WO2023001121A1 - 起偏器与检偏器配置优化方法及起偏检偏系统 - Google Patents

起偏器与检偏器配置优化方法及起偏检偏系统 Download PDF

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WO2023001121A1
WO2023001121A1 PCT/CN2022/106351 CN2022106351W WO2023001121A1 WO 2023001121 A1 WO2023001121 A1 WO 2023001121A1 CN 2022106351 W CN2022106351 W CN 2022106351W WO 2023001121 A1 WO2023001121 A1 WO 2023001121A1
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polarizer
measurement
analyzer
wave plate
configuration
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PCT/CN2022/106351
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English (en)
French (fr)
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马辉
赵千皓
胡峥
黄彤宇
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清华大学深圳国际研究生院
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Priority claimed from CN202110811657.6A external-priority patent/CN113624690B/zh
Priority claimed from CN202210840465.2A external-priority patent/CN115272041A/zh
Application filed by 清华大学深圳国际研究生院 filed Critical 清华大学深圳国际研究生院
Publication of WO2023001121A1 publication Critical patent/WO2023001121A1/zh

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/01—Arrangements or apparatus for facilitating the optical investigation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/21—Polarisation-affecting properties

Definitions

  • the invention relates to the technical field of polarization optical imaging, in particular to a configuration optimization method for a polarizer and an analyzer and a polarizer and analyzer system.
  • Polarization imaging technology has the advantages of non-invasive, non-invasive, in situ, large amount of data, etc., and is widely used in biomedicine, marine science, atmospheric remote sensing and other fields. According to the different forms of polarization information finally obtained, polarization imaging can be divided into Stokes vector measurement and Mueller matrix measurement.
  • the Stokes vector is mainly used to describe the polarization characteristics of light, while the Mueller matrix is used to characterize the polarization characteristics of the sample, and the microstructure information of the medium can be further extracted through the Mueller matrix. The biggest advantage of optical measurement lies.
  • the device that modulates the polarization state of the incident light is called a polarizer (PSG)
  • the device that detects the polarization properties of light is called a polarizer (PSA).
  • the structure of the polarizer is similar to that of the analyzer, and its core is to modulate the polarization state of the light.
  • the polarizer modulates the natural light into a polarized light of a specific polarization state; In this way, the size of the incident polarized light on a specific polarization state component can be obtained, and the polarization property of the light can be obtained through calculation.
  • the Poincare sphere is a unit sphere used to graphically describe the Stokes vector of the polarization state. Any polarization state can be mapped to a point on the Poincare sphere.
  • S 1 , S 2 , S 3 is plotted in the Cartesian coordinate system as x, y, and z coordinates respectively, which is the Poincare sphere representation of the Stokes vector.
  • the Mueller matrix is a transformation matrix, which reflects the change of the Stokes vector of a beam of light before and after scattering, and
  • S out is the Stokes vector of the outgoing light
  • S in is the Stokes vector of the incident light
  • M is the Mueller matrix, which is a 4 ⁇ 4 matrix. Since the CCD (Charge Coupled Device) cannot receive polarization information, it can only receive light intensity information. Therefore, in the actual measurement, it is necessary to perform at least four mutually independent polarization and polarization analysis.
  • Polarization is to use a beam of polarized light with a known polarization state to be incident, and polarization analysis is to obtain the polarization state S out of the outgoing light through measurement and calculation.
  • the Stokes vector has four components, it is necessary to measure the light intensity of the four projected components at least during polarization analysis to obtain the Stokes vector of a beam of light. In this way, the change matrix of the Stokes vector, that is, the Mueller matrix, can be calculated by measuring the outgoing polarization states of the polarized light with different polarization states after illumination.
  • polarization modulation is mainly realized through a polarizer, plus one or a series of phase retardation devices, and multiple different polarization states are obtained through the cooperation between different fast axis angles of the phase retardation devices and the magnitude of the phase delay. Therefore, it is necessary to first explain the influence of the fast axis angle and the phase delay on the polarization state.
  • the Mueller matrix M ⁇ , ⁇ of a phase delay device is:
  • ⁇ is the linear phase delay and ⁇ is the angular direction of the fast axis.
  • S out S in ⁇ M ⁇
  • ⁇ means.
  • Phase delay devices can be further divided into fixed phase delays (wave plates that change the fast axis angle by rotation) and electronically controlled polarizers (variable phase delays).
  • the main advantage of the former lies in its high precision, but the disadvantage is that it has moving parts, and it needs a rotating motor to drive the wave plate to rotate to realize the modulation of various polarization states. Therefore, the modulation speed is affected by the speed of the motor, which is often time-consuming.
  • the latter mainly include liquid crystal phase retarder (LCVR), electro-optical phase retarder (EO) and photoelastic modulator (PEM), etc., which change the phase delay by changing the voltage applied to both ends.
  • LCVR liquid crystal phase retarder
  • EO electro-optical phase retarder
  • PEM photoelastic modulator
  • the polarizer and analyzer can be designed and optimized.
  • the present invention proposes a polarizer and analyzer configuration optimization method and a polarizer and analyzer system to solve the problems of limited precision and inability to suppress noise well in Mueller matrix measurement.
  • the invention discloses a configuration optimization method of a polarizer and a polarizer, comprising the following steps:
  • the configuration conditions for making the polarization states of the polarizer and the analyzer orthogonal to each other satisfy the following relationship:
  • ⁇ P is the transmission axis direction of the polarizer configured for the first measurement
  • ⁇ R is the fast axis angle direction of the 1/4 wave plate configured for the first measurement
  • ⁇ P ' is the polarizer configured for the second measurement
  • the direction of the light transmission axis, ⁇ R ' is the fast axis angle direction of the 1/4 wave plate configured for the second measurement; the method adjusts the main light passing direction of the polarization through the polarizer, and then realizes the specific polarization through the 1/4 wave plate state modulation.
  • the configuration condition that the polarization states of the polarizer and the analyzer are orthogonal to each other satisfies The following relationship:
  • ⁇ H is the fast axis angle direction of the 1/2 wave plate configured for the first measurement
  • ⁇ R is the fast axis angle direction of the 1/4 wave plate configured for the first measurement
  • ⁇ H ' is the configuration of the second measurement 1/2 wave plate fast axis angle direction
  • ⁇ R ' is the 1/4 wave plate fast axis angle direction configured for the second measurement
  • the modulation of the linearly polarized light direction of the method is changed from a single polarizer modulation to a fixed polarizer plus a 1/2 wave plate, which can avoid linearly polarized light in different directions caused by rotating the polarizer when the incident light is not ideal natural light Inconsistencies in light intensity.
  • the configuration conditions for making the polarization states of the polarizer and analyzer orthogonal to each other satisfy the following relationship:
  • ⁇ F1 is the phase delay of the first full-wave delay phase modulation device in the first measurement configuration
  • ⁇ F1 is its fast axis angle
  • ⁇ F2 is the second full-wave delay phase modulation in the first measurement configuration
  • the phase delay of the device, ⁇ F2 is its fast axis angle
  • ⁇ F1 ′ is the phase delay of the first full-wave delay phase modulation device in the second measurement configuration
  • ⁇ F2 ′ is the second full-wave delay phase modulation device in the second measurement configuration
  • the method first uses the first full-wave delay phase modulation device to modulate the polarization state on the circle of the S 1 OS 3 plane on the Poincare sphere, and then uses the second full-wave delay phase modulation device to obtain the target polarization state.
  • the optimal four-point measurement configuration of the polarizer and analyzer satisfies the following relationship:
  • ⁇ P is the transmission axis direction of the polarizer configured for the first measurement
  • ⁇ R is the fast axis angle direction of the 1/4 wave plate configured for the first measurement
  • ⁇ P ' is the polarizer configured for the second measurement
  • the direction of the transmission axis ⁇ R 'is the direction of the fast axis angle of the 1/4 wave plate configured for the second measurement
  • ⁇ P ′′ is the direction of the transmission axis of the polarizer configured for the third measurement
  • ⁇ R ” is the direction of the third measurement
  • ⁇ P "' is the direction of the transmission axis of the polarizer configured for the fourth measurement
  • ⁇ R "' is the direction of the fast axis angle of the 1/4 wave plate configured for the fourth measurement .
  • the optimal four-point measurement configuration of the polarizer and analyzer satisfies the following relationship :
  • ⁇ H is the fast axis angle direction of the 1/2 wave plate configured for the first measurement
  • ⁇ R is the fast axis angle direction of the 1/4 wave plate configured for the first measurement
  • ⁇ H ' is the configuration of the second measurement 1/2 wave plate fast axis angle direction
  • ⁇ R ' is the 1/4 wave plate fast axis angle direction configured for the second measurement
  • ⁇ H ” is the 1/2 wave plate fast axis angle direction configured for the third measurement
  • ⁇ R ” is the direction of the fast axis angle of the 1/4 wave plate configured for the third measurement
  • ⁇ H ”’ is the direction of the fast axis angle of the 1/2 wave plate configured for the fourth measurement
  • ⁇ R ”’ is the direction of the fast axis angle of the fourth measurement Measure the angular direction of the fast axis of the configured 1/4 wave plate.
  • the optimal four-point measurement configuration of the polarizer and analyzer satisfies the following relationship:
  • ⁇ F1 is the phase delay of the first full-wave delay phase modulation device in the first measurement configuration
  • ⁇ F1 is its fast axis angle
  • ⁇ F2 is the second full-wave delay phase modulation in the first measurement configuration
  • the phase delay of the device, ⁇ F2 is its fast axis angle
  • ⁇ F1 ′ is the phase delay of the first full-wave delay phase modulation device in the second measurement configuration
  • ⁇ F2 ′ is the second full-wave delay phase modulation device in the second measurement configuration
  • the phase delay of the wave delay phase modulation device, ⁇ F1 ′′ is the phase delay of the first full wave delay phase modulation device of the third measurement configuration
  • ⁇ F2 ′′ is the second full wave delay phase modulation of the third measurement configuration
  • the phase delay of the device, ⁇ F1 "' is the phase delay of the first full-wave delay phase modulation device configured in the fourth measurement
  • ⁇ F2 "' is the phase delay of the second full-wave delay phase modulation device configured in the fourth measurement
  • the optimal four-point measurement configuration of the polarizer and analyzer satisfies the following relationship:
  • ⁇ H1 and ⁇ H2 are the linear phase delays of the two half-wave delay phase modulation devices configured for the first measurement
  • ⁇ H1 and ⁇ H2 are the fast axis angles respectively
  • ⁇ H1 ′ and ⁇ H2 ′ are respectively
  • the linear phase delays of the two half-wave delay phase modulation devices configured for the second measurement ⁇ H1 ′′, ⁇ H2 ′′ are the linear phase delays of the two half-wave delay phase modulation devices configured for the third measurement
  • ⁇ H1 "', ⁇ H2 "' are the linear phase delays of the two half-wave delay phase modulation devices configured for the fourth measurement, respectively.
  • the polarization state represented by the actual configuration forms an instrument matrix
  • the minimum EWV optimization of the instrument matrix is carried out by using the genetic algorithm or similar optimization algorithm, that is, a variable is set for each group, and a variable is obtained according to the variable
  • the remaining polarization states in the group that can be clearly represented by this variable; Afterwards, these polarization states will form an instrument matrix with several unknown variables; through the genetic algorithm to optimize the minimum EWV of the instrument matrix, it can be calculated when the number of When the value of the unknown variable is unknown, the EWV of the instrument matrix can reach the minimum value.
  • both the polarizer and the analyzer satisfy the modulation of the full polarization state.
  • the present invention also discloses a polarization analysis system, including a rotating polarizer and a rotating 1/4 wave plate, configured as follows:
  • this configuration satisfies that the sum of each row of the instrument matrix W and A of the polarizer and the analyzer is 0, and the EWV of the instrument matrix of the polarizer and the analyzer is optimal, so as to optimize the resistance of the Mueller measurement system to Gauss-Poise performance of loosely mixed noise.
  • the present invention also discloses a polarization analysis system, including a fixed polarizer, a rotating 1/2 wave plate and a rotating 1/4 wave plate, configured as follows:
  • this configuration satisfies that the sum of each row of the instrument matrix W of the polarizer and the instrument matrix A of the analyzer is 0, and the EWV of the instrument matrix of the polarizer and the analyzer is optimal, so as to optimize the Gauss resistance of the Muller measurement system - Performance of Poisson mixture noise.
  • the invention also discloses a polarization analysis system, which includes a fixed polarizer and two full-wave delay phase modulation devices, configured as follows:
  • this configuration satisfies that the sum of each row of the instrument matrix W of the polarizer and the instrument matrix A of the analyzer is 0, and the EWV of the instrument matrix of the polarizer and the analyzer is optimal, so as to optimize the Gauss resistance of the Muller measurement system - Performance of Poisson mixture noise.
  • the present invention also discloses a polarization analysis system, which includes a fixed polarizer and two half-wave delay phase modulation devices, configured as follows:
  • this configuration satisfies that the sum of each row of the instrument matrix W of the polarizer and the instrument matrix A of the analyzer is 0, and the EWV of the instrument matrix of the polarizer and the analyzer is optimal, so as to optimize the Gauss resistance of the Muller measurement system - Performance of Poisson mixture noise.
  • the invention also discloses a polarizer capable of realizing arbitrary polarization state modulation, comprising: an illumination system, a rotatable polarizer and a rotatable 1/4 wave plate, wherein the illumination system is used to generate incident light; Through the combination of different rotation angles of the polarizer and the 1/4 wave plate, the incident light is modulated into required polarized light.
  • the polarizer and the 1/4 wave plate are respectively driven to rotate by the corresponding electric precision rotary displacement stage.
  • Arbitrary polarization state modulation is achieved by changing the orientation of the polarizer and rotating the 1/4 wave plate one revolution at each orientation.
  • the present invention also discloses a polarizer optimization method, the polarizer is the aforementioned polarizer capable of realizing arbitrary polarization state modulation; the optimization method includes:
  • the optimal uniform distribution state of the corresponding polarization state on the Poincar sphere is solved by the method of minimum potential iteration, which satisfies the optimal The condition of the optimal condition number.
  • the iterative method of the lowest potential is used to solve the optimal uniform distribution state of the corresponding polarization state on the Poincar sphere, including:
  • the uniform distribution optimization of the corresponding positions of each polarization state on the Poincar sphere to find the optimal polarizer instrument matrix configuration includes:
  • the corresponding position of the polarization state corresponding to each pair of rotation angles on the Poincar sphere is regarded as a point charge, and the minimum electric potential energy between the point charges is used as the search target, and the global search algorithm is used to obtain the corresponding point when the total electric potential energy is the smallest.
  • the orientation of the polarizer and the angle of the fast axis of the 1/4 wave plate are the optimal configuration, which corresponds to the configuration of the polarizer instrument matrix under the minimum condition number;
  • the pair of rotation angles includes the orientation of the polarizer and the fast axis angle of the 1/4 wave plate in primary modulation.
  • N means that the polarizer has been modulated N times, N ⁇ 4; N polarization states of N times modulation correspond to N points on the Poincar sphere, that is, corresponding to N point charges; E means N point charges The total potential energy of ; r i , r j represent the position vector of the i-th point charge relative to the center of the Poincare sphere, and the position vector of the j-th point charge relative to the center of the Poincare sphere, respectively.
  • the beneficial effects of the present invention compared with the prior art include: the polarizer and the analyzer configuration optimization method provided by the present invention, by adjusting the instrument matrix W of the polarizer and the instrument matrix A of the analyzer, the polarizer and the analyzer
  • the equal-weighted variance EWV of the instrument matrix of the polarizer is the smallest to achieve optimization for Gaussian noise, and the sum of each row of the instrument matrix W of the polarizer and the instrument matrix A of the analyzer is 0, so that the Poisson noise caused
  • the estimated variance is independent of the sample, and the estimated variance reaches the minimum value, so as to suppress the noise to the greatest extent, and make the law of the noise independent of the sample. No matter what kind of sample is measured, the distribution law of the noise is the same.
  • the present invention combines the optimization of the measurement configuration with the Gaussian-Poisson mixed noise, by adopting the optimal measurement configuration of the polarizer and the polarizer under a variety of different devices, the polarizer and the detector
  • the equal-weight variance EWV of the polarizer instrument matrix is the smallest, which further improves the performance accuracy of polarization measurement, especially in Mueller matrix measurement, and minimizes the influence of error transfer in Mueller matrix measurement, and makes the performance of Poisson noise consistent with the sample irrelevant.
  • the method is universal and can optimize various measurement systems with different structures.
  • FIGS. 1a to 1b are diagrams of a set of orthogonal polarization states formed by a rotary phase delay device in an embodiment of the present invention.
  • FIGS. 2a to 2b are diagrams of a set of orthogonal polarization states formed by the phase variable delay device in the embodiment of the present invention.
  • Fig. 3 is a schematic diagram of a rotating polarizer and a rotating 1/4 wave plate in an embodiment of the present invention.
  • Fig. 4 is a schematic diagram of an instrument of a fixed polarizer, a rotating 1/2 wave plate and a rotating 1/4 wave plate in an embodiment of the present invention.
  • Fig. 5 is an instrument schematic diagram of a fixed polarizer and two full-wave delay phase modulation devices in an embodiment of the present invention.
  • Fig. 6 is an instrument schematic diagram of a fixed polarizer and two half-wave delay phase modulation devices in an embodiment of the present invention.
  • FIGS. 7a to 7b are diagrams of all the polarization states that can be modulated and the optimal four-point measurement framework under the instrument of one fixed polarizer and two half-wave delay phase modulation devices in the embodiment of the present invention.
  • Fig. 8 is a flowchart of a configuration optimization method for a polarizer and an analyzer according to an embodiment of the present invention.
  • Fig. 9 is a schematic diagram of a Mueller matrix measurement system based on a polarizer according to an embodiment of the present invention.
  • Figure 10 shows the Poincar sphere display of the polarization states that may be traversed by the polarization mode with the polarizer fixed at 0° and the 1/4 wave plate rotated once.
  • Fig. 11 is the display on the Poincare sphere of the polarization states that may be traversed by the polarization mode that the 1/4 wave plate rotates once when the polarizer is fixed at 45° and 135° respectively.
  • Fig. 12 is the display of the polarization states that may be traversed by the polarization mode of simultaneously rotating the polarizer and the 1/4 wave plate for one revolution on the Poincare sphere.
  • orientation terms such as left, right, up, down, top, and bottom in this embodiment are only relative concepts, or refer to the normal use status of the product, and should not be regarded as having restrictive.
  • the optimization of the embodiment of the present invention is to select more suitable W and A.
  • the conditions under which the instrument matrices W and A are optimal are given by the following derivation:
  • Gaussian-Poisson mixed noise often exists in the Mueller matrix measurement system, and covariance analysis is needed to evaluate the influence of noise on the estimated variance of the Mueller matrix.
  • the relationship between the directly measured light intensity and the instrument matrix and the sample Mueller matrix can be expressed as:
  • I is the light intensity image measured by the CCD
  • M is the Mueller matrix of the sample
  • W and A represent the instrument matrix of the polarizer (PSG) and analyzer (PSA), respectively
  • T represents the transposed form of the matrix.
  • the light intensity matrix and the Mueller matrix of the sample are expanded into vector form by means of the Kronecker product:
  • V I and V M are the column vector forms of the above-mentioned light intensity matrix I and the Mueller matrix M of the sample, respectively, and -1 represents the inverse or pseudo-inverse of the matrix.
  • V M and V I the relationship between its covariance matrix can be defined as:
  • the correct performance criterion for a Mueller matrix measurement system is the sum of the variances of all elements of the Mueller matrix, namely trace of:
  • trace() means to find the trace of the matrix.
  • the covariance matrix of light intensity noise when additive Gaussian noise is present in the system Expressed as a diagonal matrix with its variance ⁇ 2 as the diagonal array element. It can be seen that the estimated variance caused by the Gaussian noise in the system to the Mueller matrix is:
  • EWV W and EWV A represent the equivalence of the polarizer and analyzer matrix respectively weight variance. It can be seen from the above formula that for the optimization of Gaussian noise, the optimal state can be achieved only if the equal weight variance (EWV) of the instrument matrix of the polarizer and the analyzer is minimized.
  • the first term of the normalized VM is always 1. Obviously, in the above formula, the first term is independent of the sample, and the second term is related to the last 15 elements of the sample, which will cause the estimated variance caused by Poisson noise to change as the sample changes . Fortunately, when the EWV of the polarizer and analyzer instrument matrix is optimal, is a constant constant. Therefore, when the following formula is satisfied, the second term of CPoission (C Poisson) will be set to zero, so that the estimated variance caused by Poisson noise to the Mueller matrix is independent of the sample:
  • the equivalent condition of the above formula is: the sum of each row of the instrument matrix W of the polarizer and the instrument matrix A of the analyzer is 0.
  • the EWV of the polarizer and analyzer matrix is optimal, the estimated variance caused by Poisson noise is independent of the sample, and the estimated variance reaches the minimum value.
  • the optimal CPoission can be expressed as:
  • the Mueller matrix measurement system is anti-Gaussian -
  • the performance of Poisson mixed noise is optimal, and the overall estimated variance of the system can be expressed as:
  • the rotary device is driven by a high-precision rotating motor, and the overall measurement error is small, but due to the slow response speed of moving parts, the measurement is generally time-consuming.
  • the electronically controlled phase-delay variable retarder has slightly lower accuracy due to the influence of temperature drift, but the response speed is on the order of milliseconds, which can achieve very fast measurement, but the cost is also high. Therefore, the two are often not mixed, and we optimize the system composed of these two types of phase delay devices respectively.
  • a set of orthogonal polarization states formed by the rotary phase retardation device is shown in Figures 1a to 1b
  • a set of orthogonal polarization states formed by the phase variable retardation device is shown in Figures 2a to 2b.
  • the embodiment of the present invention further improves the performance accuracy in polarization measurement, especially in Mueller matrix measurement, by adopting optimal configurations of polarizers and analyzers under various devices. Realize the optimal configuration that minimizes the influence of error transfer in Mueller matrix measurement and makes the Poisson noise performance irrelevant to the sample.
  • the Mueller matrix measurement system is resistant to Gaussian-Poisson mixture noise gives the best performance. Therefore, if the W and A of the measurement system satisfy this condition, the measurement system can be optimized naturally, and the noise transfer is minimized and the Poisson noise sample is irrelevant.
  • the W and A of the measurement system are determined by the polarization state generated by the polarizer and analyzer of the measurement system, and the polarization state is determined by the configuration of the measurement system (fast axis angle of each component, phase delay, etc. )decided. Therefore, the problem of optimizing W and A is transformed into the problem of optimizing the configuration of the measurement system.
  • phase delay device changes the linear phase delay at a fixed fast axis angle
  • trajectory of the polarization state on the Poincar sphere will be projected into a straight line on the S 1 and S 2 planes
  • the fast axis angle of the phase delay device determines the direction of the straight line of the projection of the trajectory formed on the S 1 and S 2 planes when the polarization state changes with different phase delays on the Poincare sphere. And the fast axis angle ⁇ and the angle between the projection and the S2 direction satisfy Relationship;
  • the phase delay device changes the linear phase delay at a fixed fast axis angle
  • the trajectory of the polarization state changing on the Poincar sphere will form a circular arc.
  • the linear phase delay varies from 0 to 2 ⁇
  • the arc becomes a complete circle.
  • the direction of the arc is from the incident polarization state, along the angle with the S2 direction (When S 3 ⁇ 0, it is reversed) Make an arc.
  • the phase delay device is specifically defined as a wave plate with a fixed phase delay and an electronically controlled element with a variable phase delay (here, a liquid crystal variable phase retarder LCVR is taken as an example).
  • the wave plate is characterized by a relatively simple structure, no need for supporting control equipment, and can be easily combined with a rotating motor to change the fast axis angle, but the phase delay of the wave plate cannot be changed freely, which is usually determined by the material of the wave plate itself a fixed value of .
  • the characteristics of LCVR are exactly the opposite of those of wave plates. It has complex controllers and circuit limitations, and cannot be used in conjunction with moving parts. Therefore, its fast axis angle usually does not change after the optical path is built, but its phase delay can be very convenient.
  • the ground is controlled by voltage, and the electronic control causes its response speed to be much faster than the motor rotation.
  • the LCVR device first determines a fast axis angle, and then can artificially change the phase delay according to needs, which is more suitable for polarization state modulation.
  • the wave plate has a fixed phase delay, and the fast axis angle is controlled by the motor.
  • the fast axis angle is controlled by the motor.
  • a rotating polarizer and a rotating 1/4 wave plate A rotating polarizer and a rotating 1/4 wave plate.
  • ⁇ P is the transmission axis direction of the polarizer configured for the first measurement
  • ⁇ R is the fast axis angle direction of the 1/4 wave plate configured for the first measurement
  • ⁇ P ' is the polarizer configured for the second measurement
  • the direction of the light transmission axis, ⁇ R ' is the direction of the fast axis angle of the 1/4 wave plate configured for the second measurement.
  • the structure mainly adjusts the main light-passing direction of the polarization through the polarizer, and then realizes the modulation of a specific polarization state through the 1/4 wave plate.
  • the schematic diagram of the instrument with a rotating polarizer and a rotating 1/4 wave plate is shown in Figure 3.
  • a fixed polarizer a rotating 1/2 wave plate, and a rotating 1/4 wave plate.
  • ⁇ H is the fast axis angle direction of the 1/2 wave plate configured for the first measurement
  • ⁇ R is the fast axis angle direction of the 1/4 wave plate configured for the first measurement
  • ⁇ H ' is the configuration of the second measurement
  • the 1/2 wave plate fast axis angle direction of , ⁇ R ' is the 1/4 wave plate fast axis angle direction of the second measurement configuration.
  • a fixed polarizer two full-wave delay phase modulation devices.
  • ⁇ F1 is the phase delay of the first full-wave delay phase modulation device in the first measurement configuration
  • ⁇ F1 is its fast axis angle
  • ⁇ F2 is the second full-wave delay phase modulation in the first measurement configuration
  • the phase delay of the device, ⁇ F2 is its fast axis angle
  • ⁇ F1 ′ is the phase delay of the first full-wave delay phase modulation device in the second measurement configuration
  • ⁇ F2 ′ is the second full-wave delay phase modulation device in the second measurement configuration
  • the structure first modulates the polarization state on the circle of S 1 OS 3 plane on the Poincare sphere through the first full-wave delay phase modulation device, and then obtains the target polarization state with the help of the second full-wave delay phase modulation device.
  • a schematic diagram of the instrument with a fixed polarizer and two full-wave delay phase modulation devices is shown in Figure 5.
  • the outgoing polarization state is symmetrical on the Poincare sphere, and the sum of the S 1 , S 2 , and S 3 components of the two measurements is zero respectively, which can satisfy the optimal instrument The first condition of the matrix.
  • a rotating polarizer and a rotating 1/4 wave plate A rotating polarizer and a rotating 1/4 wave plate.
  • ⁇ P is the transmission axis direction of the polarizer configured for the first measurement
  • ⁇ R is the fast axis angle direction of the 1/4 wave plate configured for the first measurement
  • ⁇ P ' is the polarizer configured for the second measurement
  • the direction of the transmission axis, ⁇ R ' is the direction of the fast axis angle of the 1/4 wave plate configured for the second measurement
  • ⁇ P ′′ is the direction of the transmission axis of the polarizer configured for the third measurement
  • ⁇ R ” is the direction of the third measurement
  • ⁇ P "' is the direction of the transmission axis of the polarizer configured for the fourth measurement
  • ⁇ R "' is the direction of the fast axis angle of the 1/4 wave plate configured for the fourth measurement .
  • a fixed polarizer a rotating 1/2 wave plate, and a rotating 1/4 wave plate.
  • ⁇ H is the fast axis angle direction of the 1/2 wave plate configured for the first measurement
  • ⁇ R is the fast axis angle direction of the 1/4 wave plate configured for the first measurement
  • ⁇ H ' is the configuration of the second measurement 1/2 wave plate fast axis angle direction
  • ⁇ R ' is the 1/4 wave plate fast axis angle direction configured for the second measurement
  • ⁇ H ” is the 1/2 wave plate fast axis angle direction configured for the third measurement
  • ⁇ R ” is the direction of the fast axis angle of the 1/4 wave plate configured for the third measurement
  • ⁇ H ”’ is the direction of the fast axis angle of the 1/2 wave plate configured for the fourth measurement
  • ⁇ R ”’ is the direction of the fast axis angle of the fourth measurement Measure the angular direction of the fast axis of the configured 1/4 wave plate.
  • a fixed polarizer two full-wave delay phase modulation devices.
  • ⁇ F1 is the phase delay of the first full-wave delay phase modulation device in the first measurement configuration
  • ⁇ F1 is its fast axis angle
  • ⁇ F2 is the second full-wave delay phase modulation in the first measurement configuration
  • the phase delay of the device, ⁇ F2 is its fast axis angle
  • ⁇ F1 ′ is the phase delay of the first full-wave delay phase modulation device in the second measurement configuration
  • ⁇ F2 ′ is the second full-wave delay phase modulation device in the second measurement configuration
  • the phase delay of the wave delay phase modulation device, ⁇ F1 ′′ is the phase delay of the first full wave delay phase modulation device of the third measurement configuration
  • ⁇ F2 ′′ is the second full wave delay phase modulation of the third measurement configuration
  • the phase delay of the device, ⁇ F1 "' is the phase delay of the first full-wave delay phase modulation device configured in the fourth measurement
  • ⁇ F2 "' is the phase delay of the second full-wave delay phase modulation device configured in the fourth measurement
  • a fixed polarizer and two half-wave delay phase modulation devices are used.
  • ⁇ H1 and ⁇ H2 are the linear phase delays of the two half-wave delay phase modulation devices configured for the first measurement
  • ⁇ H1 and ⁇ H2 are the fast axis angles respectively
  • ⁇ H1 ′ and ⁇ H2 ′ are respectively
  • the linear phase delays of the two half-wave delay phase modulation devices configured for the second measurement ⁇ H1 ′′, ⁇ H2 ′′ are the linear phase delays of the two half-wave delay phase modulation devices configured for the third measurement
  • ⁇ H1 "', ⁇ H2 "' are the linear phase delays of the two half-wave delay phase modulation devices configured for the fourth measurement, respectively.
  • the polarization state produced by this structure cannot traverse the entire Poincare sphere, but it can just cover the four polarization states of the optimal instrument matrix of the four-point theory (such as the four vertices of the light-colored regular tetrahedron).
  • the degrees of freedom of the four-point configuration can be reduced to one or two, greatly reducing the difficulty of configuration optimization.
  • the actual configuration of the optimal framework can be quickly obtained.
  • polarizer and the analyzer are respectively a rotating polarizer and a rotating 1/4 wave plate, according to their corresponding geometric constraints, a series of variables are set and EMW optimization is performed on the variables The process is as follows:
  • the angle of the optical axis of the polarizer is ⁇ 1P ; a quarter wave plate (hereinafter referred to as the wave plate ) has a fast axis angle of ⁇ 1R .
  • EWV is the final output of the genetic algorithm
  • OutputVariables is the optimized configuration setting
  • EWV is the equal weight variance of the instrument matrix formed by the optimized configuration.
  • the first input of the %ga function, fitfunc, is an objective function defined by itself, and its content and definition method are introduced in detail in lines 40-75 of the code section.
  • the second input 8 of the %ga function is the number of variables. In this example, there are 8 variables, so the input is set to 8.
  • the third to sixth inputs of the %ga function are some parameter settings for the genetic algorithm itself, which is selected as the default setting here, and [] is enough.
  • the seventh input of the %ga function is the minimum value range of the variable, here all 8 are given as 0, namely [0 0 0 0 0 0 0 0 0].
  • the eighth input of the %ga function is the range of the maximum value of the variable, here all 8 are given as 180, that is, [180 180 180 180 180 180 180].
  • % makes the eight variables all take values from 0 to 180 degrees.
  • theat_P1_r theat_P1+90;
  • theat_R1_r theat_R1;
  • theat_P2_r theat_P2+90
  • theat_P3_r theat_P3+90
  • theat_P4_r theat_P4+90
  • disp(strcat('The angles of the polarizers in the eight measurements are respectively', num2str(theat_P1),',',num2str(theat_P1_r),',',num2str(theat_P2),',',num2str(theat_P2_r),' ,',num2str(theat_P3),',',num2str(theat_P3_r),',',num2str(theat_P4),',',num2str(theat_P4_r)));
  • disp(strcat('The angles of the wave plates in the eight measurements are respectively', num2str(theat_R1),',',num2str(theat_R1_r),',',num2str(theat_R2),',',num2str(theat_R2_r),' ,',num2str(theat_R3),',',num2str(theat_R3_r),',',num2str(theat_R4),',',num2str(theat_R4_r)));
  • This function is an objective function defined by itself, the input is a variable, and the output is the value of the optimization objective:
  • %First define some basic values, including polarizer Muller matrix, wave plate Mueller matrix, incident natural light, to facilitate the calculation of Stokes:
  • MLR @(x,y)[1,0,0,0;
  • MLD @(x)0.5*[1,cosd(2*x),sind(2*x),0;
  • % polarizer Mueller matrix formula x is the main pass optical axis angle
  • the inputlight [1;0;0;0]; %
  • the input is a beam of natural light without polarization effect.
  • Stokes1 MLR(variables(1),90)*MLD(variables(2))*inputlight; % Get Stokes1 represented by the 1st and 2nd variables.
  • Stokes1_r MLR(variables(1),90)*MLD(variables(2)+90)*inputlight; % get Stokes1_r represented by the first and second variables and orthogonal to Stokes1, the same below, no more details .
  • InstrumentMatrix [Stokes1Stokes1_r Stokes2 Stokes2_r Stokes3 Stokes3_r Stokes4 Stokes4_r];
  • FIG. 8 the flowchart of the configuration optimization method for the polarizer and the analyzer according to the embodiment of the present invention is shown in FIG. 8 .
  • the embodiment of the present invention systematically proposes a method for optimizing the polarization measurement system (polarizer/analyzer).
  • the key to this method is to meet the estimated Poisson noise variance of the 16 array elements when the Mueller matrix is measured.
  • the sample-independent instrument matrix gives realistically achievable, specific instrument configurations. Most of the existing measurements do not consider the suppression of Poisson noise or only start from the measurement principle to explain under what instrument matrix the noise can be suppressed, and do not give a configuration that can be referenced or actually realized with the help of existing devices.
  • the embodiment of the present invention performs geometric constraints through the above-mentioned relationship, thereby calculating the configuration of the instrument during specific measurement, and satisfying the above-mentioned relationship, and obtaining the corresponding configuration deformation by this method.
  • the structure of the measurement system to be used determines whether the system is used as a polarizer or an analyzer, it needs to meet the modulation of the full polarization state.
  • determine whether to optimize the four-time acquisition measurement or multiple acquisition measurements determine the constraints on each group of polarization states for these two cases, use different polarization elements to change the law of the polarization state, and use the actual measurement system for each group of polarization states configuration constraints. After constraints, the polarization state represented by the actual configuration is used to form an instrument matrix, and the minimum EWV optimization of the instrument matrix is carried out by using genetic algorithm or similar optimization algorithm. The optimal actual configuration can be obtained.
  • a rotating polarizer and a rotating 1/4 wave plate A rotating polarizer and a rotating 1/4 wave plate.
  • a fixed polarizer a rotating 1/2 wave plate, and a rotating 1/4 wave plate.
  • a fixed polarizer two full-wave delay phase modulation devices.
  • a fixed polarizer and two half-wave delay phase modulation devices are used.
  • the configurations from a) to d) above satisfy that the sum of each row of the instrument matrix W of the polarizer and the instrument matrix A of the analyzer is 0, and the EWV of the instrument matrix of the polarizer and the analyzer is optimal, so as to optimize Müller measurement system immunity to Gaussian-Poisson mixed noise.
  • the configuration of each component needs to be set according to the parameters given in the table.
  • the first four-point configuration given in table a) can be used, that is, firstly, the polarizer is rotated to 4.87 degrees, and the wave plate is rotated to 22.5 degrees for the second Polarization once; then rotate the polarizer to 85.13 degrees, rotate the wave plate to 67.5 degrees for the second polarization; then rotate the polarizer to 94.87 degrees, rotate the wave plate to 112.5 degrees for the third polarization; finally The polarizer is rotated to 175.13 degrees, and the wave plate is rotated to 157.5 degrees for the fourth polarization.
  • polarization analysis is also required for each polarization.
  • the process of polarization analysis is similar to that of polarization analysis. According to the structure of the polarizer used, select the specific configuration given in the table corresponding to the structure and perform four or eight measurements. Check deviation. That is, if the mode of four measurements is adopted for both the polarization and the polarization analysis, a total of 16 measurements are required.
  • the polarizer and analyzer configuration optimization method of the embodiment of the present invention systematically combines the measurement configuration with the optimization of Gauss-Poisson mixed noise, which can guide the actual measurement, making The measurement system is optimized.
  • the traditional measurement system without optimal measurement configuration can still perform measurement, but its accuracy is limited, and the noise in the system cannot be well suppressed, and the noise law is not clear, so it is difficult to perform post-calculation noise reduction and other work .
  • the measurement configuration optimized by this method improves this problem. One is to minimize the noise transfer in the system and suppress the noise to the greatest extent. The other is to make the law of noise independent of the sample. No matter what sample is measured, the distribution of noise The rules are the same.
  • the method is also universal and can be optimized for various measurement systems with different structures.
  • This embodiment provides a polarizer that can realize arbitrary polarization state modulation, including: an illumination system, a rotatable polarizer and a rotatable 1/4 wave plate, wherein the illumination system is used to generate incident light; through the polarizer and The combination of different rotation angles of the 1/4 wave plate modulates the incident light into the desired polarized light.
  • Arbitrary polarization state modulation is achieved by changing the orientation of the polarizer and rotating the 1/4 wave plate one revolution at each orientation.
  • the polarizer and the 1/4 wave plate are respectively driven to rotate by the corresponding electric precision rotary displacement stage.
  • FIG. 9 is a schematic diagram of a Mueller matrix measurement system based on the above-mentioned polarizer in this embodiment, specifically, a transmission type Mueller matrix measurement system. Referring to FIG.
  • the light emitted by the LED light source 1 is incident on the sample 4 through the polarizer 2 and the 1/4 wave plate 3 , and the light transmitted from the sample 4 is received by the analyzer 5 .
  • the multiple (not less than 4) modulations of the polarizer 2 and the 1/4 wave plate 3 and the analysis of the polarizer 5 the Mueller matrix image of the sample 4 is finally calculated.
  • the polarizer of this embodiment can realize arbitrary polarization state modulation is based on the polarization mode of fixing the polarizer and rotating the 1/4 wave plate. If the polarizer is fixed at 0° and the 1/4 wave plate is rotated once, all possible polarization states that it can traverse on the Poincare sphere are shown in Figure 10, and the polarization states that it can traverse can only be Poincare An "8"-shaped area on the sphere. When the polarizers are fixed at 45° and 135° respectively, the 1/4 wave plate is rotated once to obtain two corresponding "8"-shaped areas, as can be seen in Figure 11.
  • any polarization state on the Poincar sphere can be traversed, and the polarization states that can be traversed on the sphere are shown in FIG. 12 .
  • Another modification of this embodiment proposes the optimization method of the aforementioned polarizer, by taking the actual physical configuration, that is, the orientation of the polarizer and the fast axis angle of the 1/4 wave plate as the optimization target, and by the method of minimum potential iteration, the solution The optimal uniform distribution state of the corresponding polarization state on the Poincar sphere, which also satisfies the condition of the optimal condition number.
  • the polarization produced by each modulation is calculated using the orientation of the polarizer and the fast-axis angle of the 1/4-wave plate.
  • the Stokes vector of the state, and the calculated Stokes vector is mapped to the Poincar sphere to display the corresponding position of the corresponding polarization state on the Poincar sphere; then the corresponding position of each polarization state is placed on the Poincar sphere
  • Uniform distribution optimization is carried out on to find the optimal polarizer instrument matrix configuration, which satisfies the minimum condition number index.
  • Such an optimized configuration can reduce the transfer ratio of the system error to the final measurement result, thereby achieving high-precision and low-error Mueller matrix measurement.
  • Each modulation corresponds to an orientation of the polarizer and a fast axis angle of the 1/4 wave plate, that is, each modulation corresponds to a pair of rotation angles; and each modulation corresponds to a polarization state, that is, a Stokes vector.
  • a polarization state that is, a Stokes vector.
  • the polarization state of the transmitted polarized light changes compared with the incident polarized light.
  • the image of the Mueller matrix of the sample can be calculated through the light intensity map collected by the imaging element behind the analyzer, which can be expressed as :
  • A represents the instrument matrix of the analyzer
  • W represents the instrument matrix of the polarizer
  • M represents the Mueller matrix of the sample
  • I is the detected light intensity.
  • ⁇ A the condition number of the analyzer matrix A
  • ⁇ W the condition number of the polarizer matrix W.
  • represents the error of the final measured Mueller matrix
  • represent the light intensity error, the systematic error of the analyzer and the systematic error of the polarizer, respectively. It can be seen that for the polarizer, the smaller the condition number ⁇ W of the instrument matrix, the lower the transfer ratio of the system error to the measurement result.
  • the polarizer instrument matrix can be expressed as:
  • S in represents the polarization state of the incident light, that is, the Stokes vector.
  • S in [1 0 0 0] T . Since the Muller matrix is 4 ⁇ 4, that is, R ⁇ i , are all 4 ⁇ 4 matrices, and the Stokes vector S in of the incident light is a 4 ⁇ 1 column vector, so The size of should be 4 ⁇ 1, then the size of matrix W N is 4 ⁇ N.
  • each three-dimensional coordinate point is regarded as a point charge.
  • each selected polarization/analyzer state should be as independent as possible, which means that the points on the Poincare sphere corresponding to each polarization state should be as "uniform" as possible , that is, the distance between these points should be equal and try to reach the maximum value. This is equivalent to the problem of how to distribute multiple point charges on the unit sphere to obtain the minimum potential energy in electromagnetism.
  • r i and r j represent the position vector of the i-th point charge relative to the center of the Poincare sphere, and the position vector of the j-th point charge relative to the center of the Poincare sphere, respectively.
  • the optimization problem becomes to find the optimal polarizer instrument matrix W, so that while E is the smallest, the condition number of the entire instrument matrix W is the smallest.
  • Each matrix has its own corresponding condition number, so the instrument matrix of the polarizer also has its corresponding condition number.
  • the instrument matrix of the polarizer also has its corresponding condition number.
  • C(W)
  • represents the 2-norm of the matrix).
  • the experiment is carried out by taking the polarizer as an example to perform 4 modulations.
  • the size of the instrument matrix W N is 4 ⁇ N. Therefore, the instrument matrix W is 4 ⁇ 4 under 4 modulations.
  • the angular rotation range of the polarizing plate and the 1/4 wave plate is 0-180°, and a rotation of 180° is a rotation.
  • the angle between the polarizer and the 1/4 wave plate is directly optimized, and the optimal solution is searched using the global search algorithm. Specifically include: regard the corresponding point of the polarization state (Stokes vector) corresponding to each pair of rotation angles on the Poincar sphere as "point charge", and use the minimum electric potential energy between points as the search target, Taking the angle of the polarizer and the 1/4 wave plate corresponding to the minimum potential energy is the optimal configuration, and this configuration also corresponds to the polarizer instrument matrix configuration under the minimum condition number.
  • the optimal angle configuration of the polarizer and the 1/4 wave plate (the actual phase delay of the 1/4 wave plate used in the experiment is not 90°, and the actual measured value is 92.725°) is obtained according to the following process:
  • the four angles of the polarizer are 15.586°, 53.281°, 114.957°, 176.421°, 1/4 wave plate Four angles 149.728°, 64.121°, 125.166°, 4.59°, and then according to the instrument matrix expression
  • the real W value can be obtained as follows:
  • condition number of the above matrix W is 1.732, which is in line with the theoretical minimum. It shows that the optimal angle configuration of the polarizer and the 1/4 wave plate obtained by the optimization method also satisfies the minimum condition number index at the same time, so that the transmission ratio of the system error can be minimized.
  • the Mueller matrix of the standard sample is measured through the optical path construction measurement system shown in Figure 9: According to the four angles given by the optimization method (the polarizer has four angles, the wave plate has four angles), so that the polarizer and the 1/4 wave plate are changed four times according to the corresponding angles respectively, by changing the polarizer
  • N times the specific implementation example uses 4 times
  • the Mueller matrix of the standard sample can be calculated by the following formula:
  • pinv() represents the pseudo-inverse of the matrix, and it represents the inverse of the matrix when the matrix is a square matrix.
  • k represents the sequence number of the 16 elements of the Mueller matrix.
  • the embodiment of the present invention rotates the polarizer and the wave plate at the same time to realize the polarizer of arbitrary polarization state modulation, which is optimized by the optimization method After that, the measurement error of the Mueller matrix is reduced and the measurement accuracy is improved.
  • Embodiment 1 The relationship between Embodiment 1 and Embodiment 2 is explained in principle below:
  • Example 1 the EWV index and the potential energy index can be interchanged without affecting the optimization result.
  • the electric potential energy index is proposed in Embodiment 2, while the EWV index is a traditional index.
  • Embodiment 2 proposes a polarizing system that rotates a polarizing plate and rotates a quarter-wave plate (RPRQ), while Embodiment 1 adopts an RPRQ structure, but includes a polarizing and an analyzing system. In addition, Embodiment 1 additionally proposes various structures.
  • Embodiment 2 proposes an electric potential energy index to characterize the uniformity of the distribution of the polarization state on the Poincare sphere, which has the concept of geometric optimization.
  • the electric potential energy index is replaced by a more traditional EWV index, and the influence of Poisson noise is additionally considered. Further, with the help of the concept of geometric optimization, it is proposed to limit the results through geometric constraints.
  • the geometric uniformity of the polarization state satisfies the minimum EWV and the minimum potential energy, making the system optimal for Gaussian noise;
  • Orthogonal or regular tetrahedrons on the SOP geometry satisfy the instrument matrix row sum to zero, making the system optimal for Poisson noise.
  • Embodiment 1 The former is used in Embodiment 1 and Embodiment 2, and the latter is used in Embodiment 1.
  • Embodiment 1 and Embodiment 2 all have actual configurations, rather than a simple instrument matrix. It is all through analyzing the law of changing the polarization state of the polarization element in geometry, and establishing a relationship between the polarization state and the actual configuration, so as to obtain the actual configuration.
  • Example 2 only analyzes four polarization and analysis measurements, and does not apply the method to more polarization and analysis measurements (although the method itself is possible, it is not proposed).
  • Embodiment 1 discusses four and multiple polarization and detection measurements respectively.
  • Embodiment 1 is an expansion and extension of Embodiment 2, adding several additional measurement structures, adding descriptions that can be applied to both PSA and PSG, and additionally satisfying the optimization of Poisson noise, Added discussion on optimization of multiple polarizer and polarizer measurements.

Abstract

一种起偏器与检偏器配置优化方法及起偏检偏系统，起偏器与检偏器配置优化方法包括如下步骤：调整起偏器的仪器矩阵W和检偏器的仪器矩阵A，使起偏器和检偏器仪器矩阵的等权重方差EWV最小，以实现针对高斯噪声的优化；且起偏器的仪器矩阵W和检偏器的仪器矩阵A每一行的和为0，使泊松噪声所引起的估计方差独立于样本，且估计方差达到最小值。起偏器与检偏器配置优化方法能够最大程度地抑制噪声，并使噪声的规律与样本独立，无论测量何种样本，噪声的分布规律都是相同的。

Description

起偏器与检偏器配置优化方法及起偏检偏系统 技术领域
本发明涉及偏振光学成像技术领域，特别是涉及一种起偏器与检偏器配置优化方法及起偏检偏系统。
背景技术
偏振成像技术具有非侵入、无损伤、在体原位、数据量大等优点，广泛应用于生物医学、海洋科学、大气遥感等领域。根据最终获得偏振信息形式的不同，偏振成像可以分为斯托克斯向量测量和缪勒矩阵测量。斯托克斯向量主要用于描述光的偏振特性，而缪勒矩阵则是表征样本的偏振特征，并可通过缪勒矩阵进一步提取出介质的微观结构信息，这也是偏振测量相比于传统的光学测量最大的优势所在。
在进行缪勒矩阵测量时，需要对入射光进行偏振调制，同时对出射光进行偏振属性的检测，从而获悉样本对光的偏振特性产生了何种影响与改变。通过多次调制与检测，就可以获得样本完备的偏振特性，亦即样本的缪勒矩阵。在这个过程中，调制入射光偏振态的器件被称为起偏器(PSG)，而对光的偏振属性进行检测的器件称为检偏器(PSA)。起偏器与检偏器的结构类似，其核心都是对光的偏振态进行调制，起偏器是将自然光调制为特定偏振态的偏振光；检偏器是将入射偏振光反向调制，从而得到该入射偏振光在某一特定偏振态分量上的大小，并通过计算得到光的偏振属性。
斯托克斯矢量是一种描述光的偏振属性的一种方法，其表示为S＝[S 0 S 1 S 2 S 3] T，是一个四维向量，S 0表示光的强度；S 1＝I 0-I 90，是光在0度偏振方向的光强分量和90度偏振方向的光强分量之差；S 2＝I 45-I 135，是光在45度偏振方向的光强分量和135度偏振方向的光强分量之差；S 4＝I R-I L，是光在右旋偏振方向的光强分量和左旋偏振方向的光强分量之差。通常情况下，我们只关心光的偏振属性，因此对S 0进行归一化处理，即S 0＝1，其余三个分量也按相同比例进行归一化处理。
邦加球是用来图形化描述偏振态斯托克斯矢量的一个单位球，任何一种偏振态都可以映射到邦加球上的一点，将斯托克斯矢量的S 1、S 2、S 3分别作为x、y、z坐标绘制在笛卡尔坐标系中，即为该斯托克斯矢量的邦加球表示。
而缪勒矩阵是一个变换矩阵，体现一束光的斯托克斯矢量在散射前后发生的变化，及
S out＝M×S in
式中，S out是出射光的斯托克斯矢量，S in是入射光的斯托克斯矢量，M是缪勒矩阵，是一个4×4的矩阵。由于CCD(电荷耦合器件)无法接受到偏振信息，仅能接收到光强信息。因此在实际测量中，需要进行至少四次互相独立的起偏及检偏。起偏即为用一束已知偏振态的偏振光入射，检偏即为通过测量计算得到出射光的偏振态S out。由于斯托克斯矢量有四个分量，检偏时需要至少测量四个投影分量的光强大小，才能得到一束光的斯托克斯矢量。这样通过测量多种不同偏振态的偏振光照明后的出射偏振态，即可计算出斯托克斯矢量的变化矩阵，即缪勒矩阵。
目前偏振调制主要通过一个偏振片，再加一个或一系列相位延迟器件实现的，借助相位延迟器件不同的快轴角以及相位延迟大小之间的彼此配合得到多个不同偏振态。因此需要首先对快轴角及相位延迟对偏振态的影响进行说明，一个相位延迟器件的缪勒矩阵M δ,θ为：
Figure PCTCN2022106351-appb-000001
其中δ为线性相位延迟，θ为快轴角方向。
假设此时入射光的偏振态为S in＝[1 S 1 S 2 S 3] T，其中T表示矩阵的转置，即任意的完全偏振光时，出射光的偏振态可用公式S out＝S in×M δ,θ表示。这样在同一确定的入射光(通常为线偏振片产生的0度线偏振光)从一相位延迟器出射时，我们可以得到一个确定的偏振态，通过改变相位延迟器件的快轴角θ或相位延迟δ，出射偏振态也会发生相应的改变。这样通过多次改变相位延迟器件，就可以得到多 个不同且已知的偏振态，组成起偏器的仪器矩阵W或检偏器的仪器矩阵A。
相位延迟器件又可分为固定相位延迟(通过旋转改变快轴角的波片)以及电控式起偏元件(相位延迟可变的)。前者的主要优势在于精度高，缺点则是有运动部件，需要旋转电机带动波片旋转才能实现多种不同偏振态的调制，因而调制速度受电机速度影响，往往比较耗时。而后者主要有液晶相位延迟器(LCVR)、电光相位延迟器(EO)及光弹调制器(PEM)等通过改变施加在其两端的电压从而改变相位延迟的器件。其主要优势在于响应速度快，可达到毫秒量级。但因环境温度或电压波动等会造成一定的系统误差，且成本较高。此外，由于电控式起偏元件需要线缆进行控制，往往也不适合配合电机转动，因此其快轴角在测量中是无法自由旋转的。
为了使缪勒矩阵的测量更为精确，抑制噪声表现，可以对起偏器及检偏器进行设计与优化。
发明内容
为了弥补上述背景技术的不足，本发明提出一种起偏器与检偏器配置优化方法及起偏检偏系统，以解决缪勒矩阵测量中精度有限、无法很好地抑制噪声的问题。
本发明的技术问题通过以下的技术方案予以解决：
本发明公开了一种起偏器与检偏器配置优化方法，包括如下步骤：
调整起偏器的仪器矩阵W和检偏器的仪器矩阵A，使起偏器和检偏器仪器矩阵的等权重方差EWV最小，以实现针对高斯噪声的优化；且
起偏器的仪器矩阵W和检偏器的仪器矩阵A每一行的和为0，使泊松噪声所引起的估计方差独立于样本，且估计方差达到最小值。
在一些实施例中，还可能包括以下技术方案：
配置测量系统的起偏器以及检偏器，使其偏振态两两正交；随后搜索起偏器和检偏器仪器矩阵的最小等权重方差EWV；当起偏器和检偏器的仪器矩阵同时满足行和为0及最小EWV条件时，得到最优配置。
当起偏器和检偏器分别为一个旋转偏振片及一个旋转1/4波片时，使起偏器和检偏器偏振态两两正交的配置条件满足以下关系：
Figure PCTCN2022106351-appb-000002
式中，θ P为第一次测量配置的偏振片透光轴方向，θ R为第一次测量配置的1/4波片快轴角方向，θ P'为第二次测量配置的偏振片透光轴方向，θ R'为第二次测量配置的1/4波片快轴角方向；所述方法通过偏振片调整起偏的主通光方向，再通过1/4波片实现特定偏振态的调制。
当起偏器和检偏器系统包括一个固定偏振片、一个旋转1/2波片及一个旋转1/4波片时，使起偏器和检偏器偏振态两两正交的配置条件满足以下关系：
Figure PCTCN2022106351-appb-000003
式中，θ H为第一次测量配置的1/2波片快轴角方向，θ R为第一次测量配置的1/4波片快轴角方向，θ H'为第二次测量配置的1/2波片快轴角方向，θ R'为第二次测量配置的1/4波片快轴角方向；
所述方法的线偏振光方向的调制从单偏振片调制变成了固定偏振片加一个1/2波片，能够避免入射光不是理想的自然光时，转动偏振片导致的不同方向的线偏振光光强不一致的情况。
当起偏器和检偏器系统包括一个固定偏振片，两个全波延迟相位调制器件时，使起偏器和检偏器偏振态两两正交的配置条件满足以下关系：
Figure PCTCN2022106351-appb-000004
Figure PCTCN2022106351-appb-000005
式中，δ F1是第一次测量配置的第一个全波延迟相位调制器件的相位延迟，θ F1是其快轴角，δ F2是第一次测量配置的第二个全波延迟相位调制器件的相位延迟，θ F2是其快轴角，δ F1′是第二次测量配置的第一个全波延迟相位调制器件的相位延迟，δ F2′是第二次测量配置的第二个全波延迟相位调制器件的相位延迟。所述方法首先通过第一个全波延迟相位调制器件对偏振态在邦加球上的S 1OS 3平面的圆上调制，随后借助第二个全波延迟相位调制器件得到目标偏振态。
当起偏器和检偏器分别为一个旋转偏振片及一个旋转1/4波片时，使起偏器和检偏器仪器最优的四点测量配置满足以下关系：
Figure PCTCN2022106351-appb-000006
Figure PCTCN2022106351-appb-000007
Figure PCTCN2022106351-appb-000008
式中，θ P为第一次测量配置的偏振片透光轴方向，θ R为第一次测量配置的1/4波片快轴角方向，θ P'为第二次测量配置的偏振片透光轴方向，θ R'为第二次测量配置的1/4波片快轴角方向，θ P”为第三次测量配置的偏振片透光轴方向，θ R”为第三次测量配置的1/4波片快轴角方向，θ P”'为第四次测量配置的偏振片透光轴方向，θ R”'为第四次测量配置的1/4波片快轴角方向。
当起偏器和检偏器系统包括一个固定偏振片、一个旋转1/2波片及一个旋转1/4波片时，使起偏器和检偏器最优的四点测量配置满足以下关系：
Figure PCTCN2022106351-appb-000009
Figure PCTCN2022106351-appb-000010
Figure PCTCN2022106351-appb-000011
式中，θ H为第一次测量配置的1/2波片快轴角方向，θ R为第一次测量配置的1/4波片快轴角方向，θ H'为第二次测量配置的1/2波片快轴角方向，θ R'为第二次测量配置的1/4波片快轴角方向，θ H”为第三次测量配置的1/2波片快轴角方向，θ R”为第三次测量配置的1/4波片快轴角方向，θ H”'为第四次测量配置的1/2波片快轴角方向，θ R”'为第四次测量配置的1/4波片快轴角方向。
当起偏器和检偏器系统包括一个固定偏振片，两个全波延迟相位调制器件时，使起偏器和检偏器最优的四点测量配置满足以下关系：
Figure PCTCN2022106351-appb-000012
Figure PCTCN2022106351-appb-000013
Figure PCTCN2022106351-appb-000014
Figure PCTCN2022106351-appb-000015
式中，δ F1是第一次测量配置的第一个全波延迟相位调制器件的相位延迟，θ F1是其快轴角，δ F2是第一次测量配置的第二个全波延迟相位调制器件的相位延迟，θ F2是其快轴角，δ F1′是第二次测量配置的第一个全波延迟相位调制器件的相位延迟，δ F2′是第二次测量配置的第二个全波延迟相位调制器件的相位延迟，δ F1″是第三次测量配置的第一个全波延迟相位调制器件的相位延迟，δ F2″是第三次测量配置的第二个全波延迟相位调制器件的相位延迟，δ F1″′是第四次测量配置的第一个全波延迟相位调制器件的相位延迟，δ F2″′是第四次测量配置的第二个全波延迟相位调制器件的相位延迟。
当起偏器和检偏器系统包括一个固定偏振片，两个半波延迟相位调制器件时，使起偏器和检偏器最优的四点测量配置满足以下关系：
Figure PCTCN2022106351-appb-000016
Figure PCTCN2022106351-appb-000017
Figure PCTCN2022106351-appb-000018
Figure PCTCN2022106351-appb-000019
式中，δ H1、δ H2分别为第一次测量配置的两个半波延迟相位调制器件的线性相位延迟，θ H1、θ H2则分别为其快轴角,δ H1′、δ H2′分别为第二次测量配置的两个半波延迟相位调制器件的线性相位延迟，δ H1″、δ H2″分别为第三次测量配置的两个半波延迟相位调制器件的线性相位延迟，δ H1″′、δ H2″′分别为第四次测量配置的两个半波延迟相位调制器件的线性相位延迟。
进一步地，用实际配置表示的偏振态组成一个仪器矩阵，并利用遗传算法或类似的寻优算法对该仪器矩阵进行最小EWV优化，即，对每一组设置一个变量，并根据该变量得到一组中剩余的能够由该变量明确表示的偏振态；之后，这些偏振态将组成一个有数个未知变量的仪器矩阵；通过遗传算法对仪器矩阵进行最小EWV寻优，即可计算出当这数个未知变量为何值时，仪器矩阵的EWV能达到最小值。
进一步地，起偏器和检偏器均满足全偏振态的调制。
本发明还公开了一种起偏检偏系统，包括一个旋转偏振片及一个旋转1/4波片，配置如下：
Figure PCTCN2022106351-appb-000020
，该配置满足起偏器和检偏器的仪器矩阵W与A每一行的和为0，且起偏器和检偏器仪器矩阵的EWV是最优，以优化缪勒测量系统抗高斯-泊松混合噪声的性能。
本发明还公开了一种起偏检偏系统，包括一个固定偏振片、一个旋转1/2波片及一个旋转1/4波片，配置如下：
Figure PCTCN2022106351-appb-000021
，该配置满足起偏器的仪器矩阵W和检偏器的仪器矩阵A每一行的和为0，且起偏器和检偏器仪器矩阵的EWV是最优，以优化缪勒测量系统抗高斯-泊松混合噪声的性能。
本发明还公开了一种起偏检偏系统，包括一个固定偏振片，两个全波延迟相位调制器件，配置如下：
Figure PCTCN2022106351-appb-000022
，该配置满足起偏器的仪器矩阵W和检偏器的仪器矩阵A每一行的和为0，且起偏器和检偏器仪器矩阵的EWV是最优，以优化缪勒测量系统抗高斯-泊松混合噪声的性能。
本发明还公开了一种起偏检偏系统，包括一个固定偏振片及两个半波延迟相位调制器件，配置如下：
Figure PCTCN2022106351-appb-000023
，该配置满足起偏器的仪器矩阵W和检偏器的仪器矩阵A每一行的和为0，且起偏器和检偏器仪器矩阵的EWV是最优，以优化缪勒测量系统抗高斯-泊松混合噪声的性能。
本发明还公开了一种能够实现任意偏振态调制的起偏器，包括：照明系统、可旋转的偏振片和可旋转的1/4波片，其中，所述照明系统用于产生入射光；通过所述偏振片和所述1/4波片不同转动角度的组合，将入射光调制为所需偏振光。
在一些实施例中，还可能包括以下技术方案：
所述偏振片和所述1/4波片分别由对应的电动精密旋转位移台带动旋转。
通过改变所述偏振片的取向，并在每种取向下旋转所述1/4波片一周，实现任意偏振态调制。
本发明还公开了一种起偏器的优化方法，所述起偏器为前述的能够实现任意偏振态调制的起偏器；所述优化方法包括：
将所述偏振片的取向和所述1/4波片的快轴角度作为优化目标，通过电势最低迭代的方法，求解相应偏振态在邦加球上的最优均匀分布状态，该状态满足最优条件数的条件。
进一步地，所述通过电势最低迭代的方法，求解相应偏振态在邦加球上的最优均匀分布状态，包括：
利用所述偏振片的取向和所述1/4波片的快轴角度来计算每次调制所产生的偏振态的斯托克斯矢量，并将所计算的斯托克斯矢量映射到邦加球上来显示对应的偏振态在邦加球上的相应位置；而后将各个偏振态的对应位置在邦加球上进行均匀分布优化来寻找最优的起偏器仪器矩阵配置，该配置满足最小条件数指标。
进一步地，所述将各个偏振态的对应位置在邦加球上进行均匀分布优化来寻找最优的起偏器仪器矩阵配置，包括：
将每一对旋转角度所对应的偏振态在邦加球上的对应位置点视为点电荷，以点电荷之间的最小电势能作为搜索目标，利用全局搜索算法取总电势能最小时所对应的偏振片取向和1/4波片快轴角度为最优配置，该最优配置对应最小条件数下的起偏器仪器矩阵配置；
其中，一对所述旋转角度包括一次调制中偏振片的取向和1/4波片的快轴角度。
进一步地，所述总电势能的计算公式为：
Figure PCTCN2022106351-appb-000024
其中，N表示起偏器进行了N次调制，N≥4；N次调制的N个偏振态对应邦加球上N个所述位置点，即对应N个点电荷；E表示N个点电荷的总电势能；r i、r j分别表示第i个点电荷相对于邦加球球心的 位置矢量、第j个点电荷相对于邦加球球心的位置矢量。
本发明与现有技术对比的有益效果包括：本发明提供的起偏器与检偏器配置优化方法，通过调整起偏器的仪器矩阵W和检偏器的仪器矩阵A，使起偏器和检偏器仪器矩阵的等权重方差EWV最小，以实现针对高斯噪声的优化，且起偏器的仪器矩阵W和检偏器的仪器矩阵A每一行的和为0，使泊松噪声所引起的估计方差独立于样本，且估计方差达到最小值，从而实现最大程度地抑制噪声，并使噪声的规律与样本独立，无论测量何种样本，噪声的分布规律都是相同的。
在一些实施例中，本发明将测量配置与高斯-泊松混合噪声的优化相结合，通过采用多种不同器件下的起偏器及检偏器的最优测量配置，使起偏器和检偏器仪器矩阵的等权重方差EWV最小，进一步提升偏振测量，特别是缪勒矩阵测量中的性能精度，实现将缪勒矩阵测量中的误差传递影响降至最小，且使得泊松噪声表现与样本无关。同时，本方法具备普适性，可以对各种不同结构的测量系统进行优化。
附图说明
图1a至1b为本发明实施例中的旋转式相位延迟器件形成的一组正交偏振态图。
图2a至2b为本发明实施例中的相位可变延迟器件形成的一组正交偏振态图。
图3为本发明实施例中的一个旋转偏振片及一个旋转1/4波片的仪器示意图。
图4为本发明实施例中的一个固定偏振片、一个旋转1/2波片及一个旋转1/4波片的仪器示意图。
图5为本发明实施例中的一个固定偏振片，两个全波延迟相位调制器件的仪器示意图。
图6为本发明实施例中的一个固定偏振片及两个半波延迟相位调制器件的仪器示意图。
图7a至7b为本发明实施例中的一个固定偏振片及两个半波延迟相位调制器件的仪器下可调制出的所有偏振态及最优的四点测量框架图。
图8为本发明实施例的起偏器与检偏器配置优化方法流程图。
图9是基于本发明实施例起偏器的一种穆勒矩阵测量系统示意图。
图10是将偏振片固定在0°、1/4波片旋转一周的起偏方式所可能遍历的偏振态在邦加球上的显示。
图11是将偏振片分别固定在45°和135°时1/4波片旋转一周的起偏方式所可能遍历的偏振态在邦加球上的显示。
图12为同时旋转偏振片和1/4波片一周的起偏方式所可能遍历的偏振态在邦加球上的显示。
具体实施方式
下面对照附图并结合优选的实施方式对本发明作进一步说明。需要说明的是，在不冲突的情况下，本申请中的实施例及实施例中的特征可以相互组合。
需要说明的是，本实施例中的左、右、上、下、顶、底等方位用语，仅是互为相对概念，或是以产品的正常使用状态为参考的，而不应该认为是具有限制性的。
实施例1
经研究发现，合理选择起偏器产生的入射偏振态(即起偏器的仪器矩阵W)以及检偏器的几个偏振态投影通道(即检偏器的仪器矩阵A)可以大幅提高缪勒矩阵测量系统的性能。因此本发明实施例的优化即为选取更加合适的W和A。而仪器矩阵W和A在何种情况下达到最优由以下推导给出：
在缪勒矩阵测量系统中往往存在高斯-泊松混合噪声，评估噪声对测缪勒矩阵估计方差的影响需要借助协方差分析。在缪勒矩阵测量系统中，直接测量得到的光强与仪器矩阵和样本缪勒矩阵的关系可以表示为：
I＝A TMW
其中I为CCD测得的光强图像，M为样本的缪勒矩阵，W和A分别表示起偏器(PSG)和检偏器(PSA)的仪器矩阵，T代表矩阵的转置形式。为方便计算，借助克罗内克积将光强矩阵和样本的缪勒矩阵展开为向量形式：
Figure PCTCN2022106351-appb-000025
Figure PCTCN2022106351-appb-000026
其中V I和V M分别为上述光强矩阵I和样本的缪勒矩阵M的列向量形式，-1代表矩阵的逆或伪逆。根据V M和V I的关系，其协方差矩阵之间的关系可以定义为：
Figure PCTCN2022106351-appb-000027
其中
Figure PCTCN2022106351-appb-000028
表示克罗内克积分，
Figure PCTCN2022106351-appb-000029
和
Figure PCTCN2022106351-appb-000030
分别表示与样本缪勒矩阵的列向量V M和光强矩阵的列向量V I相关的协方差矩阵。缪勒矩阵测量系统正确的性能标准是缪勒矩阵所有元素的方差之和，即
Figure PCTCN2022106351-appb-000031
的迹：
Figure PCTCN2022106351-appb-000032
其中trace()表示求矩阵的迹。当系统中存在加性高斯噪声时，光强噪声的协方差矩阵
Figure PCTCN2022106351-appb-000033
表示为以其方差σ 2为对角阵元的对角矩阵。由此可知，系统中的高斯噪声对缪勒矩阵所造成的估计方差为：
Figure PCTCN2022106351-appb-000034
其中Q A＝(A TA) -1Q W＝(W TW) -1(这是算式的一种简写形式)，EWV W和EWV A分别代表起偏器和检偏器仪器矩阵的等权重方差。由上式可以看出，针对高斯噪声的优化，仅需起偏器和检偏器仪器矩阵的等权重方差(EWV)最小，即可达到最优状态。
当系统中存在加性高斯噪声时，光强噪声的协方差矩阵
Figure PCTCN2022106351-appb-000035
需要借助泊松分布的性质，由光强矩阵I的均值给出其方差，此时
Figure PCTCN2022106351-appb-000036
的对角阵元应当表示为：
Figure PCTCN2022106351-appb-000037
其中[V M] k表示列向量V M中的第k个元素，i与k都是矩阵的坐标索引，
Figure PCTCN2022106351-appb-000038
表示矩阵
Figure PCTCN2022106351-appb-000039
的第i行第i列的值，
Figure PCTCN2022106351-appb-000040
表示
Figure PCTCN2022106351-appb-000041
的转置矩阵的第i行第k列的值。运用协方差分析，系统中的泊松噪声对缪勒矩阵所造成的估计方差为：
Figure PCTCN2022106351-appb-000042
归一化后的V M其第一项永远是1。显然，在上式中，第一项是独立于样本的，而第二项与样本的后15个阵元相关，会导致随着样本的改变，泊松噪声所引起的估计方差会随之改变。幸运的是，当起偏器和检偏器仪器矩阵的EWV是最优时，
Figure PCTCN2022106351-appb-000043
为恒定的常数。因此，当满足下式时，CPoission(C泊松)的第二项会被置零，进而使得泊松噪声对缪勒矩阵所造成的估计方差独立于样本：
Figure PCTCN2022106351-appb-000044
上式的等价条件为：起偏器的仪器矩阵W和检偏器的仪器矩阵A每一行的和为0。在满足此条件 且起偏器和检偏器仪器矩阵的EWV是最优时，泊松噪声所引起的估计方差独立于样本，且估计方差达到了最小值。此时最优化的CPoission可以表示为：
Figure PCTCN2022106351-appb-000045
综上，当起偏器的仪器矩阵W和检偏器的仪器矩阵A每一行的和为0，且起偏器和检偏器仪器矩阵的EWV是最优时，缪勒矩阵测量系统抗高斯-泊松混合噪声的性能最优，系统总体的估计方差可以表示为：
Figure PCTCN2022106351-appb-000046
至此，我们已经了解仪器矩阵W与A在何种情况下最优。但此时的仪器矩阵与实际的测量系统之间没有直接的联系，只是得到了仪器矩阵在满足什么条件时最优。若要使实际的测量系统能够实现最优，即使测量系统的仪器矩阵满足上述条件，仍需要进一步地优化。由于这一步优化是为了将实际的测量与理论联系起来，下面我们以几个实际的测量系统作为范例，展现优化的方法与过程。
考虑到旋转式与相位可变式的延迟器有着不同的特点，旋转式器件由高精度旋转电机带动，整体测量的误差较小，但由于运动部件响应速度较慢，测量一般比较耗时。而电控式相位延迟可变延迟器则由于温度漂移等的影响，精度会稍差些，但响应速度在毫秒量级，可以实现非常快速的测量，但成本也较高。因此两者往往不会混用，我们分别对这两类相位延迟器件组成的系统进行优化。旋转式相位延迟器件形成的一组正交偏振态如图1a至1b所示，相位可变延迟器件形成的一组正交偏振态如图2a至2b所示。
本发明实施例通过采用多种不同器件下的起偏器及检偏器的最优配置，进一步提升偏振测量，特别是缪勒矩阵测量中的性能精度。实现将缪勒矩阵测量中的误差传递影响降至最小，且使得泊松噪声表现与样品无关的最优配置。
前文提到，当起偏器的仪器矩阵W和检偏器的仪器矩阵A每一行的和为0，且起偏器和检偏器仪器矩阵的EWV是最优时，缪勒矩阵测量系统抗高斯-泊松混合噪声的性能最优。因此，如果使测量系统的W与A满足该条件，自然能使测量系统最优，实现噪声传递最小且泊松噪声样本无关。但是测量系统的W与A是由测量系统的起偏器与检偏器所产生的偏振态决定的，而产生何种偏振态是由测量系统的配置(各个元件的快轴角、相位延迟等)决定的。因此，优化W与A的问题就转换成对测量系统配置的优化问题。
显然，当仪器矩阵的偏振态两两正交时，两个正交偏振态的斯托克斯矢量的后三个分量互为相反数，整个仪器矩阵的行和自然为零，也就是满足了最优仪器矩阵的第一个要求。而在邦加球中，两个关于圆心对称的偏振态就是一组正交的偏振态。而仪器矩阵本身是由多个偏振态组成的，仪器矩阵的N个偏振态可以在邦加球上形成一个多面体。如果该多面体任意一个顶点都有一个关于圆心对称的顶点，那么每一个偏振态也都有着一个对应的正交偏振态。此时问题的关键就变成了如何配置测量系统的起偏器以及检偏器，使其偏振态两两正交。而根据相位延迟器件的缪勒矩阵M δ,θ：
Figure PCTCN2022106351-appb-000047
可以看出虽然我们可以很方便地计算出任意偏振光经过相位延迟器件后出射光的偏振态，但在进行偏振态调制时，我们更加注重的是什么样的快轴角及相位延迟关系能满足将入射光调制为目标偏振态。而这种情况下，常规的正向思路并不能实现我们的要求，往往需要将快轴角及相位延迟作为输入量，通过不断调整输入得到对应的输出偏振态，而不是根据需要的偏振态去设计能满足需求的相位延迟器件。
因此本发明实施例将首先从直观，而非代数的层面出发，考虑相位延迟器件的性质对偏振态变化的影响。其规律可以总结为：
相位延迟器件在固定快轴角变化线性相位延迟时，偏振态在邦加球上变化的轨迹会在S 1、S 2平面投影成一段直线；
相位延迟器件的快轴角决定偏振态在邦加球上随不同相位延迟变化时，形成的轨迹在S 1、S 2平面的投影的直线的方向。且快轴角θ和投影与S 2方向的夹角
Figure PCTCN2022106351-appb-000048
满足
Figure PCTCN2022106351-appb-000049
的关系；
相位延迟器件在固定快轴角变化线性相位延迟时，偏振态在邦加球上变化的轨迹会形成一段圆弧。当线性相位延迟从0变化到2π时，圆弧将变为一个完整的圆。同时，圆弧的方向为从入射偏振态起，沿与S 2方向成夹角
Figure PCTCN2022106351-appb-000050
(当S 3<0时，为反向)作弧线。
再将相位延迟器件具体为固定相位延迟的波片与相位延迟可变的电控式元件(此处以液晶可变相位延迟器LCVR为例)。波片的特点是结构相对简单，无需配套的控制设备，可以很方便地与旋转电机组合以改变快轴角，但波片的相位延迟却无法自由地改变，通常是一个由波片本身材料决定的一个固定值。LCVR的特点与波片恰恰相反，它有着复杂的控制器及电路限制，无法与运动部件配合来使用，因此其快轴角通常在搭建完光路后便不再改变，但其相位延迟可以很方便地借助电压进行控制，且电控式导致其响应速度远快于电机旋转。
结合波片与LCVR的特性我们可以发现，LCVR器件在实际使用中是先确定一个快轴角后，根据需要可以人为地控制改变相位延迟，更加适合进行偏振态的调制。而波片是固定相位延迟，通过电机控制快轴角，在进行偏振态调制时，较难使其达到一个能满足需求的偏振态。同时，由于波片(旋转器件)在精度上的优势及LCVR在响应速度上的优势，往往不会将两者混合使用。同时考虑不同的成本及系统需求，我们以下列几种不同结构的测量光路为例，给出当两次测量时，各个元件的配置(偏振片、波片的角度，电控式相位可变延迟器的相位延迟)满足何种关系时，可以使产生的两个偏振态正交：
一个旋转偏振片及一个旋转1/4波片。
Figure PCTCN2022106351-appb-000051
式中，θ P为第一次测量配置的偏振片透光轴方向，θ R为第一次测量配置的1/4波片快轴角方向，θ P'为第二次测量配置的偏振片透光轴方向，θ R'为第二次测量配置的1/4波片快轴角方向。
该结构主要通过偏振片调整起偏的主通光方向，再通过1/4波片实现特定偏振态的调制。一个旋转偏振片及一个旋转1/4波片的仪器示意图如图3所示。
一个固定偏振片、一个旋转1/2波片及一个旋转1/4波片。
Figure PCTCN2022106351-appb-000052
式中，θ H为第一次测量配置的1/2波片快轴角方向，θ R为第一次测量配置的1/4波片快轴角方向，θ H'为第二次测量配置的1/2波片快轴角方向，θ R'为第二次测量配置的1/4波片快轴角方向。
该结构与上一结构类似，不过线偏振光方向的调制从单偏振片调制变成了固定偏振片加一个1/2波片，可以避免入射光不是理想的自然光时，转动偏振片导致的不同方向的线偏振光光强不一致的情况。一个固定偏振片、一个旋转1/2波片及一个旋转1/4波片的仪器示意图如图4所示。
一个固定偏振片，两个全波延迟相位调制器件。
Figure PCTCN2022106351-appb-000053
Figure PCTCN2022106351-appb-000054
式中，δ F1是第一次测量配置的第一个全波延迟相位调制器件的相位延迟，θ F1是其快轴角，δ F2是第一次测量配置的第二个全波延迟相位调制器件的相位延迟，θ F2是其快轴角，δ F1′是第二次测量配置的第 一个全波延迟相位调制器件的相位延迟，δ F2′是第二次测量配置的第二个全波延迟相位调制器件的相位延迟。该结构首先通过第一个全波延迟相位调制器件对偏振态在邦加球上的S 1OS 3平面的圆上调制，随后借助第二个全波延迟相位调制器件得到目标偏振态。一个固定偏振片，两个全波延迟相位调制器件的仪器示意图如图5所示。
当两次测量配置满足以上关系时，出射偏振态在邦加球上呈对称的关系，及该两次测量的S 1、S 2、S 3分量的和分别为零，即可满足最优仪器矩阵的第一个条件。
但由于四次测量时，该方法调制出的四种偏振态两两正交，这样两组调制出的四个偏振态将形成一个条件数无限大的仪器矩阵，使缪勒矩阵无解。因此，两两正交的关系仅对四点以上，且测量次数为偶次的仪器矩阵有效。四点仅存在两种最优的仪器矩阵：
Figure PCTCN2022106351-appb-000055
这两种仪器矩阵在邦加球上恰好形成一个正四面体，且三视图均为正方形，在对行和为零进行限制时，将不再采取两两正交的方式，而是通过正四面体的特性进行限制。正四面体的三个视图均为正方形，因此如果对三视图进行约束，使测量系统产生的四个偏振态能够在邦加球上形成一个三视图均为矩形的四点测量相比多点测量来说，有着绝对的测量速度上的优势，此处给出四点测量下的最优测量框架配置：
一个旋转偏振片及一个旋转1/4波片。
Figure PCTCN2022106351-appb-000056
Figure PCTCN2022106351-appb-000057
Figure PCTCN2022106351-appb-000058
式中，θ P为第一次测量配置的偏振片透光轴方向，θ R为第一次测量配置的1/4波片快轴角方向，θ P'为第二次测量配置的偏振片透光轴方向，θ R'为第二次测量配置的1/4波片快轴角方向，θ P”为第三次测量配置的偏振片透光轴方向，θ R”为第三次测量配置的1/4波片快轴角方向，θ P”'为第四次测量配置的偏振片透光轴方向，θ R”'为第四次测量配置的1/4波片快轴角方向。当四次测量的配置满足该式给出的关系时，可使四面体的三视图均为矩形。
一个固定偏振片、一个旋转1/2波片及一个旋转1/4波片。
Figure PCTCN2022106351-appb-000059
Figure PCTCN2022106351-appb-000060
Figure PCTCN2022106351-appb-000061
式中，θ H为第一次测量配置的1/2波片快轴角方向，θ R为第一次测量配置的1/4波片快轴角方向，θ H'为第二次测量配置的1/2波片快轴角方向，θ R'为第二次测量配置的1/4波片快轴角方向，θ H”为第三次测量配置的1/2波片快轴角方向，θ R”为第三次测量配置的1/4波片快轴角方向，θ H”'为第四次测量配置的1/2波片快轴角方向，θ R”'为第四次测量配置的1/4波片快轴角方向。
一个固定偏振片，两个全波延迟相位调制器件。
Figure PCTCN2022106351-appb-000062
Figure PCTCN2022106351-appb-000063
Figure PCTCN2022106351-appb-000064
Figure PCTCN2022106351-appb-000065
式中，δ F1是第一次测量配置的第一个全波延迟相位调制器件的相位延迟，θ F1是其快轴角，δ F2是第一次测量配置的第二个全波延迟相位调制器件的相位延迟，θ F2是其快轴角，δ F1′是第二次测量配置的第一个全波延迟相位调制器件的相位延迟，δ F2′是第二次测量配置的第二个全波延迟相位调制器件的相位延迟，δ F1″是第三次测量配置的第一个全波延迟相位调制器件的相位延迟，δ F2″是第三次测量配置的第二个全波延迟相位调制器件的相位延迟，δ F1″′是第四次测量配置的第一个全波延迟相位调制器件的相位延迟，δ F2″′是第四次测量配置的第二个全波延迟相位调制器件的相位延迟。
一个固定偏振片及两个半波延迟相位调制器件。
Figure PCTCN2022106351-appb-000066
Figure PCTCN2022106351-appb-000067
Figure PCTCN2022106351-appb-000068
Figure PCTCN2022106351-appb-000069
式中，δ H1、δ H2分别为第一次测量配置的两个半波延迟相位调制器件的线性相位延迟，θ H1、θ H2则分别为其快轴角,δ H1′、δ H2′分别为第二次测量配置的两个半波延迟相位调制器件的线性相位延迟，δ H1″、δ H2″分别为第三次测量配置的两个半波延迟相位调制器件的线性相位延迟，δ H1″′、δ H2″′分别为第四次测量配置的两个半波延迟相位调制器件的线性相位延迟。
该配置无法满足全偏振态的调制，但可以满足四点的最优框架。一个固定偏振片及两个半波延迟相位调制器件的仪器示意图如图6所示，该仪器下可调制出的所有偏振态及最优的四点测量框架图如图7a至7b所示，图7a至7b中r深色部分为一个22.5度偏振片及两个半波延迟相位调制器件(67.5度、90度)结构的起偏器/检偏器所能产生的所有偏振态。这种结构能产生的偏振态无法遍历整个邦加球，但恰好可以覆盖到四点理论最优仪器矩阵的四个偏振态(如浅色正四面体的四个顶点)。
当满足以上条件时，可以将四点配置的自由度缩减到一个或两个，大幅减少配置优化的难度，借助该关系，可以快速得出最优框架的实际配置。
通过上述约束，无论是对四次测量还是多次测量，均可以得到泊松噪声与样本无关的优化配置。此时我们获得了N/2组正交偏振态(N次起偏/检偏测量)或一组满足一定关系的4个未知偏振态(4次起偏/检偏测量)。但仅知道每一组内部的关系，而实际的偏振态与配置仍是未知的。此时我们需要对每一组设置一系列变量，并根据该变量得到一组中剩余的可以由该变量明确表示的偏振态。之后，这些偏振 态将组成一个有数个未知变量的仪器矩阵，仪器矩阵本身可以视为由多个偏振态组成，即如果有四个斯托克斯矢量S1，S2，S3，S4；则这四个列向量组成的仪器矩阵就为W＝[S1S2S3S4]，无论这四个斯托克斯矢量为完全已知，还是由未知变量表示，前者可以得到一个完全已知的仪器矩阵W，后者可以得到一个由变量表示的仪器矩阵W。通过遗传算法对仪器矩阵进行最小EWV寻优，即可计算出当这数个未知变量为何值时，仪器矩阵的EWV能达到最小值。此时的仪器矩阵以及测量配置就是明确且已知的，未知变量都已经通过该算法计算出来。
在一些实施例中，当起偏器和检偏器分别为一个旋转偏振片及一个旋转1/4波片时，根据其对应的几何约束条件，设置一系列变量并针对变量进行EMW寻优的过程如下：
首先确定第一组正交偏振态：设第一组正交偏振态中，生成第一个偏振态时，偏振片的通光轴角度为θ 1P；四分之一波片(以下简称波片)的快轴角为θ 1R。则生成与其正交的偏振态时，根据给出的几何约束的关系，偏振片的角度应为θ 1P'＝θ 1P+90；波片的角度应为θ 1R'＝θ 1R。如果要生成八次测量的仪器矩阵，需要同理生成另外3组正交偏振态，其偏振片与波片角度分别为：
θ 2P、θ 2R；θ 2P+90、θ 2R
θ 3P、θ 3R；θ 3P+90、θ 3R
θ 4P、θ 4R；θ 4P+90、θ 4R
这样就获得了由θ 1P、θ 1R；θ 2P、θ 2R；θ 3P、θ 3R；θ 4P、θ 4R八个变量表示的四组正交偏振态。每一组中的两个偏振态都可以由每组对应的变量表示。之后将这八个变量产生的一系列偏振态组成仪器矩阵，就可以得到由八个变量表示的EWV。然后再对得到的EWV借助遗传算法进行寻优。本发明实施例的结果是由遗传算法计算得到，但其它的不同寻优算法也能实现这一步，即对一个由多个可变量计算出的结果进行最小化寻优这一问题。
％遗传算法示例如下：
％％该语句直接调用matlab自带的遗传算法函数ga，下面对该函数的使用进行说明：
[OutputVariables,EWV]＝ga(@(UnknowVariables)fitfunc(UnknowVariables),8,[],[],[],[],[0 0 0 0 0 0 0 0],[180 180 180 180 180 180 180 180])；
％OutputVariables,EWV为该遗传算法的最终输出，OutputVariables为优化出的配置设置，EWV为优化出的配置所形成的仪器矩阵的等权重方差。
％ga函数的第一个输入fitfunc为自己定义的目标函数，其内容及定义方法在代码部分40-75行详细介绍。
％ga函数的第二个输入8为变量的数量。在本例中，有8个变量，因此输入设置为8。
％ga函数的第三到六个输入为对遗传算法本身的一些参数设定，此处选为默认设定，及[]即可。
％ga函数的第七个输入为变量的最小值取值范围，此处8个全部给为0，即[0 0 0 0 0 0 0 0]。
％ga函数的第八个输入为变量的最大值取值范围，此处8个全部给为180，即[180 180 180 180 180 180 180 180]。
％使八个变量的取值范围均为0到180度。
％根据得到的变量与几何约束的关系，计算出其余几个由变量表示的配置：
theat_R1＝OutputVariables(1)；
theat_P1＝OutputVariables(2)；
theat_P1_r＝theat_P1+90；
theat_R1_r＝theat_R1；
theat_R2＝OutputVariables(3)；
theat_P2＝OutputVariables(4)；
theat_P2_r＝theat_P2+90；
theat_R2_r＝theat_R2；
theat_R3＝OutputVariables(5)；
theat_P3＝OutputVariables(6)；
theat_P3_r＝theat_P3+90；
theat_R3_r＝theat_R3；
theat_R4＝OutputVariables(7)；
theat_P4＝OutputVariables(8)；
theat_P4_r＝theat_P4+90；
theat_R4_r＝theat_R4；
％将得到的配置与EWV显示出来。
disp(strcat('八次测量中偏振片的角度分别为',num2str(theat_P1),',',num2str(theat_P1_r),',',num2str(theat_P2),',',num2str(theat_P2_r),',',num2str(theat_P3),',',num2str(theat_P3_r),',',num2str(theat_P4),',',num2str(theat_P4_r)))；
disp(strcat('八次测量中波片的角度分别为',num2str(theat_R1),',',num2str(theat_R1_r),',',num2str(theat_R2),',',num2str(theat_R2_r),',',num2str(theat_R3),',',num2str(theat_R3_r),',',num2str(theat_R4),',',num2str(theat_R4_r)))；
disp(strcat('最终得到的仪器矩阵的EWV为',num2str(EWV)))；
％该函数为自己定义的目标函数，输入为变量，输出为优化目标的值：
function Fitness＝fitfunc(variables)
％首先对一些基础值进行定义，包括偏振片缪勒矩阵，波片缪勒矩阵，入射自然光，方便计算Stokes：
MLR＝@(x,y)[1,0,0,0；
0,cosd(2*x)^2+sind(2*x)^2*cosd(y),cosd(2*x)*sind(2*x)*(1-cosd(y)),-sind(2*x)*sind(y)；
0,cosd(2*x)*sind(2*x)*(1-cosd(y)),sind(2*x)^2+cosd(2*x)^2*cosd(y),cosd(2*x)*sind(y)；
0,sind(2*x)*sind(y),-cosd(2*x)*sind(y),cosd(y)]；％波片穆勒矩阵公式，x为快轴角，y为相位延迟；
MLD＝@(x)0.5*[1,cosd(2*x),sind(2*x),0；
cosd(2*x),cosd(2*x)^2,-cosd(2*x)*sind(2*x),0；
sind(2*x),sind(2*x)*cosd(2*x),sind(2*x)^2,0；
0,0,0,0]；％偏振片穆勒矩阵公式，x为主通光轴角度；
inputlight＝[1；0；0；0]；％输入为一束没有偏振效应的自然光。
％之后计算出一系列Stokes。
％第一组Stokes：
Stokes1＝MLR(variables(1),90)*MLD(variables(2))*inputlight；％得到由第1和第2个变量表示的Stokes1。
Stokes1_r＝MLR(variables(1),90)*MLD(variables(2)+90)*inputlight；％得到由第1和第2个变量表示的且与Stokes1正交的Stokes1_r,下同，不再赘述。
％第二组Stokes：
Stokes2＝MLR(variables(3),90)*MLD(variables(4))*inputlight；
Stokes2_r＝MLR(variables(3),90)*MLD(variables(4)+90)*inputlight；
％第三组Stokes：
Stokes3＝MLR(variables(5),90)*MLD(variables(6))*inputlight；
Stokes3_r＝MLR(variables(5),90)*MLD(variables(6)+90)*inputlight；
％第四组Stokes：
Stokes4＝MLR(variables(7),90)*MLD(variables(8))*inputlight；
Stokes4_r＝MLR(variables(7),90)*MLD(variables(8)+90)*inputlight；
％得到所有Stokes后，将其组成一个仪器矩阵：
InstrumentMatrix＝[Stokes1Stokes1_r Stokes2 Stokes2_r Stokes3 Stokes3_r Stokes4 Stokes4_r]；
％计算该仪器矩阵的EWV：
ewv＝trace((pinv(InstrumentMatrix))'*pinv(InstrumentMatrix))；
％将优化目标确定为EWV。
Fitness＝ewv；
end
综上，本发明实施例的起偏器与检偏器配置优化方法流程图如图8所示。
本发明实施例系统地提出一种对偏振测量系统(起偏器/检偏器)进行优化的方法，该方法关键是对能满足缪勒矩阵测量时，16个阵元的估计泊松噪声方差与样本无关的仪器矩阵给出现实可实现的、具体的仪器配置。现有的测量大部分未考虑到对泊松噪声的抑制或者仅从测量原理出发，说明在什么仪器矩阵下可以抑制噪声，并未给出可以参考或可借助现有器件实际实现的配置。本发明实施例通过上述关系进行几何约束，从而计算出具体测量时的仪器配置，以及满足上述关系，由该方法得到对应的配置变形。
下面给出本发明实施例的实施流程及最终结果。
首先确定所要采用的测量系统结构，除已在上文给出的一种特殊结构外，该系统无论是作为起偏器还是检偏器，均需要满足全偏振态的调制。其次确定对四次采集测量还是多次采集测量进行优化，针对这两种情况确定对每组偏振态的约束条件，借助不同偏振元件改变偏振态的规律，将每组偏振态用测量系统的实际配置进行约束。之后将经过约束后，用实际配置表示的偏振态组成一个仪器矩阵，并利用遗传算法或类似的寻优算法对该仪器矩阵进行最小EWV优化。即可得到最优的实际配置。
经过本发明实施例的起偏器与检偏器配置优化方法给出的部分起偏检偏系统的配置如下：
一个旋转偏振片及一个旋转1/4波片。
Figure PCTCN2022106351-appb-000070
一个固定偏振片、一个旋转1/2波片及一个旋转1/4波片。
Figure PCTCN2022106351-appb-000071
一个固定偏振片，两个全波延迟相位调制器件。
Figure PCTCN2022106351-appb-000072
一个固定偏振片及两个半波延迟相位调制器件。
Figure PCTCN2022106351-appb-000073
上述a)至d)的配置均满足起偏器的仪器矩阵W和检偏器的仪器矩阵A每一行的和为0，且起偏器和检偏器仪器矩阵的EWV是最优，以优化缪勒测量系统抗高斯-泊松混合噪声的性能。
当采用相应的结构进行测量时，需要把各个元件的配置按表中给出参数进行设置即可。例如，当采用旋转偏振片和旋转波片进行测量时，可以采用a)表所给出的第一种四点配置，即，首先使偏振片旋转到4.87度，波片旋转到22.5度进行第一次起偏；再使偏振片旋转到85.13度，波片旋转到67.5度进行第二次起偏；然后使偏振片旋转到94.87度，波片旋转到112.5度进行第三次起偏；最后使偏振片旋转到175.13度，波片旋转到157.5度进行第四次起偏。同时，每次起偏也需要进行一次检偏，检偏的过程与起偏类似，根据使用的检偏器的结构，选择结构对应的表中给出的具体配置，进行四次或八次测量检偏。即，如果起偏、检偏都采用四次测量的模式，总共需要进行16次测量。
与传统的测量配置相比，本发明实施例的起偏器与检偏器配置优化方法系统性地将测量配置与高斯-泊松混合噪声的优化相结合，能够对实际测量产生指导作用，使测量系统达到最优。传统的没有采用最佳测量配置的测量系统，虽然依然能够进行测量，但是其精度有限，无法很好地抑制系统中的噪声，而且噪声规律也并不明确，难以进行后期的计算降噪等工作。该方法优化出的测量配置则改善了这一问题，一是使系统中的噪声传递最小，最大程度地抑制了噪声，二是使噪声的规律与样本独立，无论测量何种样本，噪声的分布规律都是相同的。同时，该方法也具备普适性，可以对各种不同结构的测量系统进行优化。
实施例2
本实施例提供一种能够实现任意偏振态调制的起偏器，包括：照明系统、可旋转的偏振片和可旋转的1/4波片，其中照明系统用于产生入射光；通过偏振片和1/4波片不同转动角度的组合，将入射光调制为所需偏振光。通过改变所述偏振片的取向，并在每种取向下旋转所述1/4波片一周，实现任意偏振态调制。所述偏振片和所述1/4波片分别由对应的电动精密旋转位移台带动旋转。图9所示是基于本实施例上述起偏器的一种穆勒矩阵测量系统示意图，具体而言，是一种透射式穆勒矩阵测量系统。参考图9，LED光源1发出的光经过偏振片2和1/4波片3入射到样品4上，从样品4中透射出来的光被检偏器5所接收。根据偏振片2和1/4波片3多次(不少于4次)调制和检偏器5的检偏，最终计算得到样品4的穆勒矩阵图像。
对于本实施例的起偏器可以实现任意偏振态调制这一点，是基于固定偏振片、旋转1/4波片的起偏方式。对于偏振片固定在0°，将1/4波片旋转一周，其所能在邦加球上遍历的所有可能的偏振态如图10所示，其所能遍历的偏振态只能是邦加球面上的一条“8”字型区域。当偏振片分别固定在45°、135°时，都将1/4波片旋转一周，得到对应的两条“8”字型区域，可以在图11中看到，这两条“8”字的形状相同，但由于偏振片取向的改变，这个“8”字形在邦加球上的朝向不同；且45°和135°的取向是正交的，反映在 邦加球上应位于球的两侧，图11也能很好地反应这一点。这就构成了本实施例的起偏器能产生任意偏振态，即本实施例的起偏方式可以遍历邦加球上任意一点的基础。即偏振片固定在任意角度时，单独转动1/4波片所能遍历的偏振态在邦加球上就是一个“8”字形。但“8”字形的朝向会随着偏振片的取向有所改变。因此同时旋转偏振片和1/4波片，就可以遍历邦加球上的任意偏振态，其可以在球上遍历的偏振态如图12所示。
本实施例另一变通形式提出前述起偏器的优化方法，通过将实际的物理配置，即偏振片的取向和1/4波片的快轴角度作为优化目标，通过电势最低迭代的方法，求解相应偏振态在邦加球上的最优均匀分布状态，此状态同时也满足最优条件数的条件。具体而言，通过将实际的偏振片取向和1/4波片的快轴角度作为直接优化量，利用偏振片的取向和1/4波片的快轴角度来计算每次调制所产生的偏振态的斯托克斯矢量，并将所计算的斯托克斯矢量映射到邦加球上来显示对应的偏振态在邦加球上的相应位置；而后将各个偏振态的对应位置在邦加球上进行均匀分布优化来寻找最优的起偏器仪器矩阵配置，该配置满足最小条件数指标。这样的优化配置可以降低系统误差传递到最终测量结果的传递比例，进而实现高精度、低误差的穆勒矩阵测量。
每一次调制，都对应偏振片的一个取向和1/4波片的一个快轴角度，即每一次调制都对应一对旋转角度；而每一次调制都对应一个偏振态即斯托克斯矢量。我们可以将每一对旋转角度所对应的偏振态在邦加球上的对应位置点视为点电荷，以点电荷之间的最小电势能作为搜索目标，利用全局搜索算法取总电势能最小时所对应的偏振片取向和1/4波片快轴角度为最优配置，实现起偏器的优化，该最优配置对应最小条件数下的起偏器仪器矩阵配置。
对于前向(透射式)的穆勒矩阵测量系统，当入射偏振光经过样品透射后，透射偏振光相比于入射偏振光，其偏振态发生了变化。通过不少于四次的起偏器偏振调制和检偏器的偏振调制，通过检偏器后的成像元件所采集到的光强图，即可计算出样品的穆勒矩阵图像，可以表示为：
I＝AMW
其中，A代表检偏器的仪器矩阵，W代表起偏器的仪器矩阵，M代表样品的穆勒矩阵，I为探测到的光强。
定义κ A为检偏器仪器矩阵A的条件数，κ W为起偏器仪器矩阵W的条件数。对于一个穆勒矩阵测量系统来说，最终测得的穆勒矩阵的误差和系统误差之间有如下的关系：
||ΔM||/||M||≤κ Wκ A||ΔI||/||I||+κ A||ΔA||/||A||+κ W||ΔW||/||W||
其中，||ΔM||/||M||表示最终测得的穆勒矩阵的误差，||ΔI||/||I||、||ΔA||/||A||、||ΔW||/||W||分别表示光强误差、检偏器的系统误差和起偏器的系统误差。可以看到对于起偏器来说，其仪器矩阵的条件数κ W越小，系统误差最终传递到测量结果的传递比例就越低。
对于穆勒矩阵测量系统，为了得到穆勒矩阵，起偏器最少调制四次。设调制次数为N，则起偏器仪器矩阵可表示为：
Figure PCTCN2022106351-appb-000074
其中，R θi(i＝1,2,…,N)表示1/4波片的快轴角度位于θ i(i＝1,2,…N)时波片的穆勒矩阵；
Figure PCTCN2022106351-appb-000075
表示偏振片的通光方向(取向)位于
Figure PCTCN2022106351-appb-000076
时偏振片的穆勒矩阵；S in代表入射光的偏振态即斯托克斯矢量，照明光为自然光时，S in＝[1 0 0 0] T。由于穆勒矩阵为4×4，即R θi、
Figure PCTCN2022106351-appb-000077
皆为4×4的矩阵，而入射光的斯托克斯矢量S in为4×1的列向量，因此
Figure PCTCN2022106351-appb-000078
的大小应为4×1，则矩阵W N的大小为4×N。
将起偏器仪器矩阵每一列的第2、3、4行作为一组在邦加球上的三维坐标，则N次调制在邦加球上对应N个三维坐标点。为了求解优化问题，将每个三维坐标点都看作点电荷。对于偏振测量来说，每一次选取的起偏/检偏态应当尽可能独立，这也就意味着每一个起偏态对应的其在邦加球上的点之间应当尽可能地“均匀”，即这些点相互之间的距离应当相等且尽量要达到最大值。这和电磁学上将多个点电荷在单位球上如何分布能取得最小电势能的这一问题是等价的。因为在只考虑库仑力的作用的时候，点电荷与点电荷之间距离越远，分布得越均匀，电势能才最小。因此将每次调制的偏振态在邦加球上相应的三维坐标点视为点电荷来求解优化问题是符合理论依据的。以点电荷之间的最小电势能作为搜索目标，利用全局搜索算法取总电势能最小时所对应的偏振片取向和1/4波片快轴角度为最优配置。由于电荷与电荷间只存在库仑力的作用，因此可通过电势能公式来计算N个点电荷总的电势能E：
Figure PCTCN2022106351-appb-000079
其中，r i、r j分别表示第i个点电荷相对于邦加球球心的位置矢量、第j个点电荷相对于邦加球球心的位置矢量。这样一来，优化问题就变为寻找最优的起偏器仪器矩阵W，使得E最小的同时，整个仪器矩阵W的条件数最小。
每一个矩阵都有自己相对应的条件数，故此起偏器的仪器矩阵也有其对应的条件数。对于矩阵W，其条件数C(W)＝||W||·||W^{-1}||(||…||表示矩阵的2范数)。在Matlab中可以使用cond命令直接求解一个矩阵的条件数。
下面以起偏器进行4次调制为例来进行试验。
对于四次调制的起偏器，即N＝4时，其仪器矩阵可以表示为：
Figure PCTCN2022106351-appb-000080
其中，前述已经提到起偏器调制N次时，仪器矩阵W N的大小为4×N。因此，4次调制下仪器矩阵W为4×4。
在本发明实施例中，偏振片和1/4波片的角度旋转范围均为0～180°，旋转180°即为旋转一周。以偏振片和1/4波片的角度为直接优化量，利用全局搜索算法，搜索最优解。具体包括：将每一对旋转角度所对应的偏振态(斯托克斯矢量)在邦加球上的对应点看作“点电荷”，以点与点之间的最小电势能作为搜索目标，取电势能最小时所对应的偏振片和1/4波片的角度为最优配置，同时此配置也对应最小条件数下的起偏器仪器矩阵配置。在四次调制的情况下，根据如下过程得到偏振片和1/4波片(实验所用的1/4波片实际相位延迟并非90°，实际测量值为92.725°)的最优角度配置：
在4次调制的条件下，根据所给出的4*2＝8个角度(4对旋转角度)，比如偏振片四个角度15.586°、53.281°、114.957°、176.421°，1/4波片四个角度149.728°、64.121°、125.166°、4.59°，再根据仪器矩阵表达式
Figure PCTCN2022106351-appb-000081
即可求出如下真实的W值：
Figure PCTCN2022106351-appb-000082
其中，上述W值只是一个范例。应当理解的是，并非只有一个解，应用本方法可以得到多组不同的满足最小条件数指标的解。
上述矩阵W的条件数为1.732，符合理论最小值。说明利用优化方法得到的偏振片和1/4波片的最优角度配置，也同时满足最小条件数指标，这样可以使得系统误差的传递比例最小。
将偏振片和波片作为标准样本，标准样本也有其对应的穆勒矩阵(4×4＝16个阵元)，首先通过图9所示的光路构造测量系统来测量标准样本的穆勒矩阵：根据优化方法给出的四个角度(偏振片有四个角度、波片有四个角度)，使得偏振片和1/4波片分别都按照对应的角度各改变四次，通过将起偏器调制N次(具体实施例子用的是4次)，我们就可以得到N组光强所组成的列向量I。则标准样本的穆勒矩阵用可用下式计算得出：
M＝pinv(A)·M·pinv(W)
其中，pinv()表示矩阵的伪逆，当矩阵为方阵时它表示矩阵的逆。在得到穆勒矩阵测量值之后，对每一个阵元按照所测得的穆勒矩阵阵元值measured k和该阵元实际值true k应当是多少来计算单个阵元的误差，16个阵元各自的误差作为16组误差值，采用这16组误差值用下列公式(即n＝16)计算穆勒矩阵阵元的平均均方根误差
Figure PCTCN2022106351-appb-000083
Figure PCTCN2022106351-appb-000084
其中，k代表穆勒矩阵16个阵元的序号。从而可以得到偏振片、1/4波片及1/8波片的穆勒矩阵阵雨的平均均方根误差
Figure PCTCN2022106351-appb-000085
如下表1所示：
表1平均均方根误差
Figure PCTCN2022106351-appb-000086
值
标准样本 偏振片波片起偏 单波片起偏 优化提升比
70°偏振片 0.0064 0.0102 37％
120°偏振片 0.0067 0.0117 43％
70°λ/4波片 0.0057 0.0124 54％
120°λ/4波片 0.0062 0.0116 52％
70°λ/8波片 0.0042 0.0077 45％
120°λ/8波片 0.0037 0.0069 46％
从上面的比对可以看出，与传统的单波片旋转的起偏方法相比，本发明实施例同时旋转偏振片和波片来实现任意偏振态调制的起偏器，通过优化方法进行优化后，穆勒矩阵的测量误差得以降低，测量精度提升。
实施例1和实施例2的关系说明
以下从原理上对实施例1和实施例2之间的关系进行说明：
1)电势能与EWV：
两者本质略有不同，但在该偏振优化应用场景中，虽两者计算公式不同，但EWV最小时，电势能也最小。这也意味着，对最小电势能寻优的结果同时也会使EWV最小。在最小寻优时，其作用是等价的，在实施例1和实施例2中，EWV指标和电势能指标可以互换，不影响优化的结果。但借助电势能指标是在实施例2中提出的，而EWV指标是传统的指标。
2)仪器结构上的相似于不同：
实施例2提出了旋转偏振片旋转四分之一波片(RPRQ)的起偏系统，实施例1则采用了RPRQ结构，但包含了起偏和检偏系统。此外，实施例1还额外提出了多种结构。
3)优化原理上的相似与不同：
实施例2提出电势能指标来表征偏振态在邦加球上分布的均匀性，有几何优化的理念。实施例1将电势能指标更换为了更传统的EWV指标，而且额外考虑了泊松噪声的影响，进一步借助几何优化的理念，提出了通过几何约束来对结果进行限制。
即偏振态几何上的均匀满足最小EWV以及最小电势能，使得系统对高斯噪声最优；
偏振态几何上的正交或正四面体满足仪器矩阵行和为零，使得系统对泊松噪声最优。
前者是实施例1和实施例2都用到的，后者是实施例1用到的。
4)优化结果上的相似与不同：
实施例1和实施例2优化的结果均有实际的配置，而不是单纯的仪器矩阵。都是通过分析几何上偏振元件对偏振态的改变规律，将偏振态与实际配置之间建立联系，从而得到实际的配置。
但实施例2仅对四次起偏、检偏测量进行了分析，没有将方法应用到更多次的起偏、检偏测量中(虽然方法本身可以，但并没有提出)。
实施例1则是对四次及多次起偏、检偏测量分别进行了讨论。
5)总结
总的来说，实施例1是实施例2的拓展与延申，补充了几种额外的测量结构、补充了能应用到PSA和PSG两者的说明、额外满足了对泊松噪声的优化、补充了对多次起偏检偏测量优化的讨论。
以上内容是结合具体的优选实施方式对本发明所作的进一步详细说明，不能认定本发明的具体实施只局限于这些说明。对于本发明所属技术领域的技术人员来说，在不脱离本发明构思的前提下，还可以做出若干等同替代或明显变型，而且性能或用途相同，都应当视为属于本发明的保护范围。

Claims (22)

  1. 一种起偏器与检偏器配置优化方法，其特征在于，包括如下步骤：
    调整起偏器的仪器矩阵W和检偏器的仪器矩阵A，使起偏器和检偏器仪器矩阵的等权重方差EWV最小，以实现针对高斯噪声的优化；且
    起偏器的仪器矩阵W和检偏器的仪器矩阵A每一行的和为0，使泊松噪声所引起的估计方差独立于样本，且估计方差达到最小值。
  2. 如权利要求1所述的起偏器与检偏器配置优化方法，其特征在于，配置测量系统的起偏器以及检偏器，使其偏振态两两正交；随后搜索起偏器和检偏器仪器矩阵的最小等权重方差EWV；当起偏器和检偏器的仪器矩阵同时满足行和为0及最小EWV条件时，得到最优配置。
  3. 如权利要求2所述的起偏器与检偏器配置优化方法，其特征在于，当起偏器和检偏器分别为一个旋转偏振片及一个旋转1/4波片时，使起偏器和检偏器偏振态两两正交的配置条件满足以下关系：
    Figure PCTCN2022106351-appb-100001
    式中，θ P为第一次测量配置的偏振片透光轴方向，θ R为第一次测量配置的1/4波片快轴角方向，θ P′为第二次测量配置的偏振片透光轴方向，θ R'为第二次测量配置的1/4波片快轴角方向；所述方法通过偏振片调整起偏的主通光方向，再通过1/4波片实现特定偏振态的调制。
  4. 如权利要求2所述的起偏器与检偏器配置优化方法，其特征在于，当起偏器和检偏器系统包括一个固定偏振片、一个旋转1/2波片及一个旋转1/4波片时，使起偏器和检偏器偏振态两两正交的配置条件满足以下关系：
    Figure PCTCN2022106351-appb-100002
    式中，θ H为第一次测量配置的1/2波片快轴角方向，θ R为第一次测量配置的1/4波片快轴角方向，θ H′为第二次测量配置的1/2波片快轴角方向，θ R'为第二次测量配置的1/4波片快轴角方向；
    所述方法的线偏振光方向的调制从单偏振片调制变成了固定偏振片加一个1/2波片，能够避免入射光不是理想的自然光时，转动偏振片导致的不同方向的线偏振光光强不一致的情况。
  5. 如权利要求2所述的起偏器与检偏器配置优化方法，其特征在于，当起偏器和检偏器系统包括一个固定偏振片，两个全波延迟相位调制器件时，使起偏器和检偏器偏振态两两正交的配置条件满足以下关系：
    Figure PCTCN2022106351-appb-100003
    Figure PCTCN2022106351-appb-100004
    式中，δ F1是第一次测量配置的第一个全波延迟相位调制器件的相位延迟，θ F1是其快轴角，δ F2是第一次测量配置的第二个全波延迟相位调制器件的相位延迟，θ F2是其快轴角，δ F1′是第二次测量配置的第一个全波延迟相位调制器件的相位延迟，δ F2′是第二次测量配置的第二个全波延迟相位调制器件的相位 延迟。所述方法首先通过第一个全波延迟相位调制器件对偏振态在邦加球上的S 1OS 3平面的圆上调制，随后借助第二个全波延迟相位调制器件得到目标偏振态。
  6. 如权利要求1所述的起偏器与检偏器配置优化方法，其特征在于，当起偏器和检偏器分别为一个旋转偏振片及一个旋转1/4波片时，起偏器和检偏器最优的四点测量配置满足以下关系：
    Figure PCTCN2022106351-appb-100005
    Figure PCTCN2022106351-appb-100006
    Figure PCTCN2022106351-appb-100007
    式中，θ P为第一次测量配置的偏振片透光轴方向，θ R为第一次测量配置的1/4波片快轴角方向，θ P′为第二次测量配置的偏振片透光轴方向，θ R'为第二次测量配置的1/4波片快轴角方向，θ P”为第三次测量配置的偏振片透光轴方向，θ R″为第三次测量配置的1/4波片快轴角方向，θ P″′为第四次测量配置的偏振片透光轴方向，θ R”'为第四次测量配置的1/4波片快轴角方向。
  7. 如权利要求1所述的起偏器与检偏器配置优化方法，其特征在于，当起偏器和检偏器系统包括一个固定偏振片、一个旋转1/2波片及一个旋转1/4波片时，使起偏器和检偏器仪器最优的四点测量配置满足以下关系：
    Figure PCTCN2022106351-appb-100008
    Figure PCTCN2022106351-appb-100009
    Figure PCTCN2022106351-appb-100010
    式中，θ H为第一次测量配置的1/2波片快轴角方向，θ R为第一次测量配置的1/4波片快轴角方向，θ H′为第二次测量配置的1/2波片快轴角方向，θ R′为第二次测量配置的1/4波片快轴角方向，θ H″为第三次测量配置的1/2波片快轴角方向，θ R”为第三次测量配置的1/4波片快轴角方向，θ H”'为第四次测量配置的1/2波片快轴角方向，θ R″′为第四次测量配置的1/4波片快轴角方向。
  8. 如权利要求1所述的起偏器与检偏器配置优化方法，其特征在于，当起偏器和检偏器系统包括一个固定偏振片，两个全波延迟相位调制器件时，使起偏器和检偏器最优的四点测量配置满足以下关系：
    Figure PCTCN2022106351-appb-100011
    Figure PCTCN2022106351-appb-100012
    Figure PCTCN2022106351-appb-100013
    Figure PCTCN2022106351-appb-100014
    式中，δ F1是第一次测量配置的第一个全波延迟相位调制器件的相位延迟，θ F1是其快轴角，δ F2是第一次测量配置的第二个全波延迟相位调制器件的相位延迟，θ F2是其快轴角，δ F1′是第二次测量配置的第一个全波延迟相位调制器件的相位延迟，δ F2′是第二次测量配置的第二个全波延迟相位调制器件的相位延迟，δ F1″是第三次测量配置的第一个全波延迟相位调制器件的相位延迟，δ F2″是第三次测量配置的第二个全波延迟相位调制器件的相位延迟，δ F1″′是第四次测量配置的第一个全波延迟相位调制器件的相位延迟，δ F2″′是第四次测量配置的第二个全波延迟相位调制器件的相位延迟。
  9. 如权利要求1所述的起偏器与检偏器配置优化方法，其特征在于，当起偏器和检偏器系统包括一个固定偏振片，两个半波延迟相位调制器件时，使起偏器和检偏器最优的四点测量配置满足以下关系：
    Figure PCTCN2022106351-appb-100015
    Figure PCTCN2022106351-appb-100016
    Figure PCTCN2022106351-appb-100017
    Figure PCTCN2022106351-appb-100018
    式中，δ H1、δ H2分别为第一次测量配置的两个半波延迟相位调制器件的线性相位延迟，θ H1、θ H2则分别为其快轴角,δ H1′、δ H2′分别为第二次测量配置的两个半波延迟相位调制器件的线性相位延迟，δ H1″、δ H2″分别为第三次测量配置的两个半波延迟相位调制器件的线性相位延迟，δ H1″′、δ H2″′分别为第四次测量配置的两个半波延迟相位调制器件的线性相位延迟。
  10. 如权利要求3-9中任一项所述的起偏器与检偏器配置优化方法，其特征在于，用实际配置表示的偏振态组成一个仪器矩阵，并利用遗传算法或类似的寻优算法对该仪器矩阵进行最小EWV优化，即，对每一组设置一个变量，并根据该变量得到一组中剩余的能够由该变量明确表示的偏振态；之后，这些偏振态将组成一个有数个未知变量的仪器矩阵；通过遗传算法对仪器矩阵进行最小EWV寻优，即可计算出当这数个未知变量为何值时，仪器矩阵的EWV能达到最小值。
  11. 如权利要求3-8中任一项所述的起偏器与检偏器配置行优化方法，其特征在于，起偏器和检偏器均满足全偏振态的调制。
  12. 一种起偏检偏系统，其特征在于，包括一个旋转偏振片及一个旋转1/4波片，配置如下：
    Figure PCTCN2022106351-appb-100019
    ，该配置满足起偏器的仪器矩阵W和检偏器的仪器矩阵A每一行的和为0，且起偏器和检偏器仪器矩阵的EWV是最优，以优化缪勒测量系统抗高斯-泊松混合噪声的性能。
  13. 一种起偏检偏系统，其特征在于，包括一个固定偏振片、一个旋转1/2波片及一个旋转1/4波片，配置如下：
    Figure PCTCN2022106351-appb-100020
    ，该配置满足起偏器的仪器矩阵W和检偏器的仪器矩阵A每一行的和为0，且起偏器和检偏器仪器矩阵的EWV是最优，以优化缪勒测量系统抗高斯-泊松混合噪声的性能。
  14. 一种起偏检偏系统，其特征在于，包括一个固定偏振片，两个全波延迟相位调制器件，配置如下：
    Figure PCTCN2022106351-appb-100021
    ，该配置满足起偏器的仪器矩阵W和检偏器的仪器矩阵A每一行的和为0，且起偏器和检偏器仪器矩阵的EWV是最优，以优化缪勒测量系统抗高斯-泊松混合噪声的性能。
  15. 一种起偏检偏系统，其特征在于，包括一个固定偏振片及两个半波延迟相位调制器件，配置如下：
    Figure PCTCN2022106351-appb-100022
    ，该配置满足起偏器的仪器矩阵W和检偏器的仪器矩阵A每一行的和为0，且起偏器和检偏器仪器矩阵的EWV是最优，以优化缪勒测量系统抗高斯-泊松混合噪声的性能。
  16. 一种能够实现任意偏振态调制的起偏器，其特征在于，包括：照明系统、可旋转的偏振片和可旋转的1/4波片，其中，所述照明系统用于产生入射光；通过所述偏振片和所述1/4波片不同转动角度的组合，将入射光调制为所需偏振光。
  17. 如权利要求1所述的能够实现任意偏振态调制的起偏器，其特征在于，所述偏振片和所述1/4波片分别由对应的电动精密旋转位移台带动旋转。
  18. 如权利要求1所述的能够实现任意偏振态调制的起偏器，其特征在于，通过改变所述偏振片的取向，并在每种取向下旋转所述1/4波片一周，实现任意偏振态调制。
  19. 一种起偏器的优化方法，其特征在于，所述起偏器为权利要求1至3任一项所述的能够实现任意偏振态调制的起偏器；所述优化方法包括：
    将所述偏振片的取向和所述1/4波片的快轴角度作为优化目标，通过电势最低迭代的方法，求解相应偏振态在邦加球上的最优均匀分布状态，该状态满足最优条件数的条件。
  20. 如权利要求19所述的起偏器的优化方法，其特征在于，所述通过电势最低迭代的方法，求解相应偏振态在邦加球上的最优均匀分布状态，包括：
    利用所述偏振片的取向和所述1/4波片的快轴角度来计算每次调制所产生的偏振态的斯托克斯矢量，并将所计算的斯托克斯矢量映射到邦加球上来显示对应的偏振态在邦加球上的相应位置；而后将各个偏振态的对应位置在邦加球上进行均匀分布优化来寻找最优的起偏器仪器矩阵配置，该配置满足最小条件数指标。
  21. 如权利要求20所述的起偏器的优化方法，其特征在于，所述将各个偏振态的对应位置在邦加球上进行均匀分布优化来寻找最优的起偏器仪器矩阵配置，包括：
    将每一对旋转角度所对应的偏振态在邦加球上的对应位置点视为点电荷，以点电荷之间的最小电势能作为搜索目标，利用全局搜索算法取总电势能最小时所对应的偏振片取向和1/4波片快轴角度为最优配置，该最优配置对应最小条件数下的起偏器仪器矩阵配置；
    其中，一对所述旋转角度包括一次调制中偏振片的取向和1/4波片的快轴角度。
  22. 如权利要求21所述的起偏器的优化方法，其特征在于，所述总电势能的计算公式为：
    Figure PCTCN2022106351-appb-100023
    其中，N表示起偏器进行了N次调制，N≥4；N次调制的N个偏振态对应邦加球上N个所述位置点，即对应N个点电荷；E表示N个点电荷的总电势能；r i、r j分别表示第i个点电荷相对于邦加球球心的位置矢量、第j个点电荷相对于邦加球球心的位置矢量。
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