A method for constructing a satellite complex surface optical feature lookup table and a satellite light pressure calculation method
Patent Information
- Application Number
- CN202611399205.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-09-10
- Publication Date
- 2026-10-09
AI Technical Summary
[0004]针对现有技术中的部分或全部问题,为了克服传统模型将表面简化为理想均匀漫反射或镜面反射导致的参数失真,提升大入射角及复杂光照条件下的光压计算精度,本发明第一方面提供一种卫星复杂表面光学特征查找表的构建方法,包括:
[0015]基于如前所述的构建方法,本发明第二方面提供一种卫星光压计算方法,包括:
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Figure CN122885258A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of spacecraft dynamics and optical measurement technology, and in particular to a method for constructing a lookup table of optical features of complex satellite surfaces and a method for calculating satellite optical pressure. Background Technology
[0002] When a satellite is in orbit, solar radiation hitting its surface generates light pressure, which affects the accuracy of its orbit and attitude control. Current light pressure calculations typically simplify the satellite surface as a uniformly diffuse or specular reflective surface, using only a single absorptivity or hemispherical reflectivity parameter. However, accurate light pressure calculation models must simultaneously consider the effects of absorptivity, specular reflectivity, and diffuse reflectivity on the illuminated surface. Furthermore, the satellite surface contains various materials and structures. Solar panels are composed of periodically arranged solar cells and seams; heat dissipation surfaces are covered with optical solar reflectors (OSRs) or coated with white paint; and thermal insulation is achieved through multi-layer insulation (MLI) components. These types of surfaces differ significantly in microscopic geometry and optical properties, and contain non-ideal structures such as seams and wrinkles. This means that the actual satellite surface is not smooth; its absorptivity and reflectivity vary considerably across different areas. Therefore, simplifying it to a uniformly diffuse or specular reflective surface does not reflect its true condition.
[0003] Based on this, some existing technologies calculate the solar pressure by measuring the reflection parameters of different regions on the ground. However, existing ground measurements often only target a single, intact material sheet, such as a single solar cell or a single OSR, ignoring effects such as multiple reflections from gaps and structural edges, and shading. Furthermore, they only measure solar absorptivity and hemispherical reflectivity, neglecting specular and diffuse reflection. In addition, for flexible surfaces such as MLI, the wrinkle state directly affects the reflection distribution, and existing methods lack quantitative characterization methods. Summary of the Invention
[0004] To address some or all of the problems in existing technologies, and to overcome the parameter distortion caused by simplifying surfaces to ideal uniform diffuse or specular reflection in traditional models, thereby improving the accuracy of light pressure calculation under large incident angles and complex lighting conditions, the first aspect of this invention provides a method for constructing a lookup table of optical features for complex satellite surfaces, comprising: Several types of samples were obtained, each of which was consistent with the microstructural features of a satellite surface type to characterize a satellite surface type. The satellite surface types include solar cell solar panel units with splicing seams, optical solar reflector heat dissipation units with splicing seams, white paint coating units without splicing seams, and multilayer thermal insulation component units with wrinkled surfaces. Under several sets of wavelengths, incident zenith angles, and incident azimuth angles, the hemispherical reflectivity and bidirectional reflection distribution function (BRDF) of each sample were measured. The absorption coefficient, specular reflection coefficient, and diffuse reflection coefficient of the corresponding sample are determined based on the hemispherical reflectance and bidirectional reflection distribution function. A lookup table is constructed based on the absorption coefficient, specular reflection coefficient, and diffuse reflection coefficient of each sample at different wavelengths, incident zenith angles, and incident azimuth angles.
[0005] Furthermore, the hemispherical reflectivity of each sample was measured using a directional hemispherical reflectivity measurement system based on an integrating sphere.
[0006] Furthermore, determining the specular reflection coefficient of the corresponding sample based on the bidirectional reflection distribution function includes: The bidirectional reflection distribution function was obtained by measuring each sample using a high-precision triaxial automatic scattering instrument. Within a specified range in the direction of specular reflection, the specular reflection energy is obtained by integration, wherein the specified range is determined based on the half-width at half-maximum (WWHM) of the reflection peak. The mirror reflection coefficient is determined based on the mirror reflection energy and the incident energy.
[0007] Furthermore, the absorption rate is determined according to the following formula, where the transmittance is assumed to be 0: Absorption rate = 1 - hemispherical reflectivity.
[0008] Furthermore, the diffuse reflectance is determined according to the following formula: Diffuse reflectance = hemispherical reflectance - specular reflectance.
[0009] Furthermore, the sample characterizing the solar cell solar panel unit with splicing seams includes several complete solar cells and several first splicing seams; The sample characterizing the heat dissipation unit of the optical solar reflector with splicing seams includes several complete optical solar reflectors and several second splicing seams, wherein the width of the second splicing seams is 0.2 to 0.5 mm; The sample representing the seamless white paint coating unit includes a flat substrate with white paint on its surface. The white paint is applied using the same process as the white paint heat dissipation surface of the satellite. The sample representing the seamless white paint coating unit has a size of not less than 50 mm × 50 mm. The sample characterizing the multilayer thermal insulation component unit with a wrinkled surface includes a real multilayer thermal insulation component in a wrinkled state with an outer F46 silver-plated secondary surface mirror film, and the sample has a size of not less than 50 mm × 50 mm.
[0010] Furthermore, for the sample characterizing the solar cell panel unit with splicing seams, the hemispherical reflectivity and specular reflectivity were measured within the range of incident zenith angle from 0° to 90° and incident azimuth angle from 0° to 90°, respectively, with a detection angular resolution of 5°.
[0011] Furthermore, for the sample characterizing the heat dissipation unit of the optical solar reflector with splicing seams, the hemispherical reflectivity and specular reflectivity were measured in the range of incident zenith angle from 0° to 90° and incident azimuth angle from 0° to 90°, respectively, with a detection angular resolution of 5°.
[0012] Furthermore, for the sample characterizing the seamless white paint coating unit, the hemispherical reflectivity and specular reflectivity were measured within the range of incident zenith angle from 0° to 90° and incident azimuth angle from 0° to 90°, respectively, with a detection angular resolution of 5°.
[0013] Furthermore, for the sample characterizing the multilayer thermal insulation component unit with a wrinkled surface, the hemispherical reflectivity and specular reflectivity were measured within the range of incident zenith angle from 0° to 90° and incident azimuth angle from 0° to 90°, respectively, with a detection angular resolution of 5°.
[0014] Furthermore, for samples characterizing multilayer thermal insulation component units with wrinkled surfaces, their morphological features were also measured, including: The wrinkle statistics were obtained by scanning with atomic force microscopy (AFM), including height distribution, root mean square roughness, autocorrelation length, power spectral density, and wrinkle orientation.
[0015] Based on the construction method described above, a second aspect of the present invention provides a satellite optical pressure calculation method, comprising: Construct a lookup table using the construction method described above; During the calculation of the overall star's light pressure, the corresponding optical parameters are obtained by interpolation from the lookup table based on the surface type of the surface element and the actual incident angle, and then the calculation is performed.
[0016] This invention provides a method for constructing a lookup table of optical features for complex satellite surfaces and a method for calculating satellite optical pressure. By incorporating real structures such as seams and folds, it can significantly improve the accuracy of optical pressure calculation at large incident angles. It covers four main types of satellite surfaces, forming a unified parameterized framework and providing high-fidelity input for whole-satellite optical pressure calculation. Attached Figure Description
[0017] To further illustrate the above and other advantages and features of the various embodiments of the present invention, a more specific description of the various embodiments of the present invention will be presented with reference to the accompanying drawings. It is to be understood that these drawings depict only typical embodiments of the invention and are therefore not intended to limit its scope. In the drawings, identical or corresponding parts will be indicated by identical or similar reference numerals for clarity.
[0018] Figure 1 This is a flowchart illustrating a method for constructing a lookup table of optical features of a complex satellite surface according to an embodiment of the present invention. Figure 2 A schematic diagram of the structure of a sample representing a solar cell solar panel unit with splicing seams according to an embodiment of the present invention is shown; Figure 3 This diagram illustrates the structure of a sample representing an OSR plate heat dissipation unit with splicing seams, according to an embodiment of the present invention. Detailed Implementation
[0019] In the following description, the invention is described with reference to various embodiments. However, those skilled in the art will recognize that the embodiments may be practiced without one or more specific details or with other alternatives and / or additional methods, materials, or components. In other instances, well-known structures, materials, or operations are not shown or described in detail so as not to obscure the inventive points of the invention. Similarly, for illustrative purposes, specific quantities, materials, and configurations are set forth to provide a comprehensive understanding of embodiments of the invention. However, the invention is not limited to these specific details. Furthermore, it should be understood that the embodiments shown in the drawings are illustrative representations and are not necessarily drawn to scale.
[0020] In this specification, references to "an embodiment" or "this embodiment" mean that a particular feature, structure, or characteristic described in connection with that embodiment is included in at least one embodiment of the invention. The phrase "in one embodiment" appearing throughout this specification does not necessarily refer to the same embodiment in all instances.
[0021] It should be noted that the embodiments of the present invention describe the method steps in a specific order; however, this is only for illustrating the specific embodiment and not for limiting the order of the steps. On the contrary, in different embodiments of the present invention, the order of the steps can be adjusted according to actual needs.
[0022] To provide optical parameters that cover various complex satellite surfaces, incorporate microscopic geometric features, and can be directly used in the optical pressure model, this invention offers a method for constructing a lookup table of optical features for complex satellite surfaces. This method provides a precise characterization method for the optical properties of complex satellite surfaces in the optical pressure model. For four typical surface types—solar cells with seams, optical solar reflectors with seams, white paint, and multi-layered thermal insulation components—measurement samples and experimental schemes are designed to characterize their equivalent optical parameters, providing high-fidelity input for the calculation of the entire satellite's optical pressure. Specifically, representative samples reflecting the microstructural characteristics of each type are designed, and their hemispherical reflectivity is measured using a directional hemispherical reflectivity measurement system based on an integrating sphere. Then, a high-precision three-axis automatic scatterometer (TAAS) is used to measure the bidirectional reflectance distribution function of the sample to obtain the specular reflection coefficient, and then the diffuse reflection coefficient is calculated. A lookup table of full-angle optical characteristic parameters for representative samples is established for use in the optical pressure model.
[0023] The technical solution of the present invention will be further described below with reference to the accompanying drawings of the embodiments.
[0024] Figure 1 This diagram illustrates a flowchart of a method for constructing a lookup table for complex surface optical features of a satellite, according to an embodiment of the present invention. Figure 1 As shown, a method for constructing a lookup table of optical features for complex satellite surfaces includes: First, in step 101, samples are obtained. The satellite surface is divided into four typical surface element types, including solar cell solar panel units with splicing seams, optical solar reflector heat dissipation units with splicing seams, white paint coating units without splicing seams, and multilayer thermal insulation component units with wrinkled surfaces. Based on this, a sample is designed for each type, wherein the sample of each type is consistent with the microstructural characteristics of a satellite surface element type, so as to characterize a satellite surface element type.
[0025] In one embodiment of the present invention, such as Figure 2 As shown, the sample representing a solar cell solar panel unit with splicing seams includes several complete solar cells and several first splicing seams. For example, it may include four complete solar cells and two middle first splicing seams, forming a periodic unit. Specifically, four solar cells with welded interconnecting strips can be taken and pasted onto an aluminum honeycomb substrate according to the actual process of satellite solar panels to form a sample. The solar cells are 20 mm × 20 mm in size and 0.2 mm thick. The gap width between adjacent solar cells is 0.5 mm, and the gap is filled with silicone rubber. The overall size of the sample is 40.5 mm × 40.5 mm.
[0026] Optical solar reflectors are typically made of silver-plated or aluminum-plated quartz glass with a black-coated back. They are small, square pieces attached side-by-side to a heat-dissipating surface, with gaps between them. Their optical characteristics are similar to those of solar cells, but they reflect more light and absorb less light, and the gap material is usually a black adhesive. Based on this, in one embodiment of the present invention, such as... Figure 3 As shown, the sample characterizing the heat dissipation unit of the optical solar reflector with splicing seams includes several complete optical solar reflectors and several second splicing seams, such as four complete optical solar reflectors and two middle second splicing seams, wherein the width of the second splicing seams is 0.2 to 0.5 mm. Specifically, four optical solar reflectors can be taken and pasted onto an aluminum honeycomb substrate to form a sample according to the actual mounting process of satellite optical solar reflectors. The optical solar reflectors are 40 mm × 40 mm in size and 0.3 mm thick, with a gap width of 0.3 mm between adjacent OSR sheets, and the gap is filled with black adhesive.
[0027] White paint is typically sprayed onto the hull or antenna reflector surface, resulting in a macroscopically uniform surface without periodic gaps. Its optical characteristics include strong diffuse reflection and extremely weak specular reflection. Based on this, in one embodiment of the present invention, the sample characterizing the seamless white paint coating unit includes a flat substrate with white paint applied to its surface. The white paint is obtained by spraying using the same process as the satellite's white paint heat dissipation surface. The sample characterizing the seamless white paint coating unit has dimensions of not less than 50 mm × 50 mm.
[0028] MLI is composed of multiple layers of polyimide film and polyester mesh stacked together. The outer surface is an F46 silver-plated secondary surface mirror film, exhibiting random wrinkles. Its optical properties mainly depend on the statistical distribution of the wrinkles, including amplitude, wavelength, and directionality. Based on this, in one embodiment of the present invention, the sample characterizing the multilayer thermal insulation component unit with a wrinkled surface includes a real multilayer thermal insulation component containing an outer F46 silver-plated secondary surface mirror film. The sample has a size of not less than 50 mm × 50 mm and maintains a natural wrinkled state.
[0029] Next, in step 102, the hemispherical reflectivity and bidirectional reflectance distribution function are measured. The hemispherical reflectivity and bidirectional reflectance distribution function of each sample are measured under several sets of wavelengths, incident zenith angles, and incident azimuth angles. In one embodiment of the invention, the hemispherical reflectivity of each sample is measured using a directional hemispherical reflectivity measurement system based on an integrating sphere. In one embodiment of the present invention, a high-precision triaxial automatic scattering instrument is used to perform spectral BRDF measurements on each sample to obtain the bidirectional reflectance distribution function. The angular resolution is better than 0.5°, and the light source is a halogen tungsten lamp and a monochromator. Indicates the angle of incidence at the zenith. Indicates the incident azimuth angle. , This represents the actual observation, namely the zenith angle and azimuth angle of the reflected direction.
[0030] In one embodiment of the present invention, for a sample characterizing a solar cell solar panel unit containing splicing seams, the hemispherical reflectivity and specular reflectivity are measured within the range of incident zenith angle (0° to 90°) and incident azimuth angle (0° to 90°), respectively, with a detection angular resolution of 5°. Since the diameter of a single measurement spot is much smaller than the characteristic size of the periodic unit, a two-dimensional gridded micro-area scanning statistical strategy is employed in one embodiment of the present invention. Specifically, a rectangular scanning range covering all characteristic areas, including the cell center area and the seam filling area, is delineated on the surface of the periodic unit containing a complete 'cell-slot-cell' structure. Within this range, a dense array of M rows × N columns of measurement points is arranged with equal intervals of no more than 2 mm, perpendicular and parallel to the seam direction. The directional hemispherical reflectivity and BRDF are measured for each node of the array, and all measurement data are weighted arithmetically averaged according to their spatial position. The expected value of this average is used as the equivalent optical parameter of the periodic unit under this incident state. In one embodiment of the present invention, under each incident condition, the hemispherical reflectance is repeatedly measured multiple times at each measuring point, and the spectral reflectance factor is recorded for each detection direction when the BRDF is measured.
[0031] In one embodiment of the present invention, for a sample characterizing an OSR sheet heat dissipation unit with splicing seams, the hemispherical reflectivity and specular reflectivity are measured within the range of incident zenith angle from 0° to 90° and incident azimuth angle from 0° to 90°, respectively, wherein the detection angular resolution is 5°.
[0032] In one embodiment of the present invention, for a sample characterizing a seamless white paint coating unit, the hemispherical reflectivity and specular reflectivity are measured within the range of incident zenith angle from 0° to 90° and incident azimuth angle from 0° to 90°, respectively, wherein the detection angular resolution is 5°.
[0033] In one embodiment of the present invention, for a sample characterizing a multilayer thermal insulation component unit with a wrinkled surface, the hemispherical reflectivity and specular reflectivity are measured within the range of incident zenith angle from 0° to 90° and incident azimuth angle from 0° to 90°, respectively, wherein the detection angular resolution is 5°.
[0034] In one embodiment of the invention, for a sample characterizing a multilayer thermal insulation component unit with a wrinkled surface, its morphological characteristics are also measured. Specifically, atomic force microscopy is used to scan and obtain its wrinkle statistical parameters, wherein the wrinkle statistical parameters include height distribution. Root mean square roughness Autocorrelation length Power spectral density, wrinkle directionality, etc.
[0035] Next, in step 103, optical characteristics are calculated. Based on the hemispherical reflectivity and bidirectional reflectance distribution function, the absorption coefficient, specular reflection coefficient, and diffuse reflection coefficient of the corresponding sample are determined. In one embodiment of the invention, within a specified range in the specular reflection direction, i.e. , At that point, the energy of the mirror reflection is obtained by integration. ,in , Determined based on the half-width at half-maximum (WHM) of the reflection peak. In one embodiment of the invention, for a sample characterizing a solar cell panel unit containing splicing seams, , The value ranges from 2° to 5° for samples characterizing OSR sheet heat dissipation units with splicing seams. , The value ranges from 2° to 5° for samples characterizing seamless white paint coating units. , A value of 0° is used for samples characterizing multilayer thermal insulation component units with wrinkled surfaces. , The value ranges from 10° to 15°. This is based on the specular reflection energy. The mirror reflection coefficient can be obtained. ,in The incident energy. In one embodiment of the invention, the absorption coefficient... The diffuse reflectance .
[0036] Finally, in step 104, a lookup table is generated. The lookup table is constructed based on the absorption coefficient, specular reflection coefficient, and diffuse reflection coefficient of each sample at different wavelengths, incident zenith angles, and incident azimuth angles.
[0037] Based on the aforementioned construction method, this invention also provides a satellite optical pressure calculation method. First, a lookup table is constructed using the aforementioned method. Then, during the overall satellite optical pressure calculation, corresponding optical parameters are obtained by interpolation from the lookup table based on the surface type of the surface element and the actual incident angle, and the calculation is performed. Specifically, in the overall satellite optical pressure calculation, for each surface element, the corresponding optical parameters are obtained by interpolation from the lookup table based on its surface type and local incident angle. , , Substituting this into the analytical light pressure formula, where the local incident angle is determined by the satellite attitude and the direction of the sun, the analytical light pressure formula is expressed as follows: , in, The area of the illuminated plane. This represents the solar radiation flux per unit area. Represents the speed of light. , These represent the unit vectors of the incident solar ray and the normal to the illuminated plane, respectively. for , The angle between them.
[0038] In one embodiment of the present invention, the construction method described above is implemented through a system for constructing a lookup table of optical features for complex satellite surfaces. This system includes a measurement module, a calculation module, and a lookup table generation module. The measurement module measures the hemispherical reflectivity and bidirectional reflectance distribution function of each sample at several sets of wavelengths, incident zenith angles, and incident azimuth angles. In another embodiment of the present invention, the measurement module includes a directional hemispherical reflectivity measurement system based on an integrating sphere and a high-precision triaxial automatic scattering instrument. The directional hemispherical reflectivity measurement system based on an integrating sphere measures the hemispherical reflectivity of each sample at several sets of wavelengths, incident zenith angles, and incident azimuth angles. The high-precision triaxial automatic scattering instrument measures the bidirectional reflectance distribution function of each sample at several sets of wavelengths, incident zenith angles, and incident azimuth angles. The calculation module determines the absorption coefficient, specular reflection coefficient, and diffuse reflection coefficient of the corresponding sample based on the hemispherical reflectivity and bidirectional reflectance distribution function. The lookup table generation module is used to generate a lookup table based on the absorption coefficient, specular reflection coefficient, and diffuse reflection coefficient of each sample at different wavelengths, incident zenith angles, and incident azimuth angles.
[0039] This invention provides a method for constructing a lookup table of optical features for complex satellite surfaces and a method for calculating satellite optical pressure. By incorporating real structures such as seams and folds, it can significantly improve the accuracy of optical pressure calculation at large incident angles. It covers four main types of satellite surfaces, forming a unified parameterized framework and providing high-fidelity input for whole-satellite optical pressure calculation.
[0040] Although various embodiments of the invention have been described above, it should be understood that they are presented by way of example only and not as limitations. It will be apparent to those skilled in the art that various combinations, modifications, and alterations can be made without departing from the spirit and scope of the invention. Therefore, the breadth and scope of the invention disclosed herein should not be limited by the exemplary embodiments disclosed above, but should be defined solely by the appended claims and their equivalents.
Claims
1. A method for constructing a lookup table of optical features for complex satellite surfaces, characterized in that, include: Several types of samples were obtained, each of which was consistent with the microstructural features of a satellite surface type to characterize a satellite surface type. The satellite surface types include solar cell solar panel units with splicing seams, optical solar reflector heat dissipation units with splicing seams, white paint coating units without splicing seams, and multilayer thermal insulation component units with wrinkled surfaces. Under several sets of wavelengths, incident zenith angles, and incident azimuth angles, the hemispherical reflectivity and bidirectional reflectance distribution function of each sample were measured. The absorption coefficient, specular reflection coefficient, and diffuse reflection coefficient of the corresponding sample are determined based on the hemispherical reflectance and bidirectional reflection distribution function. A lookup table is constructed based on the absorption coefficient, specular reflection coefficient, and diffuse reflection coefficient of each sample at different wavelengths, incident zenith angles, and incident azimuth angles.
2. The construction method as described in claim 1, characterized in that, The hemispherical reflectance of each sample was measured using a directional hemispherical reflectance measurement system based on an integrating sphere. The bidirectional reflection distribution function was obtained by measuring each sample using a high-precision triaxial automatic scattering instrument.
3. The construction method as described in claim 1, characterized in that, Determining the specular reflection coefficient of the corresponding sample based on the bidirectional reflection distribution function includes: Within a specified range in the direction of specular reflection, the specular reflection energy is obtained by integration, wherein the specified range is determined based on the half-width at half-maximum (WWHM) of the reflection peak. The mirror reflection coefficient is determined based on the mirror reflection energy and the incident energy.
4. The construction method as described in claim 1, characterized in that, The sample characterizing the solar cell solar panel unit with splicing seams includes several complete solar cells and several first splicing seams. The hemispherical reflectivity and specular reflectivity are measured in the range of incident zenith angle from 0° to 90° and incident azimuth angle from 0° to 90°, respectively, with a detection angular resolution of 5°.
5. The construction method as described in claim 1, characterized in that, The sample characterizing the heat dissipation unit of the optical solar reflector with splicing seams includes several complete optical solar reflectors and several second splicing seams. The hemispherical reflectivity and specular reflectivity are measured in the range of incident zenith angle from 0° to 90° and incident azimuth angle from 0° to 90°, respectively, with a detection angular resolution of 5°.
6. The construction method as described in claim 1, characterized in that, The sample characterizing the seamless white paint coating unit includes a flat substrate with white paint on its surface. The white paint is applied using the same process as the white paint heat dissipation surface of a satellite. The sample characterizing the seamless white paint coating unit has a size of not less than 50 mm × 50 mm. The hemispherical reflectivity and specular reflectivity are measured within the range of incident zenith angle from 0° to 90° and incident azimuth angle from 0° to 90°, respectively, with a detection angular resolution of 5°.
7. The construction method as described in claim 1, characterized in that, The sample characterizing the multilayer thermal insulation component unit with a wrinkled surface includes a real multilayer thermal insulation component with an outer F46 silver-plated secondary surface mirror film in a wrinkled state. The sample size is not less than 50 mm × 50 mm. The hemispherical reflectivity and specular reflectivity are measured in the range of incident zenith angle from 0° to 90° and incident azimuth angle from 0° to 90°, respectively, with a detection angular resolution of 5°.
8. The construction method as described in claim 7, characterized in that, Also includes: The morphological characteristics of the sample of a multilayer thermal insulation component unit with a wrinkled surface were measured and characterized, including: The wrinkle statistics were obtained by scanning with an atomic force microscope, including height distribution, root mean square roughness, autocorrelation length, power spectral density, and wrinkle orientation.
9. A method for calculating satellite optical pressure, characterized in that, include: The lookup table is constructed using the construction method described in any one of claims 1 to 8; During the calculation of the overall star's light pressure, the corresponding optical parameters are obtained by interpolation from the lookup table based on the surface type of the surface element and the actual incident angle, and then the calculation is performed.