-dimensional Jones matrix of the element The action yields four corresponding outgoing three-dimensional Jones vectors, where the first... A three-dimensional Jones vector can be represented as : (19) Because the three-dimensional Jones matrix is ​​about If the function is such that the output polarization state after passing through the polarization element also contains... ;in , , They represent the emitted light. , and Vibration in the direction of light propagation. Taking the component of the emitted three-dimensional Jones vector perpendicular to the direction of light propagation yields the corresponding two-dimensional Jones vector. : (20) According to the two-dimensional Jones vector The corresponding two-dimensional Stokes vector can be obtained. : (twenty one) Therefore, based on the four sets of corresponding incident and exit two-dimensional Stokes vectors, the azimuth angle containing the rotation axis can be uniquely determined. and pitch angle Two-dimensional Mueller matrix of components : (twenty two) in This represents the set of four Stokes vectors.

[0045] At this point, the two-dimensional Mueller matrix This includes the effect of oblique light incidence on the polarization effect of the element. The matrix form differs from the traditional Mueller matrix form for polarization elements, but the rotation axis azimuth angle... and pitch angle When the value is 0, the matrix degenerates into a traditional Mueller matrix.

[0046] When multiple polarization elements are connected in series, their overall polarization modulation effect can be expressed as multiple Mueller matrices. The form of multiplication. In linear polarization measurements, the incident light... The polarization state after PSG is : (twenty three) Subscript , , These represent a quarter-wave plate, a half-wave plate, and a polarizer, respectively. It is a 4×1 column vector, that is , This indicates transpose.

[0047] In DSMP, due to second-order nonlinear effects, the incident light... The polarization state after PSG needs to be calculated using a double Stokes vector. It can be represented as a linear Stokes vector. Component form: (twenty four) superscript This represents a second-order nonlinear effect. The polarization state of light after passing through the PSG is shown below. Become about The function deviates from the ideal form. This derivation method uses the Jones method to obtain the outgoing polarization state, which is relatively simple to calculate. Moreover, the components of light in the Jones vector are independent. When converting the three-dimensional Jones vector into a two-dimensional Jones vector, a pure two-dimensional polarization state can be obtained without the introduction of some three-dimensional information, which would cause the polarization state entering the calculation to change. The resulting two-dimensional Mueller matrix of the element with three-dimensional rotation is more consistent with the real situation.

[0048] The following example illustrates the optimization process of the PSG rotation angle when light is incident at an oblique angle.

[0049] In DSMP, the PSG needs to be modulated at least 9 times to obtain the complete bi-Muller matrix of the sample, which is the fast axis azimuth of the half-wave plate and quarter-wave plate in the PSG. and They must all rotate at least 9 times simultaneously. To obtain , Correspondingly, we need to obtain .Will and Consider as a set of angles Nine sets of measurements are needed. These 9 groups The rotation angle of the PSG After these nine measurements, PSG's instrument matrix... It can be expressed using equation (24), its first... Listed as the first light to pass through The double Stokes vector after the second rotation of the PSG ,but: (25) in , It is a 9×9 matrix.

[0050] For the ideal case of normal incidence of light (i.e.) ), Instrument Matrix Only with the rotation angle of PSG Related to the instrument matrix, when it takes different values. The value will change accordingly, and the measurement stability will also change accordingly. Measurement stability can be measured using an instrument matrix. The condition number is used to measure the stability of a measurement; the smaller the condition number, the higher the measurement stability. However, for the case of oblique incidence of light, it can be seen from equation (25) that the instrument matrix is... Not only with the azimuth angle of the rotation axis It is related to, and also to, the azimuth angle of the rotation axis indicating tilt. and pitch angle Related. When DSMP uses the traditional PSG rotation angle. At that time, instrument matrix The condition number as and The values ​​vary significantly, which greatly affects measurement stability. To improve the measurement stability of DSMP under oblique light incidence, a set of optimized values ​​was developed. and PSG rotation angle where the condition number does not change significantly with any value It is absolutely necessary.

[0051] To obtain a PSG rotation angle with low sensitivity to oblique light incidence This patent utilizes the instrument matrix derived above. (Equation 25) aims to minimize its condition number and uses a genetic algorithm for optimization. This step is very similar to existing optimization methods, the only difference being the setting of the tilt error. The program pre-generates several sets (e.g., 500 sets) of random errors representing different degrees of light tilt, i.e., generates several pairs (e.g., 500 pairs) of rotation axis azimuth angles. and pitch angle random value ,in To satisfy the small-angle tilt condition in the experiment, when 500 sets of tilt errors are generated... Let each individual generated by the genetic algorithm (i.e., the PSG rotation angle) be determined. They all iterated through these 500 sets of tilt errors, that is, the same Each of these 500 sets of tilt errors In combination, for the same PSG rotation angle A total of 500 instrument matrices corresponding to different tilt conditions were generated. And return the individual's error in these 500 sets. The fitness of an individual is defined by the weighted sum of the mean condition number, the standard deviation of all condition numbers, and the range of all condition numbers. , specifically set ,in This represents the average condition number of the PSG rotation angles under all tilt errors. This represents the standard deviation of all condition numbers. This represents the range of all condition numbers; These are the corresponding weights, which can be obtained through simulation.

[0052] Then, during the evolutionary process, the minimum fitness is continuously searched. When evolution is finally complete, the individual with the lowest fitness, i.e., the PSG rotation angle, will be the one with the lowest fitness. That is, the angle at which the required light is obliquely incident with the best stability.

[0053] Thus, the random error introduced by oblique incidence of light in DSMP can be greatly optimized, and the measurement can still maintain high stability when the light is obliquely incident, thereby improving the measurement accuracy, which is very beneficial to sample detection and analysis.

[0054] In summary, this invention provides an optimization method for low-sensitivity oblique-incidence dual Stokes-Mueller polarization measurement. It not only provides derivation methods for the Jones and Mueller matrices of the polarization element when light is obliquely incident, but also for the Jones and Mueller matrices of the element with three-dimensional rotation when light is normally incident, and the representation method for the instrument matrix in polarization measurement when light is obliquely incident or the polarization element has three-dimensional rotation, but also uses the Jones or Mueller matrix of the element with three-dimensional rotation, combined with the minimum condition number and genetic algorithm, to optimize the polarization measurement.

[0055] Therefore, compared with the prior art, the present invention has the following advantages: Traditional Mueller matrices assume that the polarizing element is placed in a plane perpendicular to the direction of light propagation. This fails to describe the effect of three-dimensional rotation of the polarizing element on light. Since three-dimensional rotation of the polarizing element is equivalent to oblique incidence of light, traditional Mueller matrices also cannot describe the effect of the polarizing element on obliquely incident light. This invention introduces two angles to represent the three-dimensional rotation of the element. and This allows the Mueller matrix to describe the situation where the element has three-dimensional rotation, and thus to describe the effect of the element on obliquely incident light.

[0056] This invention utilizes the Mueller matrix of a polarization element with three-dimensional rotation to characterize the instrument matrix of a DSMP (Digital Subtraction Angiography). This matrix is ​​then used in conjunction with the minimum condition number and a genetic algorithm to optimize the DSMP. The optimization results are less sensitive to random errors introduced by oblique incidence of light and maintain high measurement stability in experiments.

[0057] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. An optimized method for low-sensitivity oblique-incidence dual Stokes-Mueller polarization measurement, characterized in that, Includes the following steps: S1: Construct the instrument matrix of the polarization state generator PSG, which consists of the polarization elements to be optimized in the polarization measurement system DSMP. ;in, , , These represent the fast axis azimuth angles set for each polarization element to be optimized during the 9th modulation by the polarization state generator PSG, and the rotation axis azimuth and elevation angles, which are considered as unknown random errors in polarization measurement. , , , , N The total number of polarization elements to be optimized. Indicates the first The modulation is the first The fast axis azimuth angle set for each polarization element to be optimized; simultaneously... and The resulting combination is randomly assigned to R groups of values; S2: For Randomly set P different initial values, and assign P different values ​​to... As P individuals, ; S3: Use P different values Traversal and The R sets of values ​​form P×R possible combinations of values; S4: Obtain P×R instrument matrices under P×R possible value combinations. Then, based on each individual The corresponding R instrument matrices Obtain the fitness of each individual ; S5: Determine whether the set number of iterations has been reached. If yes, select the individual with the minimum fitness value from all iterations as the final optimization result. If no, proceed to step 6. S6: Select some individuals from the P individuals in the current iteration using the roulette wheel algorithm for crossover and mutation until a new set of P individuals is obtained. The lower the fitness, the higher the probability of being selected. Then, repeat steps S3 to S5 using the new set of P individuals.

2. The optimized method for low-sensitivity oblique-incidence dual Stokes-Mueller polarization measurement as described in claim 1, characterized in that, any individual Corresponding fitness The method to obtain it is as follows: Obtain each The corresponding R instrument matrices Average condition number Standard deviation of all condition numbers and the range of all condition numbers ; according to , , Obtain each body separately Corresponding fitness , These are the corresponding weights.

3. The optimized method for low-sensitivity oblique-incidence dual Stokes-Mueller polarization measurement as described in claim 2, characterized in that, Weight The values ​​for the rotation axis azimuth angle are set according to actual needs, and P is greater than 1. The range of values ​​for the pitch angle of the rotation axis is: .

4. The optimized method for low-sensitivity oblique-incidence dual Stokes-Mueller polarization measurement as described in claim 1, characterized in that, Constructed instrument matrix Each column These are the two Stokes vectors of the PSG after each modulation of the incident light. Among them, instrument matrix Any of the first The corresponding double Stokes vector Used to characterize incident light After the first The two-photon polarization state and dual Stokes vector of the submodulated PSG Depend on Seeking, Indicates incident light After the first The linear polarization state of the PSG after submodulation. The value is the first The product of the Mueller matrix of each polarization element to be optimized after modulation and the incident light.

5. The optimized method for low-sensitivity oblique-incidence dual Stokes-Mueller polarization measurement as described in claim 4, characterized in that, When the polarization state generator PSG consists of a quarter-wave plate, a half-wave plate, and a polarizer, the instrument matrix... The List The incident light passes through the first The dual Stokes vector of the submodulated PSG as follows: in, , , , Incident light After the first The linear polarization state of the submodulated PSG The four components; superscript It represents a second-order nonlinear effect; T represents the transpose.

6. The optimized method for low-sensitivity oblique-incidence dual Stokes-Mueller polarization measurement as described in claim 5, characterized in that, Incident light After the first polarization state of the submodulated PSG The calculation method is as follows: in, The two-dimensional Muller matrix of a quarter-wave plate. The two-dimensional Mueller matrix of a half-wave plate. The two-dimensional Mueller matrix of the polarizer. , , , They are respectively , , , product The four components.

7. The optimized method for low-sensitivity oblique-incidence dual Stokes-Mueller polarization measurement as described in any one of claims 4 to 6, characterized in that, The method for calculating the two-dimensional Mueller matrix of any polarization element to be optimized is as follows: Construct four linearly independent two-dimensional Jones vectors, the first of which is... Two-dimensional Jones vector Represented as: in, , They represent the incident light at... and Vibration in the direction; simultaneously, construct the corresponding two-dimensional Stokes vector. and three-dimensional Jones vector as follows: Among them, the three-dimensional Jones vector As the incident polarization state, and the three-dimensional Jones matrix of the polarization element to be optimized. The action yields four corresponding outgoing three-dimensional Jones vectors, where the first... One outgoing three-dimensional Jones vector Represented as: in, , , They represent the emitted light at... , and Vibration in the direction of movement; Extract the outgoing 3D Jones vector The component perpendicular to the direction of light propagation yields the corresponding two-dimensional Jones vector. : According to the two-dimensional Jones vector Obtain the corresponding two-dimensional Stokes vector : According to the two-dimensional Stokes vector and two-dimensional Stokes vector Determine the two-dimensional Mueller matrix of the polarization element to be optimized. : in, This represents the set of four Stokes vectors.

8. The optimized method for low-sensitivity oblique-incidence dual Stokes-Mueller polarization measurement as described in claim 7, characterized in that, Assuming the incident light propagates along the Z-axis, the rotation axis Located in the XY plane, and the axis of rotation The angle with the Y-axis is The angle between the normal of the polarization element to be optimized and the Z-axis is currently... ; The three-dimensional Jones matrix of the polarization element to be optimized The calculation method is as follows: in, This indicates the polarization element to be optimized around the rotation axis. Rotation The three-dimensional rotation matrix, This indicates the polarization element to be optimized around the rotation axis. Rotation The three-dimensional rotation matrix, Indicates the azimuth angle of the fast axis as The rotation matrix at time, Indicates the azimuth angle of the fast axis as Rotation matrix at time; The intrinsic Jones matrix representing the polarization element; for The third-order extended form, express The third-order extended form.

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