Optical system polarization sensitivity accurate calculation method and system

Abstract

This invention discloses a method and system for accurately calculating the polarization sensitivity of an optical system. The method includes: splitting a beam of light emitted from a field of view of the optical system into multiple sampled rays; calculating the Jones matrix of each sampled ray; obtaining the Mueller matrix of each sampled ray based on its Jones matrix; obtaining the Mueller pupil corresponding to the field of view based on its Mueller matrix; obtaining the average Mueller matrix based on its Mueller pupil; and obtaining the polarization sensitivity based on the average Mueller matrix. This invention overcomes the shortcomings of traditional single-ray estimation and definition methods, significantly improving calculation accuracy and efficiency, and enhancing the reliability of system design.

Description

Technical Field

[0001] This invention belongs to the fields of optical remote sensing, astronomical observation, and lidar imaging technology, and particularly relates to a method and system for accurately calculating the polarization sensitivity of an optical system. Background Technology

[0002] The polarization characteristics of optical remote sensors are a crucial factor affecting the accuracy of radiometric measurements and quantitative inversion. For optical systems such as small-F# submicron high-resolution imaging, optical systems containing complex films, and high-quantitation remote sensors, the polarization effect of the optical system itself must be considered. Unpolarized light emitted from the sun, after multiple scatterings by atmospheric molecules, aerosols, and the ocean surface, becomes partially polarized before entering the space remote sensor. The degree of polarization of the scattered light can reach over 20%. Due to the inherent polarization effect of optical remote sensing, incident light with equal radiant power but different polarization states will produce unequal sensor output values, affecting the detection accuracy of the remote sensor and introducing measurement uncertainty.

[0003] Polarization sensitivity (LPS) describes the degree to which the output light intensity of an optical system is sensitive to the polarization state of the incident light. It reflects the change in the output light intensity of the system when the polarization state of incident light of the same intensity changes. It is defined as: when a beam of completely polarized light is incident on an optical system, as the polarization direction of the incident light rotates 180°, the maximum output intensity of the system is... max With minimum output I min The ratio of their differences to their sum is shown in the following formula:

[0004]

[0005] A zero LPS indicates that the output light intensity is constant with the incident light intensity and is independent of the polarization state of the incident light. If the LPS is 1, the optical system can be considered equivalent to a polarizer, allowing only linearly polarized light to pass through in one direction. LPS is an inherent instrument characteristic of the optical system, a function of wavelength and field of view, and is independent of the incident light intensity and polarization characteristics.

[0006] Research on the polarization effect of optical instruments dates back to the 1960s and 70s, with reports on polarization aberrations in polarizing microscopes, spectrometers, radiometers, and phase array optical systems. In 1987, Russell A. Chipman, in his research on the polarization effect of NASA's solar electromagnetic measurement instrument, first clearly proposed the concept of polarization aberration and its basic theory. In 1992, Peter W. Maymon of NASA, in collaboration with Russell A. Chipman of the University of Alabama, based on the Medium Resolution Imaging Spectroradiometer (MODIS) project, pointed out that in high-precision radiometric measurement systems, low polarization sensitivity of the optical system is essential, and first proposed the concept of linear polarization sensitivity (LPS). In 2005, N. Souaidia et al. used polarized ray tracing and reverse engineering to roughly simulate and analyze the polarization characteristics caused by the MODIS film and scanning mirror, comparing the results with measured values ​​and performing error analysis.

[0007] However, currently, the industry uses two main methods for polarization sensitivity simulation analysis: the definition method (Technology 1, see B. Van Gorp, P. Mouroulis, D. Wilson, K. Balasubramanian. Polarization and straylight considerations for the Portable Remote Imaging Spectrometer (PRISM), Proc. of SPIE Vol. 7812, 78120R, 2010) and the single-ray estimation method (Technology 2, see Zhang Yinzhao, Wang Ganquan, Liu Dingquan. Polarization characteristics analysis of dual-scanning mirror spatial imaging system, Science Technology and Engineering, Science Technology and Engineering 13(14), 2013; Zhang E. Design and calculation of reducing the polarization sensitivity of the ocean-color scanner of Haiyang-1A satellite. Proceedings of the 90th Birthday of Mr. Daheng and the Academic Conference of the Chinese Optical Society, 2004). The former requires setting different azimuth angles of polarized light incident within the range of 0° to 360° to obtain the corresponding output light intensity. This method is computationally time-consuming and cannot intuitively describe the polarization characteristics of each component in the system, making it unsuitable for guiding polarization suppression design. The latter method involves tracing a small number of single rays and approximating the polarization sensitivity using the bidirectional attenuation characteristics of a single ray based on the incident angle of the optical surface and the film properties. While the bidirectional attenuation characteristics of a single ray can indirectly reflect the magnitude of the instrument's polarization sensitivity, it is not an accurate representation of the system's polarization sensitivity and contains a certain degree of calculation error. Summary of the Invention

[0008] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a method and system for accurately calculating the polarization sensitivity of an optical system. This method makes up for the deficiencies of the traditional single-ray estimation method and definition method, greatly improves the calculation accuracy and efficiency, and enhances the reliability of the system design.

[0009] The objective of this invention is achieved through the following technical solution: a method for accurately calculating the polarization sensitivity of an optical system, comprising: splitting a beam of light emitted from a field of view of the optical system into multiple sampling rays; calculating the Jones matrix of each sampling ray; obtaining the Mueller matrix of each sampling ray based on the Jones matrix; obtaining the Mueller pupil M(p) corresponding to the field of view based on the Mueller matrix of each sampling ray; obtaining the average Mueller matrix based on the Mueller pupil M(p) corresponding to the field of view; and obtaining the polarization sensitivity LPS based on the average Mueller matrix. single .

[0010] In the above method for accurately calculating the polarization sensitivity of the optical system, the Jones matrix of each sampled ray is obtained by the following formula:

[0011] J = J N-1,N ·J N-1 ·J N-2,N ·J N-2 …J 1,2 ·J1·J 0,1 ;

[0012] in,

[0013] J p-1,p Let J be the transfer matrix from interface p-1 to interface p. p Let J be the surface matrix of the sampling ray passing through the p-th interface, J be the Jones matrix of a sampling ray, N be the total number of interfaces, p be the index of the interface, and W be the surface matrix of the interface. p-1,p Let be the optical path difference between interface p-1 and interface p.

[0014] In the above method for accurately calculating the polarization sensitivity of the optical system, the Mueller matrix for each sampled ray is obtained using the following formula:

[0015]

[0016] Among them, S in S is the Stokes vector of the incident light. out Let M be the Stokes vector of the emitted light, M be the Mueller matrix, and m be the value of the emitted light. 00 m 01 m 02 m 03 m 10 m 11 m 12 m 13m 20 m 21 m 22 m 23 m 30 m 31 m 32 and m 33 All of these are elements in the Mueller matrix, and s0, s1, s2 and s3 are elements in the Stokes vector of the incident light.

[0017] In the above method for accurately calculating the polarization sensitivity of an optical system, the average Mueller matrix is ​​obtained using the following formula:

[0018]

[0019] in, i=0, 1, 2, 3, j=0, 1, 2, 3; The average Mueller matrix, represents the elements in the average Mueller matrix, and M is the total number of sampled rays.

[0020] In the above-mentioned method for accurately calculating the polarization sensitivity of an optical system, the polarization sensitivity LPS single It can be obtained through the following formula:

[0021]

[0022] Among them, LPS single For polarization sensitivity, and All are elements in the average Mueller matrix.

[0023] A system for accurately calculating the polarization sensitivity of an optical system includes: a first module for splitting a beam of light emitted from a field of view of the optical system into multiple sampled rays and calculating the Jones matrix of each sampled ray; a second module for obtaining the Mueller matrix of each sampled ray based on the Jones matrix; a third module for obtaining the Mueller pupil M(p) corresponding to the field of view based on the Mueller matrix of each sampled ray; a fourth module for obtaining the average Mueller matrix based on the Mueller pupil M(p) corresponding to the field of view; and a fifth module for obtaining the polarization sensitivity LPS based on the average Mueller matrix. single .

[0024] In the aforementioned optical system polarization sensitivity calculation system, the Jones matrix of each sampled ray is obtained using the following formula:

[0025] J = J N-1,N ·J N-1 ·J N-2,N ·J N-2 …J 1,2 ·J1·J0,1 ;

[0026] in,

[0027] J p-1,p Let J be the transfer matrix from interface p-1 to interface p. p Let J be the surface matrix of the sampling ray passing through the p-th interface, J be the Jones matrix of a sampling ray, N be the total number of interfaces, p be the index of the interface, and W be the surface matrix of the interface. p-1,p Let be the optical path difference between interface p-1 and interface p.

[0028] In the aforementioned system for accurately calculating the polarization sensitivity of the optical system, the Mueller matrix for each sampled ray is obtained using the following formula:

[0029]

[0030] Among them, S in S is the Stokes vector of the incident light. out Let M be the Stokes vector of the emitted light, M be the Mueller matrix, and m be the value of the emitted light. 00 m 01 m 02 m 03 m 10 m 11 m 12 m 13 m 20 m 21 m 22 m 23 m 30 m 31 m 32 and m 33 All of these are elements in the Mueller matrix, and s0, s1, s2 and s3 are elements in the Stokes vector of the incident light.

[0031] In the above-mentioned system for accurately calculating the polarization sensitivity of the optical system, the average Mueller matrix is ​​obtained by the following formula:

[0032]

[0033] in, i=0, 1, 2, 3, j=0, 1, 2, 3; The average Mueller matrix, represents the elements in the average Mueller matrix, and M is the total number of sampled rays.

[0034] In the aforementioned optical system polarization sensitivity accurate calculation system, polarization sensitivity LPS single It can be obtained through the following formula:

[0035]

[0036] Among them, LPS single For polarization sensitivity, and All are elements in the average Mueller matrix.

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] This invention overcomes the large calculation error of the traditional single-ray estimation method and solves the technical problem of the inability to accurately model and simulate. Attached Figure Description

[0039] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0040] Figure 1 This is a flowchart of the method for accurately calculating the polarization sensitivity of an optical system provided in an embodiment of the present invention;

[0041] Figure 2 This is a schematic diagram of the polarization sensitivity curves for different spectral bands and different fields of view provided in the embodiments of the present invention. Detailed Implementation

[0042] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0043] This embodiment provides a method for accurately calculating the polarization sensitivity of an optical system, which includes the following steps:

[0044] A beam of light emitted from a field of view of an optical system is split into multiple sampled rays, and the Jones matrix of each sampled ray is calculated.

[0045] The Mueller matrix for each sample ray is obtained from the Jones matrix for each sample ray;

[0046] The Mueller pupil corresponding to the field of view point is obtained from the Mueller matrix of each sampled ray;

[0047] The average Mueller matrix is ​​obtained from the Mueller pupil corresponding to the field of view point;

[0048] The polarization sensitivity is obtained from the average Mueller matrix.

[0049] The Jones matrix for each sampled ray is obtained using the following formula:

[0050] J = J N-1,N ·J N-1 ·J N-2,N ·J N-2 …J 1,2 ·J1·J 0,1 ;

[0051] in,

[0052] J p-1,p Let J be the transfer matrix from interface p-1 to interface p. p Let J be the surface matrix of the sampling ray passing through the p-th interface, J be the Jones matrix of a sampling ray, N be the total number of interfaces, p be the index of the interface, and W be the surface matrix of the interface. p- 1 ,p Let be the optical path difference between interface p-1 and interface p.

[0053] The Mueller matrix for each sampled ray is obtained using the following formula:

[0054]

[0055] Among them, S in S is the Stokes vector of the incident light. out Let M be the Stokes vector of the emitted light, M be the Mueller matrix, and m be the value of the emitted light. 00 m 01 m 02 m 03 m 10 m 11 m 12 m 13 m 20 m 21 m 22 m 23 m 30 m 31 m 32 and m 33 All of these are elements in the Mueller matrix, and s0, s1, s2 and s3 are elements in the Stokes vector of the incident light.

[0056] The average Mueller matrix is ​​obtained by the following formula:

[0057]

[0058] in, i=0, 1, 2, 3, j=0, 1, 2, 3; The average Mueller matrix, represents the elements in the average Mueller matrix, and M is the total number of sampled rays.

[0059] Polarization sensitivity LPS single It can be obtained through the following formula:

[0060]

[0061] Among them, LPS single For polarization sensitivity, and All are elements in the average Mueller matrix.

[0062] Figure 1 This is a flowchart of a method for accurately calculating the polarization sensitivity of an optical system provided in an embodiment of the present invention. Figure 1 As shown, the method specifically includes: Step 101: Input the field of view and wavelength of the optical system. The polarization effect of the optical system is a function of the field of view and wavelength. Calculate the polarization sensitivity of one field of view at a single wavelength.

[0063] Step 102: A beam of light is emitted from a point in the field of view. The polarization effect of this beam can be characterized by calculating the Jones matrix of a single sampled ray by selecting an entrance pupil grid for sampling. The Jones pupil corresponding to a given field of view is represented as:

[0064]

[0065] The Jones matrix above consists of four complex numbers with eight components, where p is the pupil coordinate. The calculation of the Jones matrix is ​​based on the principle of polarized ray tracing. Ray tracing requires calculating two types of matrices: a ray transmission matrix between surfaces and a surface matrix. The Jones matrix of a single ray passing through an optical system is a cascade of transmission and surface matrices:

[0066] J = J N-1,N ·J N-1 ·J N-2,N ·J N-2 …J 1,2 ·J1·J 0,1 ;

[0067] Among them, J N-1,N Let be the transmission matrix from the (N-1)th plane to the Nth plane, obtained by conventional geometric ray tracing. For isotropic media, ray transmission within the medium does not affect the polarization state of the light wave; therefore, is the product of an identity matrix and a scalar phase factor, expressed as:

[0068]

[0069] In the formula, J N-1 The surface matrix (Jones matrix) is the light beam passing through the (N-1)th interface. It is determined by the amplitude and phase characteristics of the interface or film. The calculation principle is Fresnel formula or thin film calculation theory.

[0070] Step 103: Convert the Jones matrix to the Mueller matrix. Using the conversion formula from Jones to Mueller, calculate the system Mueller matrix corresponding to the ray. The Mueller matrix M reflects the Stokes vector S of the incident light. in And the Stokes vector S of the emitted light out The coupling transformation relationship between them is shown in the following equation. Where the element related to the linear bidirectional attenuation characteristics is m. 01 m 02 m 10 and m 20 Each sampled ray within the pupil corresponds to a Mueller matrix M.

[0071]

[0072] Step 104: Following steps 102 and 103, calculate the Mueller matrix for all grid rays within the pupil.

[0073] Step 105: Obtain the Mueller matrix of all rays to construct the Mueller pupil M(p) corresponding to the field of view point.

[0074] Step 106: Calculate the average Mueller matrix of the system. Polarization sensitivity only concerns light intensity information. The incoherent superposition of the intensities of each tracing ray within the pupil represents the system's output light intensity. The average Mueller matrix of the system reflects the coupling relationship between the input and output light intensities. The average Mueller matrix is ​​the arithmetic mean of the same Mueller element for all rays in the Mueller pupil M(p), as shown in the following formula:

[0075]

[0076] in, M represents the total number of light rays sampled within the pupil.

[0077] Step 107: Based on the relationship between single-ray polarization sensitivity and single-ray Mueller matrix, derive the polarization sensitivity LPS of the optical system at a certain field of view and spectral band. single With the average Mueller matrix The relationship between the elements is:

[0078]

[0079] Furthermore, this calculation can rely on the polarization ray tracing function of the commercial software Code v, and the output Jones matrix can be used as the raw data for the subsequent data calculations in steps 103 to 107 of this invention.

[0080] Furthermore, when calculating polarization sensitivity, the simulation model of the optical system includes the optical structure model and the film file corresponding to each optical surface. Both must be complete in order to effectively simulate and calculate the polarization sensitivity of the system.

[0081] Furthermore, after calculating the polarization sensitivity of a field of view at a single wavelength according to steps 101 to 107 above, the polarization sensitivity at other field of view points and wavelengths can be calculated by repeating steps 101 to 107, and the overall characteristics of the system can be statistically evaluated.

[0082] Furthermore, the number of pupil grids in this invention is recommended to be at least 128×128 to improve the simulation accuracy of the system.

[0083] Taking a marine imaging camera in a specific visible-near-infrared spectral band as an example, its polarization sensitivity is analyzed. The system employs a Ritchey-Chretien+ correction mirror assembly design, consisting of a primary mirror, secondary mirror, two folding mirrors, and six lenses. The focal length is 13m, the primary mirror aperture is 1070mm, and the field of view is 0.8°×0.8°. This system features a wide imaging spectral band, large aperture, long focal length, and good geometric stability. The full-field modulation transfer function (MTF) is close to the diffraction limit, and the full-field distortion is less than 0.7%. The analysis results are shown below. Figure 2 As shown, the polarization sensitivity gradually increases with the increase of the field of view; within the same field of view, the polarization sensitivity of the shorter wavelength spectral band is greater than that of the longer wavelength spectral band. The system exhibits the highest polarization sensitivity (3.17%) at the lower edge of the 402nm spectral band (0.4°, 0.4°). If estimated based on the bidirectional attenuation characteristics of a single ray, the maximum value is 5.4%. Therefore, the ray approximation method has a significant calculation error, with an absolute error reaching 2.2%.

[0084] This embodiment also provides a system for accurately calculating the polarization sensitivity of an optical system. The system includes: a first module for splitting a beam of light emitted from a field of view of the optical system into multiple sampled rays and calculating the Jones matrix of each sampled ray; a second module for obtaining the Mueller matrix of each sampled ray based on the Jones matrix of each sampled ray; a third module for obtaining the Mueller pupil corresponding to the field of view based on the Mueller matrix of each sampled ray; a fourth module for obtaining the average Mueller matrix based on the Mueller pupil corresponding to the field of view; and a fifth module for obtaining the polarization sensitivity based on the average Mueller matrix.

[0085] In the above embodiments, the Jones matrix of each sampling ray is obtained by the following formula:

[0086] J = J N-1,N ·J N-1 ·J N-2,N ·J N-2 …J 1,2 ·J1·J 0,1 ;

[0087] in,

[0088] J p-1,p Let J be the transfer matrix from interface p-1 to interface p. p Let J be the surface matrix of the sampling ray passing through the p-th interface, J be the Jones matrix of a sampling ray, N be the total number of interfaces, p be the index of the interface, and W be the surface matrix of the interface. p- 1 ,p Let be the optical path difference between interface p-1 and interface p.

[0089] In the above embodiments, the Mueller matrix of each sampling ray is obtained by the following formula:

[0090]

[0091] Among them, S in S is the Stokes vector of the incident light. out Let M be the Stokes vector of the emitted light, M be the Mueller matrix, and m be the value of the emitted light. 00 m 01 m 02 m 03 m 10 m 11 m 12 m 13 m 20 m 21 m 22 m 23 m 30 m 31 m 32 and m 33 All of these are elements in the Mueller matrix, and s0, s1, s2 and s3 are elements in the Stokes vector of the incident light.

[0092] In the above embodiments, the average Mueller matrix is ​​obtained by the following formula:

[0093]

[0094] in, i=0, 1, 2, 3, j=0, 1, 2, 3; The average Mueller matrix, represents the elements in the average Mueller matrix, and M is the total number of sampled rays.

[0095] In the above embodiments, the polarization sensitivity LPS single It can be obtained through the following formula:

[0096]

[0097] Among them, LPS single For polarization sensitivity, and All are elements in the average Mueller matrix.

[0098] This invention overcomes the large calculation error of the traditional single-ray estimation method and solves the technical problem of the inability to accurately model and simulate.

[0099] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A method for accurately calculating the polarization sensitivity of an optical system, characterized in that... include: A beam of light emitted from a field of view of an optical system is split into multiple sampled rays, and the Jones matrix of each sampled ray is calculated. The Mueller matrix for each sample ray is obtained from the Jones matrix for each sample ray; The Mueller pupil corresponding to the field of view point is obtained from the Mueller matrix of each sampled ray; The average Mueller matrix is ​​obtained from the Mueller pupil corresponding to the field of view point; The polarization sensitivity is obtained from the average Mueller matrix; The Jones pupil corresponding to the viewing location is represented as: ； The Jones matrix above has four complex elements and a total of eight components. The coordinates are the pupil coordinates; the calculation of the Jones matrix is ​​based on the principle of polarized ray tracing; ray tracing requires the calculation of two types of matrices: a ray transmission matrix between surfaces and a surface matrix. The Jones matrix for each sampled ray is obtained using the following formula: ； in, ; This is the transmission matrix from interface p-1 to interface p. Let p be the surface matrix through which the sampled light passes. The Jones matrix of a certain sampled ray. Let p be the total number of interfaces, and p be the index of each interface. The optical path difference is between the (p-1)th interface and the pth interface. The Mueller matrix for each sampled ray is obtained using the following formula: ； in, Let Stokes be the incident light vector. The Stokes vector of the emitted light. For Muller matrix, , , , , , , , , , , , , , , and All of these are elements in the Mueller matrix. , , and All of these are elements in the Stokes vector of the incident light; The average Mueller matrix is ​​obtained by the following formula: ； in, , , ; The average Mueller matrix, The elements are in the average Mueller matrix. This represents the total number of sampled rays; polarization sensitivity It can be obtained through the following formula: ； in, For polarization sensitivity, , and All are elements in the average Mueller matrix.

2. A system for accurately calculating the polarization sensitivity of an optical system, characterized in that... include: The first module is used to split a beam of light emitted from a field of view of an optical system into multiple sampled rays and calculate the Jones matrix of each sampled ray. The second module is used to obtain the Mueller matrix of each sample ray based on the Jones matrix of each sample ray; The third module is used to obtain the Mueller pupil corresponding to the field of view point based on the Mueller matrix of each sampled ray; The fourth module is used to obtain the average Mueller matrix based on the Mueller pupil corresponding to the field of view point; The fifth module is used to obtain the polarization sensitivity based on the average Mueller matrix; The Jones pupil corresponding to the viewing location is represented as: ； The Jones matrix above has four complex elements and a total of eight components. The coordinates are the pupil coordinates; the calculation of the Jones matrix is ​​based on the principle of polarized ray tracing; ray tracing requires the calculation of two types of matrices: a ray transmission matrix between surfaces and a surface matrix. The Jones matrix for each sampled ray is obtained using the following formula: ； in, ; This is the transmission matrix from interface p-1 to interface p. Let p be the surface matrix through which the sampled light passes. The Jones matrix of a certain sampled ray. Let p be the total number of interfaces, and p be the index of each interface. The optical path difference is between the (p-1)th interface and the pth interface. The Mueller matrix for each sampled ray is obtained using the following formula: ； in, Let Stokes be the incident light vector. The Stokes vector of the emitted light. For Muller matrix, , , , , , , , , , , , , , , and All of these are elements in the Mueller matrix. , , and All of these are elements in the Stokes vector of the incident light; The average Mueller matrix is ​​obtained by the following formula: ； in, , , ; The average Mueller matrix, The elements are in the average Mueller matrix. This represents the total number of sampled rays; polarization sensitivity It can be obtained through the following formula: ； in, For polarization sensitivity, , and All are elements in the average Mueller matrix.

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