A method for modeling the visible bidirectional scattering distribution function of a pleated wrap material

Abstract

This invention provides a method for modeling the visible light bidirectional scattering distribution function (BRDF) of wrinkled coated materials. The method includes obtaining BRDF data of the unwrinkled coated material; calculating the length reduction ratio in the X and Y directions of the satellite surface coated material under flat conditions compared to wrinkled conditions; establishing a statistical analysis function for the distribution of the area proportion coefficient of wrinkled fragments; deflecting the unwrinkled BRDF according to the tilt angle to obtain the fragment reflectivity values ​​relative to the base coordinate system; discretizing the tilt angle and substituting it into the analysis function to obtain the area proportion coefficient of the wrinkled fragments; multiplying the reflectivity of any orientation fragment by the corresponding area proportion coefficient to obtain the reflection contribution rate of that fragment, and then summing them to obtain the reflection contribution rate of all wrinkled fragments. This method utilizes the BRDF model under flat conditions to calculate the BRDF characteristics after wrinkling based on the coating conditions, providing data support for the simulation of target optical scattering characteristics.

Description

Technical Field

[0001] This invention belongs to the field of modeling and simulation technology, specifically relating to a method for modeling the visible light bidirectional scattering distribution function of wrinkled coated materials. Background Technology

[0002] Modern communication satellites, reconnaissance satellites, deep space probes, and other targets are all coated with a protective material to ensure their safety in deep space. This protective material is a composite, multi-layered material; the outermost layer is a highly reflective, metal-like material that exhibits extremely high brightness under sunlight, a crucial factor determining the target's visibility.

[0003] The two-way scattering distribution function (BRDF) characteristics of the coating material are very stable and easy to measure when the coating material is flat. However, in order to fit the satellite surface tightly during use, the coating material is often wrinkled. The degree of wrinkling is random, which means that the BRDF parameters obtained under flat conditions cannot accurately describe the surface reflection characteristics of the target.

[0004] The BRDF test for wrinkled surfaces is performed using actual materials. The procedure involves manually kneading the material before placing it on a measuring platform to measure its BRDF characteristics under these conditions. This measured data is then used as the BRDF of the wrinkled surface. This simple approximation method can be used within a certain range of accuracy requirements, but it is not conducive to high-precision data simulation calculations. Furthermore, the degree of wrinkling varies under different usage conditions, and the same set of BRDF data cannot adapt to all application conditions. Repeated measurements will also incur significant economic and time costs.

[0005] When performing finite element analysis calculations, the accuracy of the geometric model construction is limited, making it impossible to accurately describe the tilt of each fold. At the same time, it cannot respond to each tilted surface when dividing the surface source, and specific reflectivity values ​​cannot be used when calculating the surface source. Therefore, it is necessary to invent a visible light bidirectional scattering distribution modeling method for folded coated materials to provide BRDF parameter values ​​for the random surface after folding. Summary of the Invention

[0006] In view of this, the present invention provides a method for modeling the BRDF characteristics of a wrinkled coating material on a satellite surface. Using this method, modelers can use the BRDF model measured under flat conditions to calculate the BRDF characteristics of the material after wrinkling based on the coating conditions, thus providing data support for the simulation of the target's optical scattering characteristics.

[0007] This invention utilizes accurate BRDF measurements under flat conditions to construct a BRDF model for wrinkled materials through a statistical model of wrinkled fragments and the application of coating materials. The specific technical solution is as follows:

[0008] Step 1. Define the satellite surface to which the coating material is attached as the base plane. The coating material can be understood as a complex plane composed of countless small facets attached to the base plane. Construct a coordinate system with the incident light and the base plane, with the base normal as the Z-axis, the direction of the incident light in the base plane as the X-axis, and the Y-axis determined according to the right-hand rule; the normal direction of each fragment is (u, v), where u is the tangent of the angle between the normal angle of the folded fragment and the YZ plane, and v is the tangent of the angle between the normal angle of the fragment and the XZ plane.

[0009] Step 2. Measure the BRDF of the flat covering material to obtain the standard BRDF data of the material or obtain the BRDF data of the material before wrinkling treatment through other means. The format of the BRDF data is R(a, α, β), where a is the angle between the incident direction of the light and the Z axis, α is the angle between the measurement direction and the YZ plane mentioned in Step 1, and β is the angle between the measurement direction and the XZ plane mentioned in Step 1.

[0010] Step 3. Analyze the usage conditions of the coating material to obtain the area of ​​the coating material before and after wrinkling. Solve for the length reduction ratio A in the X direction and the length reduction ratio B in the Y direction of the satellite surface coating material under flat conditions compared to the wrinkled conditions. Taking A as an example, let L be the original length of the satellite surface wrinkled coating material under flat conditions in the X direction. o The length of the wrinkled coating material on the satellite surface in the X direction is L. n Then there is Generally, the shrinkage ratio of satellite covering material ranges from [1, 1.5]. The calculation method for B is the same as that for A, except that the original length and the length after folding are the lengths in the Y direction.

[0011] Step 4. Statistical analysis function for the distribution of material folded fragments: f(u, v), where u is the tangent of the angle between the normal angle of the folded fragment and the YZ plane, and v is the tangent of the angle between the normal angle of the fragment and the XZ plane. According to statistical laws, f(u, v) satisfies a two-dimensional normal distribution. Where σ1 and σ2 are the standard deviations of the probability distributions of u and v in the X and Y directions;

[0012] Step 5. Based on the fragment tilt angle, deflect the unwrinkled material BRDF to obtain the reflectivity r(a, α, β, u, v) of the wrinkled fragment. The specific calculation formula is as follows:

[0013] r(a,α,β,u,v)=R(a,α-2actan(u),β-actan(v));

[0014] Step 6. Discretize the probability distribution function obtained in Step 4. Using u = ±3σ1 and v = ±3σ2 as boundaries, discretize the values ​​of u and v in the X and Y directions into M and N parts respectively, according to u = (m - 0.5 * M)6σ1 / M and v = (n - 0.5 * N)6σ1 / N, where (m, n) are the indexes of the angle intervals in the X and Y directions, taking integer values ​​from 1 to M and 1 to N respectively. Iterate through the values ​​of m and n, and substitute them into the normal distribution formula mentioned in Step 4 to calculate the area proportion coefficient F(m, n) of all folded fragments within the ranges of ±3σ1 and ±3σ2 for u and v.

[0015] Step 7. Multiply the reflectivity value of the facet at the corresponding angle calculated in Step 5 by the area ratio coefficient obtained in Step 6 to obtain the reflection contribution rate I of the folded fragment at the corresponding angle. m，n Then, the reflectivity model R of the entire surface after wrinkling is obtained by summing. 褶皱 (a, α, β).

[0016] In step 2, most of the coating materials have isotropic reflectivity, the angle α of the incident light ranges from 0° to 90°, the value of α ranges from -90° to 90°, and the value of β ranges from -90° to 90°.

[0017] In step 3, the reduction ratios A and B of the length in the two directions after the material is folded are independent of each other and can be obtained by dividing the measured values ​​of the material in the X and Y directions before folding by the measured values ​​of the material in the X and Y directions after folding.

[0018] In step 4, σ1 and σ2 are related to the values ​​of A and B in step 3, and the equation is solved as follows:

[0019]

[0020]

[0021] Beneficial effects

[0022] 1) This invention provides a method for accurately estimating the BRDF coefficient under target folding conditions when the BRDF coefficient is known;

[0023] 2) It can provide data support for target modeling and simulation as well as light scattering analysis;

[0024] 3) This invention can accurately predict the BRDF parameters of the material after the target wrinkles without repeatedly measuring the material in different states;

[0025] 4) Restricting the range of values ​​for u and v helps simplify calculations;

[0026] 5) BRDF model of the material after folding褶皱 (a, α, β) can be converted into other models, making it convenient to use without affecting the scattering results.

[0027] 6) This invention has a short calculation time and high model accuracy. Attached Figure Description

[0028] Figure 1 Schematic diagram of cross-section of material folding results

[0029] Figure 2 Schematic diagram of incident angle and observation angle

[0030] Figure 3 Schematic diagram defining the angle of wrinkled fragments

[0031] Figure 4 Flowchart of the method of this invention Detailed Implementation

[0032] This invention provides a method for modeling the visible light bidirectional scattering distribution function of wrinkled coated materials, such as... Figure 1 The flat material shown will be shorter after being folded on the cross-section shown. The length reduction ratio L / l before and after folding is measured. It is assumed that the length reduction ratio is the same in all directions under random rubbing.

[0033] like Figure 2 As shown, 101 is the incident light direction and 102 is the detection direction. Since the material is isotropic, rotating the material along the normal direction does not affect the overall scattering characteristics of the material. Let the incident direction and the normal of the base plane form the XZ plane. The YZ plane is determined according to the right-hand screw rule. a is the incident angle direction, α is the angle between the measurement direction and the XZ plane, and β is the angle between the measurement direction and the YZ plane. The BRDF model R(a, α, β) of the material based on a, α, β can be found by measurement or by looking up a table.

[0034] like Figure 3 As shown, 203 is the normal direction of the folded fragment, 201 is the angle between the normal direction and the XZ plane, and 202 is the angle between the normal direction and the YZ plane. Find the tangents of the two angles 201 and 202 to obtain u and v, and establish a two-dimensional normal distribution. The equation f(u, v) only describes the proportion of area covered by the wrinkled fragments at different tilt angles, and does not reflect the specific location of the fragments, which is consistent with the randomness of the surface after material wrinkling. Where σ1 and σ2 are the standard deviations of the probability distributions of u and v in the X and Y directions, respectively; based on the length shortening ratio L / l and the formula... By determining σ1 and σ2, the specific values ​​of the area of ​​the folded fragments at different dip angles can be calculated; A and B are the general case, and in this example, it is assumed that A and B are equal.

[0035] For ease of calculation, the range of values ​​for u and v is restricted, with u = ±3σ1 and v = ±3σ2 set as boundaries. The tilt angle is discretized, and M and N parts are discretized for the X and Y directions respectively, to obtain the calculation formula for discretizing the area of ​​folded fragments in different orientations. Each part is calculated according to u = (m - 0.5 * M) 6σ1 / M and v = (n - 0.5 * N) 6σ1 / N. The area ratio coefficient of all folded fragments in the range of ±3σ1 and ±3σ2 is calculated by substituting u = (m - 0.5 * M) 6σ1 / M and v = (n - 0.5 * N) 6σ1 / N into the two-dimensional normal distribution formula obtained in the previous step. Then, a normal distribution function F(m, n) based on the index m and n is established.

[0036] Based on the fragment tilt angle, the BRDF of the unwrinkled material is deflected to obtain the approximate reflectance value of the wrinkled fragment relative to the base coordinate system as r(a, α, β, m, n) = R(a, α - 2actan((m - 0.5*M)6σ1 / M), β - actan((n - 0.5*N)6σ1 / N)). The reflectance of the wrinkled fragments of the facet is obtained by iterating through all angles and using the formula...

[0037]

[0038] The BRDF model R of the wrinkled material can be calculated. 褶皱 (a, α, β) This model can be converted into other models for easy use without affecting the scattering results.

Claims

1. A method of modeling the visible bidirectional scattering distribution function of a pleated wrap material, the method comprising: Includes the following steps, ​ 1) Obtain BRDF data for the unwrinkled covering material; 2) Solve for the length reduction ratios A and B in the X and Y directions of the satellite surface covering material under flat conditions compared to under wrinkled conditions; 3) Establish the distribution statistical analysis function f(u, v) of the material fold fragment area ratio coefficient, where u is the tangent of the angle between the normal angle of the fold fragment and the YZ plane, and v is the tangent of the angle between the normal angle of the fragment and the XZ plane. 4) Deflect the unwrinkled BRDF according to the tilt angles u and v to obtain the fragment reflectivity values ​​relative to the base coordinate system; 5) Discretize u and v and substitute them into the analysis function f(u, v) to obtain the area ratio coefficient F(m, n) of all folded fragments. 6) The reflectance of any orientation fragment multiplied by the corresponding area fraction coefficient to get the reflectance contribution of that fragment Then the reflectance contribution of all the folded fragments is accumulated to get the reflectance model of the whole cladding material. The statistical analysis function f(u, v) for the distribution of material fold fragments satisfies a two-dimensional normal distribution, as follows: ， wherein are the standard deviations of the probability distribution of u and v in the X and Y directions, respectively; With the values of A and B, the equation is solved as: ， 。 2. The method of claim 1, wherein: Obtaining BRDF data for the material before wrinkling further includes the following steps: Step 1. Set the satellite surface to which the covering material is attached as the base plane. The covering material is a complex plane composed of countless small pieces attached to the base plane. Construct a coordinate system with the incident light and the base plane, with the base normal as the Z-axis and the direction of the incident light in the base plane as the X-axis. Determine the Y-axis according to the right-hand rule. The normal direction of each fragment is (u, v), where u is the tangent of the angle between the normal angle of the folded fragment and the YZ plane, and v is the tangent of the angle between the normal angle of the fragment and the XZ plane. Step 2. Measure the BRDF of the flat covering material to obtain the standard BRDF data of the material. The format of the BRDF data is R(a, α, β), where a is the angle between the incident direction of the light and the Z-axis, α is the angle between the observation direction and the XZ plane described in Step 1, and β is the angle between the observation direction and the YZ plane described in Step 1.

3. The method for modeling the visible light two-way scattering distribution function of a wrinkled coated material according to claim 1, characterized in that: The method for calculating the length reduction ratio A in the X direction is as follows: Let the original length of the satellite surface wrinkle covering material under the condition of flatness in the X direction be... The length of the wrinkled coating material on the satellite surface in the X direction is... Then there is .

4. A method for modeling the visible light bidirectional scattering distribution function of a wrinkled coated material according to claim 1 or 3, characterized in that: The calculation method for B is the same as that for A, except that the original length and the length after folding are the lengths in the Y direction.

5. The method for modeling the visible light bidirectional scattering distribution function of a wrinkled coated material according to claim 2, characterized in that: The reflectance values of the creased fragments The specific calculation formula is as follows: 。 6. The method for modeling the visible light two-way scattering distribution function of a wrinkled coated material according to claim 1, characterized in that: The process of obtaining the area proportion coefficient F(m,n) of the wrinkled fragment is as follows: with u= and As the boundary, the values ​​of u and v are discretized into M and N parts in the X and Y directions respectively, and then processed according to... , (m, n) are the indices of the angle intervals in the X and Y directions, taking integer values ​​from 1 to M and 1 to N respectively; by iterating through the values ​​of m and n and substituting them into the distribution statistical analysis function f(u, v), the values ​​of u and v in the intervals are calculated. and The area ratio coefficient F(m, n) of all folded fragments within the range.

7. The method for modeling the visible light two-way scattering distribution function of a wrinkled coated material according to claim 2, characterized in that: The angle a of the incident light ranges from 0° to 90°, The angle a of the incident light ranges from 0° to 90°, The angle a of the incident light ranges from 0° to 90°.

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