A three-polarization modulation type Mueller matrix polarization system and parameter correction method

Abstract

This application belongs to the field of precision optical measurement, specifically disclosing a three-photoelastic modulation type Mueller matrix polarization system and its parameter correction method. In this application, the polarizing arm includes a first photoelastic modulator and a second photoelastic modulator, while the analyzing arm contains only a third photoelastic modulator. The three photoelastic modulators have different modulation frequencies. For the optical path after the third photoelastic modulator, a beam splitter divides the optical signal into two sub-beams for separate polarization analysis. By controlling the azimuth angles of the analyzers in the two split paths, two different three-photoelastic azimuth angle polarization system configurations are achieved. The measured two sets of 12 Mueller matrix elements are combined into a complete Mueller matrix element, thus achieving the measurement of the complete Mueller matrix element in a single measurement. This application, by combining three photoelastics with different modulation frequencies and the splitting principle, achieves high-speed acquisition of the entire Mueller matrix of a sample in a single measurement, filling the gap in mid-infrared high-speed Mueller matrix ellipsometers.

Description

Technical Field

[0001] This application belongs to the field of precision optical measurement, and more specifically, relates to a three-photoelastic modulation type Mueller matrix polarization system and parameter correction method. Background Technology

[0002] A Mueller matrix polarimeter refers to an instrument that can measure the full Mueller matrix information of a sample in a single measurement, enabling the characterization of more complex optical properties such as anisotropy and depolarization. Photoelastic modulators, with their advantages of simple modulation, wide spectral coverage, and good system stability, are a crucial means of realizing high-speed Mueller matrix polarimeters. Generally, by configuring four photoelastic modulators of different frequencies, the full Mueller matrix of a sample under corresponding wavelength and incident angle conditions can be obtained in a single measurement. For example, patent CN119413729A includes a polarizer, four photoelastic modulators with different modulation frequencies, and an analyzer. However, because only three different modulation frequencies of commercially available photoelastic modulators are available in the mid-infrared band, this Mueller matrix polarization system is difficult to implement in engineering applications for the mid-infrared band.

[0003] In addition, some scholars have achieved the measurement of the entire Mueller matrix through beam splitting. However, this method involves complex optical paths, and traditional calibration methods are based on a specific system model with a defined configuration. This involves extracting frequency domain components related to system parameters and then calibrating the measurement system based on the relationship between these frequency components and system parameters. The azimuth error of the calibrated polarization element is used to further adjust the installation error of the polarization element, requiring a precise rotary displacement stage and stringent requirements on the system model of key components. Therefore, system calibration is difficult, resulting in low measurement accuracy and significant limitations. Especially for the mid-infrared band, the polarization characteristics of commercially available polarization elements are often not ideal, making system calibration even more complex, and traditional calibration methods have poor accuracy.

[0004] Therefore, for the mid-infrared band, there is an urgent need for a method to implement a Mueller matrix ellipsometer containing only three photoelastics of different frequencies. Furthermore, a relatively simple calibration method is proposed for this system, which can achieve accurate calibration of this complex system and thus enable rapid and accurate measurement of the Mueller matrix in the mid-infrared band. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this application aims to provide a three-photoelastic modulation Mueller matrix polarization system and parameter correction method, which aims to solve the problems of existing technologies such as the lack of photoelastic modulation Mueller matrix ellipsometers in certain bands (e.g., mid-infrared), the cumbersome calibration steps of model-based calibration methods, the stringent requirements on the polarization characteristic models of components, and the poor calibration accuracy.

[0006] To achieve the above objectives, in a first aspect, this application provides a three-photoelastic modulation type Mueller matrix polarization system. The Mueller matrix polarization system supports mid-infrared band measurements and, along its optical path, sequentially comprises a light source module, a polarizing arm, a sample position, an analyzer arm, and a detection module. The polarizing arm sequentially comprises a polarizer 103, a first photoelastic modulator 104, and a second photoelastic modulator 105. The analyzer arm includes a third photoelastic modulator 107, a non-polarizing beam splitter 108, a first analyzer 109, and a second analyzer 112. The non-polarizing beam splitter 108 splits the optical path after the third photoelastic modulator 107 into two optical paths with the same polarization state; one path enters the first analyzer 109 for polarization analysis, and the other path enters the second analyzer 112 for polarization analysis. The three photoelastic modulators have different modulation frequencies, and the fast axis azimuth angle of the two analyzers deviates by 45°.

[0007] Preferably, the polarizer is a mid-infrared grating polarizer.

[0008] Preferably, the three photoelastic modulators are photoelastic modulators made of zinc selenide crystal material.

[0009] Preferably, the polarization arm and the polarization detector arm are distributed on both sides of the sample position and mounted on the rotating base plate, which can switch between the transmission and reflection systems.

[0010] Preferably, the detection module includes a first converging lens 110, a first detector 111, a second converging lens 113, and a second detector 114; the optical signal after the first analyzer 109 is focused by the first converging lens 110 onto the first detector 111; the optical signal after the second analyzer 112 is focused by the second converging lens 113 onto the second detector 114.

[0011] Preferably, it further includes: a data acquisition module; the data acquisition module includes a high-speed data acquisition card and a memory, used to synchronously acquire the light intensity signals of the two detectors and store them in different locations for independent processing.

[0012] To achieve the above objectives, in a second aspect, this application provides a parameter calibration method for a three-photoelastic modulation Mueller matrix polarization system as described in the first aspect, comprising: First, conducting a polarization experiment, simultaneously acquiring experimental light intensity signals from two detectors for each measurement, establishing a calculation model of the light intensity signal with respect to the analyzer arm basis vector, the light intensity projection matrix, and the polarizer arm basis vector, obtaining the light intensity and its calculation model based on the polarization experiment, calibrating the photoelastic parameters in the analyzer arm basis vector and the polarizer arm basis vector using a nonlinear regression method, and obtaining two light intensity projection matrices; Second, combining the two obtained light intensity projection matrices to obtain the overall light intensity projection matrix of the polarization system, selecting multiple reference samples for measurement according to the requirements of the eigenvalue calibration method, solving for the modulation matrix and analysis matrix using the eigenvalue calibration method, realizing the calibration of the polarization element azimuth angle and the static delay information of the photoelastic modulator, and completing the overall calibration of the polarization system; Finally, measuring the light intensity of the sample to be tested, obtaining the overall light intensity projection matrix of the sample to be tested using the same method as above, and combining the results of the above eigenvalue calibration, solving for the Mueller matrix of the sample to be tested using matrix calculation or optimization methods.

[0013] Preferably, the calculation model for the light intensity signal and the calculation model for the light intensity projection matrix are as follows:

[0014]

[0015]

[0016]

[0017] in, , These are the light intensity signals detected by the two detectors, respectively. For detecting the basis vectors of the bias arm; Let these be the basis vectors of the starting arm; These are the light intensity projection matrices corresponding to the two light intensity signals; These are the analysis matrices corresponding to the two optical paths of the polarizer arm; This is the modulation matrix for the off-arm; The Mueller matrix of the sample, This represents the dynamic delay component in the phase delay of the photoelastic modulator. The subscripts 1, 2, and 3 represent the designation of the photoelastic modulator. These represent the peak delay, frequency, and initial phase of the photoelastic modulator, respectively, and their accurate values ​​are obtained through a nonlinear regression method. Indicates time.

[0018] Preferably, the plurality of reference samples are any of the following combinations: air, two polarizers at different azimuth angles, and a waveplate at one azimuth angle; air, waveplates at multiple azimuth angles, and a polarizer at one azimuth angle; air, waveplates at multiple azimuth angles, and an isotropic thin film; wherein the Mueller matrix of air is a strict identity matrix, and the Mueller matrices of the reference samples other than air are... As shown below:

[0019] in, All are quantities to be calibrated, and the solution is obtained based on their relationship with eigenvalues. Using the azimuth angle of the polarizer or waveplate in the reference sample, the solution is obtained by maximizing the ratio of the reference frame to the corresponding eigenvalue. It is the rotation matrix of the polarization element relative to the reference coordinate system.

[0020] Preferably, the analysis matrix A corresponding to the overall polarizer arm and the modulation matrix of the polarizer arm are obtained by combining the eigenvalue calibration solution. It can be directly used to measure the Mueller matrix of the sample under test:

[0021] in, The Mueller matrix of the sample to be tested is obtained. and The matrix A obtained for eigenvalue calibration and , This represents the light intensity projection matrix of the sample to be tested.

[0022] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art: (1) This application proposes a three-photoelastic modulation type Mueller matrix polarization system. Its polarizing arm contains two photoelastics, namely the first photoelastic modulator and the second photoelastic modulator, and the modulation frequencies of the two photoelastic modulators are different. Its analyzing arm contains only one photoelastic, namely the third photoelastic modulator, and its modulation frequency should be different from that of the first and second photoelastic modulators. The optical path after the third photoelastic modulator of the analyzing arm is split into two optical paths by a non-polarizing beam splitter. Each optical path is equipped with an analyzer and detector with different azimuth angles, thus constructing two system optical paths with different azimuth angle configurations to realize the measurement of the full Mueller matrix. In this process, the non-polarizing beam splitter splits the optical signal into two sub-beams for separate polarization analysis. By controlling the different azimuth angles of the analyzers in the two split paths, two different three-photoelastic azimuth angle polarization system configurations are realized. The two measured 12 Mueller matrix elements are combined into a complete Mueller matrix element, thereby realizing the measurement of the complete Mueller matrix element in a single measurement. This application combines three photoelastic modulators with different modulation frequencies and the principle of splitting to achieve high-speed acquisition of the entire Mueller matrix of a sample in a single measurement. This breaks the current situation where traditional three-photoelastic modulators cannot measure the entire Mueller matrix, providing a new principle for the realization of mid-infrared Mueller matrix ellipsometers. It is expected to fill the gap in mid-infrared high-speed Mueller matrix ellipsometers. The structure is relatively simple, with no moving parts, and it acquires richer measurement information, which can effectively improve the measurement accuracy and stability of the system.

[0023] (2) This application proposes a parameter calibration method for a three-photoelastic modulation type Mueller matrix polarization system. Combined with eigenvalue calibration, it eliminates the need to consider the coupling between parameters in the modulation matrix and analysis matrix, treating them as a whole to achieve system calibration, reducing the difficulty of system calibration, and also reducing the stringent requirements on the polarization element system model, such as the extinction ratio of the polarizer; and only a few calibration samples need to be measured. Compared with traditional methods, it does not require knowing the accurate information of the samples, and the calculation results are more accurate and robust; at the same time, it proposes more reference sample combinations, further reducing the requirements for reference samples and enhancing the operability of this method; by measuring a series of reference samples, the in-situ calibration of the system can be achieved, and it is a complete calibration, including all system parameters in the system. It is applicable to any effective azimuth angle configuration, and there is no need for further feedback to adjust the azimuth angle error of the polarization element, reducing the alignment requirements of the optical path construction. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the structure of a three-photoelastic modulation type Mueller matrix polarization system provided in an embodiment of this application.

[0025] Figure 2 This is a flowchart of a parameter calibration method for a three-photoelastic modulation type Mueller matrix polarization system provided in an embodiment of this application.

[0026] Figure 3This is a comparison result between the Mueller matrix elements of the multi-azimuth angle sample provided in the embodiments of this application and the reference value.

[0027] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein: 101-Light source, 102-Collimating lens, 103-Polarizer, 104-First photoelastic modulator, 105-Second photoelastic modulator, 106-Sample position, 107-Third photoelastic modulator, 108-Unpolarized beam splitter, 109-First analyzer, 110-First converging lens, 111-First detector, 112-Second analyzer, 113-Second converging lens, 114-Second detector. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0029] The embodiments of this application are described below with reference to the accompanying drawings.

[0030] like Figure 1 As shown, this application proposes a three-photoelastic modulation type Mueller matrix polarization system, including: a light source 101, a collimating lens 102, a polarizer 103, a first photoelastic modulator 104, a second photoelastic modulator 105, a sample position 106, a third photoelastic modulator 107, a non-polarizing beam splitter 108, a first analyzer 109, a first converging lens 110, a first detector 111, a second analyzer 112, a second converging lens 113, and a second detector 114. Wherein, The light source 101 and collimating lens 102 constitute a light source module, which is used to provide a parallel illumination beam to the Mueller matrix polarization system. Among them, the light source 101 is a single-wavelength laser source or a wavelength-tunable laser source; for the mid-infrared band, a mid-infrared quantum cascade laser is selected.

[0031] The polarizer 103, the first photoelastic modulator 104, and the second photoelastic modulator 105 form a polarizing arm, which is used to modulate the polarization state of the beam incident on the sample.

[0032] The third photoelastic modulator 107, the non-polarizing beam splitter 108, the first polarizer 109, and the second polarizer 112 form a polarization analyzer arm, which is used to analyze the polarization state of the light emitted after passing through the sample.

[0033] It should be noted that the three photoelastic modulators 104, 105, and 107 are driven by their respective controllers and belong to different modulation frequencies; their corresponding fast axis azimuth angles exhibit differences to ensure that the overall system matrix of their corresponding polarizer and analyzer arms has a rank of 4 and a good condition number, rather than being limited to a specific azimuth angle configuration.

[0034] Preferably, the non-polarizing beam splitter is selected with a 50:50 splitting ratio. The fast axis azimuth angles of the analyzers on the two optical paths exhibit differences, and the azimuth angle deviation between the two analyzers should be controlled at approximately 45° to ensure that the corresponding two sets of azimuth angle configurations can measure all elements of the Mueller matrix of the sample. By constructing two system optical paths with different azimuth angle configurations through the beam splitter, millisecond-level measurement of the full Mueller matrix at a single wavelength can be achieved.

[0035] Preferably, the polarizer is a mid-infrared grating polarizer, and the photoelastic modulator is a photoelastic modulator made of zinc selenide crystal material.

[0036] Preferably, the detection module includes: a first converging lens 110, a first detector 111, a second converging lens 113, and a second detector 114, wherein the optical signal after the first analyzer 109 is focused by the first converging lens 110 onto the first detector 111, and the optical signal after the second analyzer 112 is focused by the second converging lens 113 onto the second detector 114.

[0037] The Mueller matrix polarization system also includes a data acquisition module, which includes a high-speed data acquisition card and a memory, used to acquire light intensity data of different wavelengths in conjunction with the light source module and store them in different locations for independent processing, thereby realizing multi-wavelength measurement.

[0038] Preferably, the polarization arm and the polarization detector are distributed on both sides of the sample position 106 and mounted on the rotating base plate, which can switch between the transmission and reflection systems.

[0039] The working process of the Mueller matrix polarization system is as follows: The laser beam emitted by the light source module enters the polarizing arm in the form of parallel light, is modulated, passes through the sample, and is transmitted or reflected to the photoelastic modulator of the analyzer arm. Then, it is split into two beams by the non-polarizing beam splitter, passes through the analyzers at different azimuth angles, and is focused onto the detector by their respective converging mirror groups. The two detectors are synchronously acquired through different channels of the high-speed data acquisition card.

[0040] The oblique incidence system is based on the direct-through system. By adjusting the angle between the polarizing arm and the polarizing arm, the attitude of the sample position is adjusted in a coordinated manner. Its calibration method adds an isotropic thin film sample to the measurement and calibration of the direct-through system. Therefore, when calibrating, taking the transmission type as an example, its calibration principle is also applicable to the reflection type system.

[0041] like Figure 2 As shown, this application proposes a parameter calibration method for a three-photoelastic modulation type Mueller matrix polarization system, including: S1. Based on the polarization system, a polarization experiment is conducted. The experimental light intensity signals of the two detectors are collected synchronously for each measurement. Corresponding basis vectors are introduced for the analyzer arm and the polarizer arm. A calculation model of the light intensity signal with respect to the analyzer arm basis vector, the light intensity projection matrix, and the polarizer arm basis vector is constructed. The photoelastic parameters in the analyzer arm basis vector and the polarizer arm basis vector are calibrated by nonlinear regression method, and two light intensity projection matrices are obtained.

[0042] Specifically, the basis vectors of the polarization arm and the polarization detector arm are established by the sine and cosine functions of the corresponding dynamic phase delay of the photoelastic modulator and their product, which include the relevant parameters of the corresponding photoelastic modulator, namely, the photoelastic modulation frequency, the photoelastic peak delay, and the initial phase.

[0043] The calculation model for the two light intensity signals consists of the multiplication of the introduced basis vectors and the light intensity projection matrix. While performing light intensity projection through optimization, the relevant parameters of the aforementioned photoelastic modulator and the light intensity projection matrix are used as quantities to be optimized. The relevant parameters of the aforementioned photoelastic modulator are then calibrated, and the light intensity projection matrix is ​​obtained.

[0044] S2. Combine the two acquired light intensity projection matrices to obtain the overall light intensity projection matrix of the system. According to the requirements of the eigenvalue calibration method, select multiple reference samples for measurement. Convert the azimuth information and photoelastic static delay information to be calibrated on the polarizing arm and analyzer arm into the corresponding modulation matrix and analysis matrix. Solve the above modulation matrix and analysis matrix using the eigenvalue calibration method to realize the calibration of the polarization element azimuth and photoelastic modulator static delay information, and complete the overall calibration of the polarization system.

[0045] The plurality of reference samples includes several combinations, such as air, two polarizers at different azimuth angles and a waveplate at an azimuth angle; air, waveplates at multiple azimuth angles and a polarizer at an azimuth angle; air, waveplates at multiple azimuth angles and an isotropic thin film. In one illustrated embodiment, the reference sample includes: air, polarizers, waveplates and an isotropic thin film. The polarization system is a transmission system, therefore the reference sample combination includes air, a polarizer with an azimuth angle of 0°, a polarizer with an azimuth angle of approximately 90° and a quarter-waveplate with an azimuth angle of approximately 30°.

[0046] S3. Measure the light intensity of the sample to be tested, and obtain the overall light intensity projection matrix of the sample to be tested using the same method as above. Combine the results of the above eigenvalue calibration, and solve the Mueller matrix of the sample to be tested by matrix calculation or optimization methods.

[0047] In step S1, the sample is placed at sample position 106, aligned with the optical path, and the light source and detector are turned on. The three photoelastic modulators 104, 105, and 107 are also turned on. The peak delay of the three photoelastic modulators is set to an appropriate value. The high-speed acquisition card is controlled to synchronously acquire the light intensity signals acquired by the two detectors 111 and 114. It is important to select an appropriate sampling frequency to satisfy the Nyquist sampling theorem to ensure that the acquired signal is not distorted. At the same time, it is necessary to ensure a sufficient number of data points to improve the success rate of subsequent light intensity fitting and reduce the impact of random noise on the calibration results.

[0048] For a single measurement sample, two detectors acquire the measured light intensity signal. and The theoretical calculation model is as follows: (1) (2) in, The Stokes vector representing the light emitted from the light source. These are the Mueller matrices for the polarizer, sample, first analyzer, and second analyzer, respectively. The Mueller matrix represents a phase delay unit with a phase delay of δ. The azimuth angle of the polarizer. and These are the azimuth angles of the first and second analyzers, respectively. and (k=1,2,3) represent the nth, 2nd, and 3rd respectively. The azimuth angle and phase delay of each photoelastic modulator, where the phase delay of the photoelastic modulator is: , where F, , , The parameters are, in order, the peak delay, frequency, initial phase, and static delay of the photoelastic modulator. Simultaneously, suitable basis vectors need to be selected; the bias arm basis vector is... The basis vectors of the two optical paths of the polarizer arm are The polarization arm basis vector and the polarization starting arm basis vector are specifically established based on the system model of the polarization starting arm and the polarization arm, i.e., formulas (1) and (2), by selecting the sine and cosine functions of the dynamic delay part of the phase delay of the included photoelastic modulator and their product. For each time , It is a 9×1 vector. Given a 1×3 vector, a 3×9 light intensity projection matrix is ​​obtained from the time-domain continuously modulated light intensity signal. : (3) (4) (5) (6) in, , These are the light intensity signals detected by the two detectors, respectively. For detecting the basis vectors of the bias arm; Let these be the basis vectors of the starting arm; , indicates the dynamic delay component in the phase delay of a photoelastic modulator, and the subscript indicates the designation of the photoelastic modulator; F, , The parameters are, in order, the peak delay, frequency, and initial phase of the photoelastic modulator; These are the light intensity projection matrices corresponding to the two light intensity signals, both of which are 3×9 matrices; These are the analysis matrices corresponding to the two optical paths of the analyzer arm, both of which are 3×4 matrices; W is the modulation matrix of the polarizer arm, which is a 4×9 matrix; Let be the Mueller matrix of the sample. While performing light intensity projection through optimization, the relevant parameters of the aforementioned photoelastic modulator and the light intensity projection matrix are used as quantities to be optimized. The relevant parameters of the aforementioned photoelastic modulator are then calibrated, and the light intensity projection matrix is ​​obtained.

[0049] In S2, the combination of the two light intensity projection matrices is for the system configuration of the three-photon missile. The combination method of the light intensity projection matrices and their relationship with the modulation matrix and analysis matrix are shown in the following formula: (7) in, The analysis matrix corresponding to the entire check arm is a 6×4 matrix. The overall light intensity projection matrix is ​​a 6×9 matrix. Based on the relationships described above... Matrix and The matrices all have a rank of 4, therefore calibration can be performed using the eigenvalue calibration method, which is an extended eigenvalue solution for overdetermined systems. The reference sample combination consists of air, a polarizer with an azimuth angle of 0°, a polarizer with an azimuth angle of approximately 90°, and a quarter-wave plate with an azimuth angle of approximately 30°. During the eigenvalue calibration process, the Mueller matrix of air is considered the identity matrix, and the Mueller matrices of the other reference samples are modeled as follows: (8) Where τ, a, b, c, and θ are all quantities to be calibrated, θ is its azimuth angle, R(·) is a 4×4 rotation matrix, and τ, a, b, and c are all solved by the relationship between them and the eigenvalues ​​of the transition matrix.

[0050] The above model further reduces the requirements for the polarization model of the reference sample, such as the extinction ratio of the reference sample polarizer, and does not require its system model to be a strictly linear polarizer model. It is important to note that the eigenvalue calibrations at different wavelengths are independent and do not interfere with each other. The transition matrix is ​​obtained by processing the light intensity projection matrices of multiple calibration samples.

[0051] In S3, the combination of the light intensity projection matrix of the sample under test is consistent with the above combination method, combined with the eigenvalue calibration solution obtained in step S2. Matrix and The matrix can be directly used to measure the Mueller matrix of the sample under test. Specifically, it is shown in the following formula: (9) in, The Mueller matrix of the sample to be tested is obtained. and The modulation matrix and analysis matrix obtained by eigenvalue calibration in step S2 and , The light intensity projection matrix of the sample to be tested is obtained by combining the light intensity projection in step S1 and the matrix in step S2.

[0052] Example This embodiment is a transmission-type three-photonic modulated Mueller matrix ellipsometer, and the system optical path is as follows: Figure 1 As shown, the azimuth angle configuration uses the azimuth angle of the polarizer as the reference zero degree, and the azimuth angles of other polarization elements are all relative to the polarizer. It should be noted that the configuration in this example is only one valid configuration, and the azimuth angle configuration is not limited to this example. The specific system configuration in this embodiment is shown in Table 1.

[0053] Table 1 System Configuration Table

[0054] The specific calibration and measurement process for the aforementioned three-photonic modulation type Mueller matrix ellipsometer is as follows: By opening the three photoelastic modulators as described above, and connecting the two detectors to different channels of the same high-speed acquisition card, the synchronous acquisition of two light intensity signals can be achieved. The signals are measured separately for air, a polarizer with an azimuth angle of 0°, a polarizer with an azimuth angle of approximately 90°, and a quarter-wave plate with an azimuth angle of approximately 30°.

[0055] Introducing the basis vectors as shown in formulas (5) and (6), where the initial value of the peak delay is selected from the reference value on the photoelastic modulator controller, the initial values ​​of the frequency and initial phase are obtained from the reference signal of the photoelastic, and the initial value of the light intensity projection matrix is ​​a randomly generated 3×9 real matrix. Then, by fitting the measured light intensity of the two detectors according to formulas (3) and (4), the corresponding light intensity projection matrix can be obtained.

[0056] The light intensity projection matrix obtained above is combined according to formula (7), and the modulation matrix and analysis matrix are obtained by eigenvalue calibration method, thus realizing system calibration, namely the system azimuth information and the static delay of the photoelastic modulator.

[0057] To verify the accuracy of the calibration results, a multi-azimuth polarizer (a non-ideal linear polarizer with an extinction ratio of 100:1) and a 1 / 3 wave plate were selected as the test samples for simulation verification. A random fluctuation of 0.05 (26dB noise) was added to the theoretical light intensity generated based on formulas (1) and (2). Similarly, the light intensity projection matrix of the test sample was obtained first by nonlinear regression. With the modulation matrix and analysis matrix already calibrated, the Mueller matrix of the test sample was solved analytically. Figure 3 The comparison between the Mueller matrix of the sample to be tested and the reference value is based on the calibration method of this application. Taking the configuration in Table 1 as an example, with 26dB noise interference added to the probe light intensity, the measurement error is within 0.7%.

[0058] In this application, the terms "first" and "second," etc., are used to distinguish different objects, not to describe a specific order of objects. For example, "first response message" and "second response message," etc., are used to distinguish different response messages, not to describe a specific order of response messages.

[0059] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0060] In the description of the embodiments in this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, and multiple elements means two or more elements. It should be understood that expressions such as "comprising" and "may include" used in this application indicate the existence of the disclosed functions, operations, or constituent elements, and do not limit one or more additional functions, operations, and constituent elements. In this application, terms such as "comprising" and / or "having" can be interpreted as indicating a specific characteristic, number, operation, constituent element, component, or combination thereof, but should not be interpreted as excluding the existence or possibility of adding one or more other characteristics, numbers, operations, constituent elements, components, or combinations thereof.

[0061] Furthermore, in this application, the expression "and / or" includes any and all combinations of the associated listed words. For example, the expression "A and / or B" may include A, may include B, or may include both A and B.

[0062] In the description of the embodiments of this application, it should be noted that, unless otherwise explicitly specified and limited, the term "connection" should be interpreted broadly. For example, "connection" can be a detachable connection or a non-detachable connection; it can be a direct connection or an indirect connection through an intermediate medium. "Fixed connection" refers to a connection where the relative positional relationship remains unchanged after connection. "Rotary connection" refers to a connection where the components can rotate relative to each other after connection. "Sliding connection" refers to a connection where the components can slide relative to each other after connection. The directional terms mentioned in the embodiments of this application, such as "top," "bottom," "inner," "outer," "left," and "right," are only for reference to the directions in the accompanying drawings. Therefore, the directional terms used are for better and clearer explanation and understanding of the embodiments of this application, and are not intended to indicate or imply that the device or component referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the embodiments of this application.

[0063] Furthermore, the mathematical concepts mentioned in the embodiments of this application, such as symmetry, equality, parallelism, and perpendicularity, are limitations specific to the current technological level, rather than absolute and strict mathematical definitions. Slight deviations are permissible; approximations of symmetry, equality, parallelism, and perpendicularity are all acceptable. For example, "A and B are parallel" means that A and B are parallel or approximately parallel, and the angle between A and B can be between 0 and 10 degrees. "A and B are perpendicular" means that A and B are perpendicular or approximately perpendicular, and the angle between A and B can be between 80 and 100 degrees.

[0064] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A three-photoelastic modulation type Mueller matrix polarization system, characterized in that, The Mueller matrix polarization system supports mid-infrared measurements, and the optical path is sequentially configured with a light source module, a polarizing arm, a sample position, an analyzer arm, and a detector module; wherein, A polarizer (103), a first photoelastic modulator (104), and a second photoelastic modulator (105) are sequentially arranged along the optical path of the polarizing arm. The polarization analyzer arm includes a third photoelastic modulator (107), a non-polarizing beam splitter (108), a first polarizer (109), and a second polarizer (112); wherein, the non-polarizing beam splitter (108) splits the optical path after the third photoelastic modulator (107) into two optical paths with the same polarization state, one of which enters the first polarizer (109) for polarization analysis, and the other enters the second polarizer (112) for polarization analysis; The three photoelastic modulators have different modulation frequencies; The fast axis azimuth angle deviation between the two analyzers is 45°.

2. The three-photoelastic modulation type Mueller matrix polarization system as described in claim 1, characterized in that, The polarizer is a mid-infrared grating polarizer.

3. The three-photoelastic modulation type Mueller matrix polarization system as described in claim 1, characterized in that, The three photoelastic modulators are photoelastic modulators made of zinc selenide crystal material.

4. The three-photoelastic modulation type Mueller matrix polarization system as described in claim 1, characterized in that, The polarization arm and the polarization detector arm are located on both sides of the sample position and are mounted on the rotating base plate, allowing switching between transmission and reflection systems.

5. The three-photoelastic modulation type Mueller matrix polarization system as described in claim 1, characterized in that, The detection module includes a first converging lens (110), a first detector (111), a second converging lens (113), and a second detector (114). The optical signal after the first analyzer (109) is focused onto the first detector (111) by the first converging lens (110); The optical signal after the second analyzer (112) is focused onto the second detector (114) by the second converging lens (113).

6. The three-photonic modulation type Mueller matrix polarization system as described in any one of claims 1 to 5, characterized in that, Also includes: Data acquisition module; The data acquisition module includes a high-speed data acquisition card and a memory, used to synchronously acquire the light intensity signals of the two detectors and store them in different locations for independent processing.

7. A parameter calibration method for a three-photonic modulation type Mueller matrix polarization system as described in any one of claims 1 to 6, characterized in that, include: First, a polarization experiment is conducted. Experimental light intensity signals from two detectors are collected simultaneously for each measurement. A calculation model of the light intensity signal with respect to the polarizer arm basis vector, the light intensity projection matrix, and the polarizer arm basis vector is established. Based on the polarization experiment, the light intensity and its calculation model are obtained. The photoelastic parameters in the polarizer arm basis vector and the polarizer arm basis vector are calibrated using a nonlinear regression method, and two light intensity projection matrices are obtained. Secondly, the two obtained light intensity projection matrices are combined to obtain the overall light intensity projection matrix of the polarization system. According to the requirements of the eigenvalue calibration method, multiple reference samples are selected for measurement. The modulation matrix and analysis matrix are solved by the eigenvalue calibration method to calibrate the polarization element azimuth angle and the static delay information of the photoelastic modulator, and complete the overall calibration of the polarization system. Finally, the light intensity of the sample under test is measured, and the overall light intensity projection matrix of the sample under test is obtained using the same method as above. Combined with the results of the above eigenvalue calibration, the Mueller matrix of the sample under test is solved by matrix calculation or optimization methods.

8. The parameter calibration method as described in claim 7, characterized in that, The specific calculation models for light intensity signals and light intensity projection matrices are as follows: in, , These are the light intensity signals detected by the two detectors, respectively. For detecting the basis vectors of the bias arm; Let these be the basis vectors of the starting arm; These are the light intensity projection matrices corresponding to the two light intensity signals; These are the analysis matrices corresponding to the two optical paths of the polarizer arm; This is the modulation matrix for the off-arm; The Mueller matrix of the sample, This represents the dynamic delay component in the phase delay of the photoelastic modulator. The subscripts 1, 2, and 3 represent the designation of the photoelastic modulator. These represent the peak delay, frequency, and initial phase of the photoelastic modulator, respectively, and their accurate values ​​are obtained through a nonlinear regression method. Indicates time.

9. The parameter calibration method as described in claim 7, characterized in that, The plurality of reference samples are any of the following combinations: Air, two polarizers at different azimuth angles, and a waveplate at one azimuth angle; Air, waveplates with multiple azimuth angles, and a polarizer with one azimuth angle; Air, waveplates at multiple azimuth angles, and an isotropic thin film; The Mueller matrix for air is a strict identity matrix, while the Mueller matrix for the reference sample other than air is... As shown below: in, All of these are quantities to be calibrated, and the solution is obtained based on their relationship with eigenvalues. Using the azimuth angle of the polarizer or waveplate in the reference sample, the solution is obtained by maximizing the ratio of the reference frame to the corresponding eigenvalue. It is the rotation matrix of the polarization element relative to the reference coordinate system.

10. The parameter calibration method as described in claim 7, characterized in that, The analysis matrix A and the modulation matrix of the polarizer arm are obtained by combining eigenvalue calibration. It can be directly used to measure the Mueller matrix of the sample under test: in, The Mueller matrix of the sample to be tested is obtained. and The matrix A obtained for eigenvalue calibration and , This represents the light intensity projection matrix of the sample to be tested.

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