High-speed high-precision four-photoelastic modulation closed-loop control Mueller matrix measurement device and method

Abstract

The invention belongs to the technical field of photoelastic modulation, and particularly relates to a high-speed and high-precision four-photoelastic modulation closed-loop control Mueller matrix measuring device and method, a first photoelastic modulator is arranged in the light path direction of a polarizer, a second photoelastic modulator is arranged in the light path direction of the first photoelastic modulator, and a third photoelastic modulator is arranged in the light path direction of the second photoelastic modulator. The Muller matrix sample to be measured is arranged in the light path direction of the second photoelastic modulator, the third photoelastic modulator is arranged in the light path direction of the Muller matrix sample to be measured, the fourth photoelastic modulator is arranged in the light path direction of the third photoelastic modulator, the polarization analyzer is arranged in the light path direction of the fourth photoelastic modulator, and the polarization analyzer is arranged in the light path direction of the second photoelastic modulator. And the detector is arranged in the light path direction of the polarization analyzer. According to the invention, the four photoelastic modulators are adopted for modulation, the phase delay amplitudes of the four photoelastic modulators are obtained in real time through phase locking of different sum frequency and difference frequency signals of the four photoelastic modulators and the amplitude ratio of different frequency signals, and the influence of light intensity fluctuation of a light source is eliminated.

Description

Technical Field

[0001] The present invention belongs to the technical field of photoelastic modulation, and in particular relates to a high-speed and high-precision four-photoelastic modulation closed-loop control Mueller matrix measurement device and method. Background Art

[0002] With the development of technology, the high-speed and high-precision measurement of optical Muller matrix has a wide range of applications in many fields, such as analysis and design of various polarization devices, such as polarizers, polarization beam splitters and polarization rotators. By studying and mastering the Muller matrix of polarization devices, we can have a deeper understanding and application of polarization light phenomena, and promote the development and application of polarization light technology in optics, communications and other fields.

[0003] Common Muller matrix measurement methods include double rotating wave plate method, phase modulation method, multiple rotation method, ball trajectory measurement method, photoelastic modulation, etc. The double rotating wave plate method involves fixing the polarizing film before and after the sample. The wave plates are rotated simultaneously at an angle of 1:5, and then the Muller matrix is ​​obtained through Fourier analysis. However, the manual adjustment of the azimuth angle of the wave plate leads to large errors and long measurement time. The phase modulation method uses two phase modulators to perform four measurements to obtain the Muller matrix, but the sample needs to be coated to eliminate stray light interference, and the number of measurements is large and easily affected by vibration. In the multiple rotation method, the polarizers and wave plates before and after the sample can be rotated arbitrarily, and the Muller matrix is ​​obtained by solving the linear equations after multiple measurements. The Poincaré sphere trajectory measurement method links the Muller matrix with its trajectory on the Poincaré sphere, and obtains the Muller matrix based on the positional relationship between the polarization states of the input and output light waves on the Poincaré sphere. However, the phase difference of the linear birefringent optical fiber is easily affected by the external environment, thereby introducing measurement errors.

[0004] Photoelastic modulator (PEM) is a polarization modulation device with a high phase of the photoelastic effect of optical refractive crystal materials, operating at a resonant frequency state. Its advantages such as no mechanical vibration, large incident angle, high modulation frequency, low loss, and wide band range (from vacuum ultraviolet to far infrared) have played a positive role in promoting the field of optical polarization. It is also widely used in the field of fast and high-precision Muller matrix detection. The "Miller Matrix Measurement Technology Based on Single Photoelastic Modulator [P]" was published in the Journal of Optics. In view of the shortcomings of the existing Muller matrix measurement methods, a Muller matrix measurement technology based on a single photoelastic modulator was proposed. This technology calibrates and measures the system parameters through a two-step calibration method, and uses an optimization algorithm to calculate the Muller matrix of the sample to be measured. Experimental results show that this method can achieve high-precision phase delay measurement and fast axis azimuth measurement; Acta Physica Sinica published "Large-area measurement of nanostructure geometric parameters based on Muller matrix imaging ellipsometer [P]", introducing a Muller matrix imaging ellipsometer (MMIE) that combines traditional scattering technology and imaging technology for fast, large-scale, and high-precision measurement of nanostructure geometric parameters. The article mentioned that a spectral Muller matrix imaging ellipsometer was developed by replacing the complementary metal oxide semiconductor (CMOS) camera with a spectrometer and adding a telecentric lens to the polarization state analysis arm. The instrument is capable of measuring typical silicon grating templates and reconstructing three-dimensional microscopic geometric parameter maps over a large range. The measurement results show that the instrument's Muller matrix element measurement accuracy is better than 0.05 in the full image and full spectral range. However, the above method cannot simultaneously meet the requirements of high-speed, high-precision, and high-stability measurement, the ability to measure all 16 Muller matrix elements in a single shot, and the complete polarization characteristics of the sample. Summary of the invention

[0005] In view of the technical problem that the above method cannot simultaneously meet the requirements of high-speed, high-precision, high-stability measurement, and the ability to measure all 16 Muller matrix elements and the complete polarization characteristics of the sample in a single time, the present invention provides a high-speed, high-precision four-photoelastic modulation closed-loop control Mueller matrix measurement device and method, which uses four photoelastic modulators for modulation, and by phase-locking the different sum-frequency and difference-frequency signals of the four photoelastic modulators, and using the amplitude ratio of different frequency signals, the phase delay amplitude of the four photoelastic modulators is obtained in real time, and the influence of light source intensity fluctuation is eliminated. By using the optical characteristics and Bessel function properties of the photoelastic modulator, experimental measurements and signal amplitude component analysis are performed on the photoelastic modulators with different driving frequencies to accurately calculate the phase delay amplitude of the photoelastic modulator and the 16 elements in the Muller matrix. The system can realize high-speed and high-precision closed-loop control measurement of the Muller matrix.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A high-speed and high-precision four-photoelastic modulation closed-loop control Mueller matrix measurement device includes a light source, a polarizer, a first photoelastic modulator, a second photoelastic modulator, a Muller matrix sample to be measured, a third photoelastic modulator, a fourth photoelastic modulator, an analyzer, and a detector. The polarizer is arranged in the optical path direction of the light source, the first photoelastic modulator is arranged in the optical path direction of the polarizer, the second photoelastic modulator is arranged in the optical path direction of the first photoelastic modulator, the Muller matrix sample to be measured is arranged in the optical path direction of the second photoelastic modulator, the third photoelastic modulator is arranged in the optical path direction of the Muller matrix sample to be measured, the fourth photoelastic modulator is arranged in the optical path direction of the third photoelastic modulator, the analyzer is arranged in the optical path direction of the fourth photoelastic modulator, and the detector is arranged in the optical path direction of the analyzer.

[0008] It also includes a photoelastic drive control and a multi-channel digital phase-locked amplifier circuit, and a computer. The photoelastic drive control and the multi-channel digital phase-locked amplifier circuit are respectively connected to the first photoelastic modulator, the second photoelastic modulator, the third photoelastic modulator, the fourth photoelastic modulator, and the detector. The photoelastic drive control and the multi-channel digital phase-locked amplifier circuit are electrically connected to the computer.

[0009] The polarizer adopts a 90° polarizer, the first photoelastic modulator adopts a 45° photoelastic modulator, the second photoelastic modulator adopts a 0° photoelastic modulator, the third photoelastic modulator adopts a 0° photoelastic modulator, the fourth photoelastic modulator adopts a 45° photoelastic modulator, and the analyzer adopts a 0° analyzer.

[0010] The high-speed and high-precision four-photoelastic modulation closed-loop control Mueller matrix measurement method includes the following steps:

[0011] S1, the light from the light source passes through the polarizer, the first photoelastic modulator, the second photoelastic modulator, the Muller matrix sample to be measured, the third photoelastic modulator, the fourth photoelastic modulator, the analyzer and the detector in sequence to form a measuring optical path;

[0012] S2, according to the frequency signals of the four photoelastic modulators provided by the photoelastic drive control and multi-channel digital phase-locked amplifier circuit, the photoelastic drive control and multi-channel digital phase-locked amplifier circuit performs phase-locked amplification on the obtained modulation signals;

[0013] S3. Finally, the phase delay amplitudes of the four photoelastic modulators are obtained in real time through computer data processing, and then the 16 elements in the Muller matrix sample to be tested are accurately obtained.

[0014] The calculation method of the frequency signals of the four photoelastic modulators in S2 is:

[0015] Stokes parameter S of the light source in The Stokes parameter S after the entire measurement optical path is modulated out for:

[0016] S out =M A M PEM4 M PEM3 M X M PEM2 M PEM1 M P S in

[0017] Among them, S in =[I in ,Q in ,U in ,V in ] T ,S out =[I out ,Q out ,U out ,V out ] T ;M P 、M X 、M A 、M PEM1 、M PEM2 、M PEM3 and M PEM4 They are the Muller matrices corresponding to the polarizer, the Muller matrix sample to be tested, the analyzer, the first photoelastic modulator, the second photoelastic modulator, the third photoelastic modulator, and the fourth photoelastic modulator:

[0018]

[0019] The modulation phase δ of the photoelastic modulator i =δ i0 sinω i t(i=1,2,3,4), δ1, δ2, δ3 and δ4 are the modulation phases of the first, second, third and fourth photoelastic modulators respectively, δ 10 ,δ 20 ,δ 30 and δ 40 are the modulation phase delay amplitudes of the first photoelastic modulator, the second photoelastic modulator, the third photoelastic modulator and the fourth photoelastic modulator respectively, and ω1=2πf1, ω2=2πf2, ω3=2πf3 and ω4=2πf4 are the modulation driving angular frequencies of the first photoelastic modulator, the second photoelastic modulator, the third photoelastic modulator and the fourth photoelastic modulator respectively.

[0020] The detector detects light intensity I out for:

[0021]

[0022] From the Bessel function expansion:

[0023]

[0024] Where m i is an odd number, n i is an even number (i=1,2,3,4;m i =1,3,5,6,7…;m i =0,2,4,6…),J x (y) is the x-th order Bessel function corresponding to y.

[0025] The method for obtaining 16 elements in the Muller matrix sample to be tested in S3 is:

[0026] By M 13 With M 31 The corresponding Bessel function expansion is calculated to obtain δ 10 ,δ 20 ,δ 30 and δ 40 :

[0027]

[0028] According to the above formula, the inverse function of the ratio of different difference frequency signals and the ratio of Bessel functions, δ is calculated in real time. 10 ,δ 20 ,δ 30 and δ 40 :

[0029]

[0030] The calculated δ 10 ,δ 20 ,δ 30 and δ 40 Substitute the Bessel function expansion, select the appropriate difference frequency signal, obtain the values ​​of 16 elements in the Muller matrix sample to be tested, and obtain the generalized polarization state of the sample.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] The present invention uses four photoelastic modulators for modulation. By phase-locking the different sum-frequency and difference-frequency signals and the amplitude ratios of the different frequency signals of the four photoelastic modulators, the phase delay amplitudes of the four photoelastic modulators are obtained in real time, and the influence of the light source intensity fluctuation is eliminated. Then, the values ​​of the corresponding 16 elements in the Muller matrix are solved in turn according to the amplitudes corresponding to the difference-frequency signals. The four-photoelastic modulation technology of the present invention can obtain the sixteen Muller matrix elements of the sample at the same time at the ms level and has higher accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the implementation methods of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the implementation methods or the description of the prior art. Obviously, the drawings in the following description are only exemplary, and for ordinary technicians in this field, other implementation drawings can be derived from the provided drawings without creative work.

[0034] The structures, proportions, sizes, etc. illustrated in this specification are only used to match the contents disclosed in the specification so as to facilitate understanding and reading by persons familiar with the technology. They are not used to limit the conditions under which the present invention can be implemented, and therefore have no substantial technical significance. Any structural modification, change in proportion or adjustment of size shall still fall within the scope of the technical contents disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.

[0035] Figure 1 This is a diagram of the high-speed and high-precision four-photoelastic modulation closed-loop control Mueller matrix measurement device of the present invention;

[0036] Among them: 1 is the light source, 2 is the polarizer, 3 is the first photoelastic modulator, 4 is the second photoelastic modulator, 5 is the Muller matrix sample to be tested, 6 is the third photoelastic modulator, 7 is the fourth photoelastic modulator, 8 is the analyzer, 9 is the detector, 10 is the photoelastic drive control and multi-channel digital phase-locked amplifier circuit, and 11 is the computer. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. These descriptions are only to further illustrate the features and advantages of the present invention, rather than to limit the claims of the present invention. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0038] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0039] The terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of this application, unless otherwise specified, "plurality" means two or more.

[0040] In the description of this application, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in this application can be understood according to specific circumstances.

[0041] This embodiment provides a high-speed and high-precision four-photoelastic modulation closed-loop control Mueller matrix measurement device, such as Figure 1 As shown, the test system consists of a light source 1, a polarizer 2, a first photoelastic modulator 3, a second photoelastic modulator 4, a Muller matrix sample to be tested 5, a third photoelastic modulator 6, a fourth photoelastic modulator 7, an analyzer 8, a detector 9, a photoelastic drive control and multi-channel digital phase-locked amplifier circuit 10 and a computer 11.

[0042] Further, preferably, the polarizer 2 adopts a 90° polarizer, the first photoelastic modulator 3 adopts a 45° photoelastic modulator, the second photoelastic modulator 4 adopts a 0° photoelastic modulator, the third photoelastic modulator 6 adopts a 0° photoelastic modulator, the fourth photoelastic modulator 7 adopts a 45° photoelastic modulator, and the analyzer 8 adopts a 0° analyzer.

[0043] A high-speed and high-precision four-photoelastic modulation closed-loop control Mueller matrix measurement method, the light from the light source 1 passes through the 90° polarizer 2, the 45° first photoelastic modulator 3, the 0° second photoelastic modulator 4, the Muller matrix sample to be measured 5, the 0° third photoelastic modulator 6, the 45° fourth photoelastic modulator 7, the 0° analyzer 8 and the detector 9 in sequence to form a measurement optical path; according to the four PEM frequency signals provided by the photoelastic drive control and multi-channel digital phase-locked amplifier circuit 10, the modulation signal obtained by the photoelastic drive control and multi-channel digital phase-locked amplifier circuit 10 is phase-locked amplified, and finally the phase delay amplitude of the four PEMs is obtained in real time through data processing by the computer 11, thereby accurately obtaining the sixteen elements in the Muller matrix of the sample to be measured. Taking the x-axis method as the reference 0° direction, the specific scheme is as follows:

[0044] Stokes parameter S of source 1 in The Stokes parameter S after the entire measurement optical path is modulated out for:

[0045] S out =M A M PEM4 M PEM3 M X M PEM2 M PEM1 M P S in (1)

[0046] Among them, S in =[I in ,Q in ,U in ,V in ] T ,S out =[I out ,Q out ,U out ,V out ] T ;M P 、M X 、M A 、M PEM1 、M PEM2 、M PEM3 and M PEM4 The Muller matrices corresponding to the 90° polarizer 2, the Muller matrix sample 5, the 0° analyzer, the 45° first photoelastic modulator 3, the 0° second photoelastic modulator 4, the 0° third photoelastic modulator 6, and the 45° fourth photoelastic modulator 7 are as follows:

[0047]

[0048] The modulation phase δ of the photoelastic modulator i=δ i0 sinω i t(i=1,2,3,4) (ignoring the residual stress birefringence phase delay), we can get δ1, δ2, δ3 and δ4 are the modulation phases of PEM1, PEM2, PEM3 and PEM4 respectively, δ 10 ,δ 20 ,δ 30 and δ 40 are the modulation phase delay amplitudes of PEM1, PEM2, PEM3 and PEM4, ω1=2πf1, ω2=2πf2, ω3=2πf3 and ω4=2πf4 are the modulation drive angular frequencies of PEM1, PEM2, PEM3 and PEM4, respectively;

[0049] Since the detector can only obtain the Stokes parameter S out I out , so substituting (2) into (1) yields the detector detection light intensity I out for:

[0050]

[0051] From the Bessel function expansion:

[0052]

[0053] Expanding equation (3) by Bessel function yields the coefficients corresponding to each item in the Muller matrix. It can be seen from Table 1 that

[0054] Table 1 Coefficient table corresponding to each item in Muller matrix

[0055]

[0056]

[0057]

[0058] Where m i is an odd number, n i is an even number (i=1,2,3,4;m i =1,3,5,6,7…;m i =0,2,4,6…),J x (y) is the x-th order Bessel function corresponding to y.

[0059] Combining the formula in Table 1 and phase-locked amplification of different difference frequency signals, the 16 element values ​​in the Muller matrix and the phase delay amplitudes of the four photoelastic modulators are calculated.

[0060] Table 2M ij The difference frequency signal calculation formula table

[0061]

[0062]

[0063]

[0064] Note: The value of A in the table is M 12 -M 44 The result of multiplying the 15 elements in by their coefficients.

[0065] By M 13 With M 31 The corresponding formula can be used to calculate δ 10 ,δ 20 ,δ 30 and δ 40。

[0066]

[0067] According to formula (5), the inverse function of the ratio of different difference frequency signals and the ratio of Bessel functions, δ is calculated in real time. 10 ,δ 20 ,δ 30 and δ 40 .

[0068]

[0069] The calculated δ 10 ,δ 20 ,δ 30 and δ 40 Substitute the calculation formulas in Table 2, select the appropriate difference frequency signal, obtain the values ​​of 16 elements in the Muller matrix, and obtain the generalized polarization state of the sample.

[0070] Only the preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the above embodiments. Various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention, and various changes should be included in the protection scope of the present invention.

Claims

1. High-speed and high-precision four-photoelastic modulation closed-loop control Mueller matrix measurement device, characterized by: The invention comprises a light source (1), a polarizer (2), a first photoelastic modulator (3), a second photoelastic modulator (4), a Muller matrix sample to be tested (5), a third photoelastic modulator (6), a fourth photoelastic modulator (7), an analyzer (8), and a detector (9), wherein the polarizer (2) is arranged in the light path direction of the light source (1), the first photoelastic modulator (3) is arranged in the light path direction of the polarizer (2), the second photoelastic modulator (4) is arranged in the light path direction of the first photoelastic modulator (3), the Muller matrix sample to be tested (5) is arranged in the light path direction of the second photoelastic modulator (4), the third photoelastic modulator (6) is arranged in the light path direction of the Muller matrix sample to be tested (5), the fourth photoelastic modulator (7) is arranged in the light path direction of the third photoelastic modulator (6), the analyzer (8) is arranged in the light path direction of the fourth photoelastic modulator (7), and the detector (9) is arranged in the light path direction of the analyzer (8).

2. The high-speed and high-precision four-photoelastic modulation closed-loop control Mueller matrix measurement device according to claim 1 is characterized in that: The invention also includes a photoelastic drive control and multi-channel digital phase-locked amplifier circuit (10) and a computer (11). The photoelastic drive control and multi-channel digital phase-locked amplifier circuit (10) are respectively connected to the first photoelastic modulator (3), the second photoelastic modulator (4), the third photoelastic modulator (6), the fourth photoelastic modulator (7), and the detector (9). The photoelastic drive control and multi-channel digital phase-locked amplifier circuit (10) are electrically connected to the computer (11).

3. The high-speed and high-precision four-photoelastic modulation closed-loop control Mueller matrix measurement device according to claim 1 is characterized in that: The polarizer (2) adopts a 90° polarizer, the first photoelastic modulator (3) adopts a 45° photoelastic modulator, the second photoelastic modulator (4) adopts a 0° photoelastic modulator, the third photoelastic modulator (6) adopts a 0° photoelastic modulator, the fourth photoelastic modulator (7) adopts a 45° photoelastic modulator, and the analyzer (8) adopts a 0° analyzer.

4. High-speed and high-precision four-photoelastic modulation closed-loop control Mueller matrix measurement method, characterized in that: The following steps are involved: S1, light from a light source (1) passes through a polarizer (2), a first photoelastic modulator (3), a second photoelastic modulator (4), a Muller matrix sample to be measured (5), a third photoelastic modulator (6), a fourth photoelastic modulator (7), an analyzer (8) and a detector (9) in sequence, forming a measuring optical path; S2, according to the frequency signals of the four photoelastic modulators provided by the photoelastic drive control and multi-channel digital phase-locked amplifier circuit (10), the photoelastic drive control and multi-channel digital phase-locked amplifier circuit (10) performs phase-locked amplification on the obtained modulation signals; S3. Finally, the phase delay amplitudes of the four photoelastic modulators are obtained in real time through data processing by a computer (11), thereby accurately obtaining the 16 elements in the Muller matrix sample (5) to be tested.

5. The high-speed and high-precision four-photoelastic modulation closed-loop control Mueller matrix measurement method according to claim 4 is characterized in that: The calculation method of the frequency signals of the four photoelastic modulators in S2 is: Stokes parameter S of source (1) in The Stokes parameter S after the entire measurement optical path is modulated out for: S out =M A M PEM4 M PEM3 M X M PEM2 M PEM1 M P S in Among them, S in =[I in ,Q in ,U in ,V in ] T ,S out =[I out ,Q out ,U out ,V out ] T ;M P 、M X 、M A 、M PEM1 、M PEM2 、M PEM3 and M PEM4 The Muller matrices corresponding to the polarizer (2), the Muller matrix sample to be tested (5), the analyzer (8), the first photoelastic modulator (3), the second photoelastic modulator (4), the third photoelastic modulator (6), and the fourth photoelastic modulator (7) are: The modulation phase δ of the photoelastic modulator i =δ i0 sinω i t(i=1,2,3,4), δ1, δ2, δ3 and δ4 are the modulation phases of the first photoelastic modulator (3), the second photoelastic modulator (4), the third photoelastic modulator (6) and the fourth photoelastic modulator (7), respectively. 10 , δ 20 , δ 30 and δ 40 are the modulation phase delay amplitudes of the first photoelastic modulator (3), the second photoelastic modulator (4), the third photoelastic modulator (6) and the fourth photoelastic modulator (7), respectively; ω1=2πf1, ω2=2πf2, ω3=2πf3 and ω4=2πf4 are the modulation driving angular frequencies of the first photoelastic modulator (3), the second photoelastic modulator (4), the third photoelastic modulator (6) and the fourth photoelastic modulator (7), respectively.

6. The high-speed and high-precision four-photoelastic modulation closed-loop control Mueller matrix measurement method according to claim 4 is characterized in that: The detector (9) detects the light intensity I out for: From the Bessel function expansion: Where m i is an odd number, n i is an even number (i=1,2,3,4;m i =1,3,5,6,7…;m i =0,2,4,6…),J x (y) is the x-th order Bessel function corresponding to y.

7. The high-speed and high-precision four-photoelastic modulation closed-loop control Mueller matrix measurement method according to claim 4 is characterized in that: The method for obtaining the 16 elements in the Muller matrix sample (5) to be tested in S3 is: By M 13 With M 31 The corresponding Bessel function expansion is calculated to obtain δ 10 , δ 20 , δ 30 and δ 40 : According to the above formula, the inverse function of the ratio of different difference frequency signals and the ratio of Bessel functions, δ is calculated in real time. 10 , δ 20 , δ 30 and δ 40 : The calculated δ 10 , δ 20 , δ 30 and δ 40 Substitute the Bessel function expansion, select the appropriate difference frequency signal, obtain the 16 element values ​​in the Muller matrix sample (5) to be tested, and obtain the generalized polarization state degree of the sample.

Images