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CN101901302A - Light Scattering Modeling Method for Complex Space Objects - Google Patents

Light Scattering Modeling Method for Complex Space Objects Download PDF

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Publication number
CN101901302A
CN101901302A CN 201010228868 CN201010228868A CN101901302A CN 101901302 A CN101901302 A CN 101901302A CN 201010228868 CN201010228868 CN 201010228868 CN 201010228868 A CN201010228868 A CN 201010228868A CN 101901302 A CN101901302 A CN 101901302A
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effective
light scattering
incident
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蓝朝桢
徐青
孙伟
李建胜
周杨
邢帅
何钰
张衡
施群山
靳国旺
马东洋
王栋
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PLA Information Engineering University
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Abstract

本发明涉及复杂空间目标光散射建模方法，属于航天空间目标建模技术领域，本发明首先根据材料的综合光散射强度，建立材料光散射经验模型；采用平行投影变换获得空间目标的入射截面，并判断选出有效入射截面；根据材料光散射经验模型，统计绘制的有效入射截面上像素的反射率均值得到平均反射率ρ；根据有效入射截面像素总个数与绘制窗口的面积比例关系，求得有效入射截面面积S；建立复杂空间目标光散射模型P＝ρE0S；本发明在考虑了材料非相干散射特性和相干散射特性的基础上，根据光线实际传播特性，将三维空间的复杂计算投影到二维平面，并利用计算机图形学理论实现了有效入射截面和截面平均反射率的快速确定，较好的解决了复杂空间目标的光散射计算问题。

Figure 201010228868

The invention relates to a light scattering modeling method for complex space objects, which belongs to the technical field of aerospace space object modeling. The invention firstly establishes an empirical model of light scattering of materials according to the comprehensive light scattering intensity of materials; adopts parallel projection transformation to obtain the incident section of space objects, And judge and select the effective incident section; according to the material light scattering empirical model, the average reflectance ρ of the pixels on the effective incident section is statistically drawn to obtain the average reflectance ρ; according to the relationship between the total number of pixels in the effective incident section and the area ratio of the drawing window, find The effective incident cross-sectional area S is obtained; the complex space object light scattering model P=ρE 0 S is established; the present invention considers the incoherent scattering characteristics and coherent scattering characteristics of materials, and according to the actual propagation characteristics of light, the complex calculation of three-dimensional space Projected to a two-dimensional plane, and using computer graphics theory to realize the rapid determination of the effective incident section and the average reflectance of the section, and better solve the problem of light scattering calculation of complex space targets.

Figure 201010228868

Description

复杂空间目标光散射建模方法 Light Scattering Modeling Method for Complex Space Objects

技术领域technical field

本发明涉及复杂空间目标光散射建模方法，属于航天空间目标建模技术领域。The invention relates to a complex space object light scattering modeling method, belonging to the technical field of aerospace space object modeling.

背景技术Background technique

空间目标的光学特性分析，是目标的光学探测、识别的前提，空间目标光散射特性是光学特性的重要内容，正受到越来越多的关注。很多学者在这方面开展了大量研究工作，综合起来，其方法集中在以下两个方面：一是将空间目标看成由几种典型形状的漫反射朗伯表面，根据辐射理论和朗伯余弦定律，计算其在空间的光照度；二是利用实际测量的材料样片精确的双向反射分布函数(BRDF)，基于物理模型的方法来计算目标的光散射特性。第一种方法模型简单，计算结果与实际情况相差较大，只能用于光散射特性的估算；第二种方法可以精确计算材料的光散射特性，但获取、表示与计算的复杂性，限制了其在工程领域的应用。已有的研究工作，大多都将空间目标假设成简单形状，而对于具有复杂几何形体的空间目标的光散射的计算，都没有提出很好的解决方法。The analysis of optical characteristics of space targets is the premise of optical detection and identification of targets. Light scattering characteristics of space targets are an important part of optical properties and are receiving more and more attention. Many scholars have carried out a lot of research work in this area. In summary, their methods focus on the following two aspects: one is to regard the space target as a diffuse reflection Lambertian surface with several typical shapes. According to the radiation theory and Lambert's cosine law, Calculate its illuminance in space; the second is to use the accurate bidirectional reflectance distribution function (BRDF) of the actual measured material sample to calculate the light scattering characteristics of the target based on the method of physical model. The first method has a simple model, and the calculation results are quite different from the actual situation, so it can only be used to estimate the light scattering characteristics; the second method can accurately calculate the light scattering characteristics of materials, but the complexity of acquisition, representation and calculation is limited. its application in engineering field. Most of the existing research work assumes that the space object is a simple shape, but for the calculation of the light scattering of the space object with complex geometric shapes, no good solution has been proposed.

发明内容Contents of the invention

本发明的目的是提供一种复杂空间目标光散射建模方法，以解决现有复杂空间目标建模方法精确度与计算复杂性矛盾的问题。The object of the present invention is to provide a complex space target light scattering modeling method to solve the problem of the contradiction between the accuracy and calculation complexity of the existing complex space target modeling method.

为实现上述目的，本发明的复杂空间目标光散射建模方法的步骤如下：In order to achieve the above object, the steps of the complex space object light scattering modeling method of the present invention are as follows:

（1）根据材料的综合光散射强度，建立材料光散射经验模型；(1) According to the comprehensive light scattering intensity of the material, an empirical model of material light scattering is established;

（2）采用平行投影变换获得空间目标的入射截面，并判断选出有效入射截面；(2) Use parallel projection transformation to obtain the incident section of the space target, and judge and select the effective incident section;

（3）根据材料光散射经验模型，统计绘制的有效入射截面上像素的反射率均值得到平均反射率

Figure 64545DEST_PATH_IMAGE001
；(3) According to the empirical model of material light scattering, the average reflectance of the pixels on the effective incident section is statistically drawn to obtain the average reflectance
Figure 64545DEST_PATH_IMAGE001
;

（4）根据有效入射截面像素总个数与绘制窗口的面积比例关系，求得有效入射截面面积

Figure 612070DEST_PATH_IMAGE002
；(4) According to the relationship between the total number of pixels in the effective incident section and the area ratio of the drawing window, the effective incident section area is obtained
Figure 612070DEST_PATH_IMAGE002
;

（5）建立复杂空间目标光散射模型

Figure 999189DEST_PATH_IMAGE003
，式中
Figure 306674DEST_PATH_IMAGE004
为太阳在空间目标处的照度；
Figure 197269DEST_PATH_IMAGE002
为有效入射截面的面积；为截面上的平均反射率。(5) Establish light scattering model of complex space target
Figure 999189DEST_PATH_IMAGE003
, where
Figure 306674DEST_PATH_IMAGE004
is the illuminance of the sun at the space target;
Figure 197269DEST_PATH_IMAGE002
is the area of the effective incident cross-section; is the average reflectance of the cross section.

进一步的，所述步骤（1）中材料的综合光散射强度为漫反射分量和镜面反射总和，表示为

Figure 229259DEST_PATH_IMAGE006
，其中
Figure 402751DEST_PATH_IMAGE007
为物体的漫反射系数，与物体表面性质有关；
Figure 600383DEST_PATH_IMAGE008
是光源的光强；
Figure 568339DEST_PATH_IMAGE009
为光线入射角；
Figure 602154DEST_PATH_IMAGE010
为物体的镜面反射系数，为视线与反射方向的夹角。Further, the comprehensive light scattering intensity of the material in the step (1) is the sum of the diffuse reflection component and the specular reflection, expressed as
Figure 229259DEST_PATH_IMAGE006
,in
Figure 402751DEST_PATH_IMAGE007
is the diffuse reflection coefficient of the object, which is related to the surface properties of the object;
Figure 600383DEST_PATH_IMAGE008
is the light intensity of the light source;
Figure 568339DEST_PATH_IMAGE009
is the incident angle of light;
Figure 602154DEST_PATH_IMAGE010
is the specular reflection coefficient of the object, is the angle between the line of sight and the reflection direction.

进一步的，所述步骤（1）中材料光散射经验模型为Further, the material light scattering empirical model in the step (1) is

Figure 861502DEST_PATH_IMAGE012
，其中为综合反射率，是当光线以
Figure 521471DEST_PATH_IMAGE009
角入射到某材料表面上时，在
Figure 771186DEST_PATH_IMAGE014
方向上的反射光强与入射光强之比。
Figure 861502DEST_PATH_IMAGE012
,in is the integrated reflectance, which is when the light is
Figure 521471DEST_PATH_IMAGE009
When the angle is incident on a material surface, the
Figure 771186DEST_PATH_IMAGE014
The ratio of the reflected light intensity to the incident light intensity in a direction.

进一步的，所述步骤（2）中空间目标入射截面的获得是在OpenGL中，利用函数glOrtho(l,r,b,t,n,f)完成平行投影变换，函数参数为平行投影的左右、上下和远近裁剪面，用这些参数计算投影区域的实际面积

Figure 943411DEST_PATH_IMAGE015
，再用函数glViewport(x,y,w,h)将投影变换后的左边变换到屏幕像素坐标，参数（x,y）为视口左下角坐标，（w,h）为窗口大小，取x=y=0，则整个显示窗口的像素总数为
Figure 253169DEST_PATH_IMAGE016
。Further, the acquisition of the incident cross section of the space object in the step (2) is in OpenGL, using the function glOrtho(l, r, b, t, n, f) to complete the parallel projection transformation, and the function parameters are the left and right of the parallel projection, Top and bottom and far and near clipping planes, use these parameters to calculate the actual area of the projection area
Figure 943411DEST_PATH_IMAGE015
, and then use the function glViewport(x, y, w, h) to transform the left side after projection transformation to the screen pixel coordinates, the parameter (x, y) is the coordinate of the lower left corner of the viewport, (w, h) is the window size, take x =y=0, the total number of pixels in the entire display window is
Figure 253169DEST_PATH_IMAGE016
.

进一步的，所述步骤（2），在绘制入射截面时，在GPU片元着色器中，进行有效截面判断，剔除不满足判断条件的截面点；对满足有效截面条件的点，根据材料的材质属性，在GPU着色器中对每一个像素代表的截面元反射率经验模型进行计算，形成反射率分布图。Further, in the step (2), when drawing the incident section, in the GPU fragment shader, the effective section judgment is performed, and the section points that do not meet the judgment condition are eliminated; for the points that meet the effective section condition, according to the material of the material attribute, in the GPU shader, the empirical model of the reflectance of the section element represented by each pixel is calculated to form a reflectance distribution map.

进一步的，所述有效截面是在入射截面中能反射光线到观测方向的部分，当光源方向L与观测方向V确定时，当面元dA的法线N满足于L和V的夹角都小于90度时，该面被光线照射，并且能反射光线到观测设备，该有效截面的判断条件用向量内积表示为：

Figure 261576DEST_PATH_IMAGE017
。Further, the effective section is the part that can reflect light to the observation direction in the incident section. When the light source direction L and the observation direction V are determined, when the normal line N of the surface element dA satisfies that the angle between L and V is less than 90° When the degree is , the surface is illuminated by light and can reflect light to the observation equipment. The judgment condition of the effective section is expressed by the vector inner product as:
Figure 261576DEST_PATH_IMAGE017
.

进一步的，所述反射率分布图由空间目标有效入射截面上每一个像素的反射率构成的二维图像，用模型数据中的漫反射与镜面反射参数为每一个三角形的材质赋值，在OpenGL片元着色器中根据光源属性、材质属性以及几何关系，利用式Further, the reflectance distribution map is a two-dimensional image composed of the reflectance of each pixel on the effective incident section of the space object, and the diffuse reflection and specular reflection parameters in the model data are used to assign values to the materials of each triangle, and the OpenGL sheet In the element shader, according to the light source properties, material properties and geometric relations, the formula

，完成对入射截面上每一个像素反射率的计算，模型绘制完毕后，就构成了整个空间目标的反射率分布图。 , to complete the calculation of the reflectance of each pixel on the incident section, and after the model is drawn, the reflectance distribution map of the entire space object is formed.

 进一步的，所述步骤（3）中平均反射率

Figure 843179DEST_PATH_IMAGE018
是将反射率分布图上每一个像素的反射率求和，并除以有效像素总数
Figure 323839DEST_PATH_IMAGE019
得到。Further, the average reflectance in the step (3)
Figure 843179DEST_PATH_IMAGE018
It is to sum the reflectance of each pixel on the reflectance distribution map and divide it by the total number of effective pixels
Figure 323839DEST_PATH_IMAGE019
get.

进一步的，所述步骤（4）中有效入射截面面积的计算公式如下：

Figure 411060DEST_PATH_IMAGE020
，其中有效像素总数为。Further, the effective incident cross-sectional area in the step (4) The calculation formula is as follows:
Figure 411060DEST_PATH_IMAGE020
, where the total number of effective pixels is .

本发明的方法在考虑了材料非相干散射特性和相干散射特性的基础上，根据光线实际传播特性，提出了一种复杂空间目标光散射建模方法，将三维空间的复杂计算投影到二维平面，并利用计算机图形学理论实现了有效入射截面和截面平均反射率的快速确定，较好的解决了复杂空间目标的光散射计算问题。In the method of the present invention, on the basis of considering the incoherent scattering characteristics and coherent scattering characteristics of materials, according to the actual propagation characteristics of light, a complex space object light scattering modeling method is proposed, and the complex calculation of three-dimensional space is projected to a two-dimensional plane , and using the theory of computer graphics to realize the rapid determination of the effective incident section and the average reflectance of the section, and better solve the problem of light scattering calculation of complex space objects.

本发明所建立的材料光散射经验模型比单纯采用漫反射模型来表示空间目标材料更具有合理性，其中，漫反射系数

Figure 943859DEST_PATH_IMAGE007
、镜面反射系数
Figure 926858DEST_PATH_IMAGE021
、镜面反射指数与材料本身特性有关，可以用这三个参数近似表达材料的光散射特性，并且相对于基于物理模型的BRDF方法，在效果接近的情况下，简化了表示与计算的复杂性，使其更加灵活方便。The material light scattering empirical model established by the present invention is more reasonable than simply using the diffuse reflection model to represent the space target material, wherein the diffuse reflection coefficient
Figure 943859DEST_PATH_IMAGE007
, Specular reflection coefficient
Figure 926858DEST_PATH_IMAGE021
, specular index Related to the characteristics of the material itself, these three parameters can be used to approximate the light scattering characteristics of the material, and compared with the BRDF method based on the physical model, when the effect is close, the complexity of representation and calculation is simplified, making it more flexible convenient.

所述

Figure 559276DEST_PATH_IMAGE005
为有效截面上每一个
Figure 585001DEST_PATH_IMAGE023
对应的目标表面微元
Figure 852034DEST_PATH_IMAGE024
的反射率的均值，由于目标具有复杂的构型，入射截面上的一个微元
Figure 237885DEST_PATH_IMAGE023
可能是多个目标表面微面元的投影，而不同
Figure 837811DEST_PATH_IMAGE024
由于材料不同，反射率也不同，这为
Figure 17567DEST_PATH_IMAGE023
的反射率
Figure 540953DEST_PATH_IMAGE013
的确定造成了困难，考察光的传播过程发现，当一条光线入射到空间目标表面时，在光线传播方向上第一个与光线相交的面为受晒面，其后的面都会由于遮挡产生阴影，即对于一条入射光线，只有距离光源最近的面才对反射能量有贡献，因此本发明
Figure 908480DEST_PATH_IMAGE024
取距离光源最近的面元，既确定了
Figure 884526DEST_PATH_IMAGE023
的反射率
Figure 612180DEST_PATH_IMAGE013
，又有效防止了被遮挡的阴影部分参与计算。said
Figure 559276DEST_PATH_IMAGE005
for each effective section
Figure 585001DEST_PATH_IMAGE023
Corresponding target surface microelements
Figure 852034DEST_PATH_IMAGE024
The mean value of the reflectivity of the target, because the target has a complex configuration, a microelement on the incident section
Figure 237885DEST_PATH_IMAGE023
May be multiple target surface microfacets projection of different
Figure 837811DEST_PATH_IMAGE024
Due to the different materials, the reflectivity is also different, which is
Figure 17567DEST_PATH_IMAGE023
reflectivity
Figure 540953DEST_PATH_IMAGE013
The determination of the ray has caused difficulties. It is found that when a ray of light is incident on the surface of a space object, the first surface that intersects with the ray in the direction of ray propagation is the irradiated surface, and the subsequent surfaces will produce shadows due to occlusion. , that is, for an incident ray, only the surface closest to the light source contributes to the reflected energy, so the present invention
Figure 908480DEST_PATH_IMAGE024
Take the surface element closest to the light source, and determine
Figure 884526DEST_PATH_IMAGE023
reflectivity
Figure 612180DEST_PATH_IMAGE013
, and effectively prevent the occluded shadow part from participating in the calculation.

附图说明Description of drawings

图1是本发明的复杂空间目标光散射建模流程图；Fig. 1 is the complex space target light scattering modeling flowchart of the present invention;

图2是入射、反射、视线方向示意图；Figure 2 is a schematic diagram of incident, reflection, and line of sight directions;

图3是镜面反射曲线图；Fig. 3 is a specular reflection curve;

图4是Qiuckbird-2卫星几何外形结构图；Fig. 4 is a geometrical structure diagram of the Qiuckbird-2 satellite;

图5是观测条件曲线图；Fig. 5 is a graph of observation conditions;

图6(a)是总入射截面图；Figure 6(a) is a total incident cross-sectional view;

图6(b)是有效入射截面图；Figure 6(b) is an effective incident sectional view;

图7是有效入射截面与总入射截面比较图；Figure 7 is a comparison diagram of the effective incident cross section and the total incident cross section;

图8是目标反射率图；Fig. 8 is a target reflectivity figure;

图9是目标平均反射率变化曲线图；Fig. 9 is a curve diagram of target average reflectance variation;

图10是反射光通量变化曲线图。Fig. 10 is a graph showing changes in reflected luminous flux.

具体实施方式Detailed ways

本发明的复杂空间目标光散射建模方法实施例的流程图如图1所示，步骤如下：The flow chart of the embodiment of the complex space object light scattering modeling method of the present invention is shown in Figure 1, and the steps are as follows:

（1）根据材料的综合光散射强度，建立材料光散射经验模型；(1) According to the comprehensive light scattering intensity of the material, an empirical model of material light scattering is established;

（2）采用平行投影变换获得空间目标的入射截面，并判断选出有效入射截面；(2) Use parallel projection transformation to obtain the incident section of the space target, and judge and select the effective incident section;

（3）根据材料光散射经验模型，统计绘制的有效入射截面上像素的反射率均值得到平均反射率；(3) According to the empirical model of material light scattering, the average reflectance of the pixels on the effective incident section is statistically drawn to obtain the average reflectance ;

（4）根据有效入射截面像素总个数与绘制窗口的面积比例关系，求得有效入射截面面积

Figure 528500DEST_PATH_IMAGE002
；(4) According to the relationship between the total number of pixels in the effective incident section and the area ratio of the drawing window, the effective incident section area is obtained
Figure 528500DEST_PATH_IMAGE002
;

（5）建立复杂空间目标光散射模型

Figure 257422DEST_PATH_IMAGE003
，式中
Figure 42230DEST_PATH_IMAGE004
为太阳在空间目标处的照度；
Figure 540207DEST_PATH_IMAGE002
为有效入射截面的面积；
Figure 983958DEST_PATH_IMAGE005
为截面上的平均反射率。(5) Establish light scattering model of complex space target
Figure 257422DEST_PATH_IMAGE003
, where
Figure 42230DEST_PATH_IMAGE004
is the illuminance of the sun at the space target;
Figure 540207DEST_PATH_IMAGE002
is the area of the effective incident cross-section;
Figure 983958DEST_PATH_IMAGE005
is the average reflectance of the cross section.

1材料光散射经验模型1 Material Light Scattering Empirical Model

无论是空间目标主体包覆材料还是太阳能板的光散射一般均存在非相干散射分量（又称漫反射）和相干散射分量（又称镜面反射）。因此，要实现空间目标光散射特性的精确计算，必须建立空间目标表面材料的漫反射与镜面反射特性模型。由于光线满足叠加性，因此，在假设目标表面的散射特性与波长无关的前提下，将漫反射光与镜面反射光分别考虑。Whether it is the cladding material of the space target body or the light scattering of the solar panel, there are generally incoherent scattering components (also known as diffuse reflection) and coherent scattering components (also known as specular reflection). Therefore, in order to realize the accurate calculation of the light scattering characteristics of the space target, it is necessary to establish a model of the diffuse reflection and specular reflection characteristics of the surface material of the space target. Since the light satisfies the superposition property, on the premise that the scattering characteristics of the target surface are independent of the wavelength, the diffuse reflection light and the specular reflection light are considered separately.

1.1 漫反射模型1.1 Diffuse reflection model

当入射光从一个完全不光滑的表面向所有方向等量散射时出现漫反射现象。假设材料中漫反射光的空间分布是均匀的，根据Lambert余弦定律，反射光强与入射角的余弦成正比。因此，反射光强

Figure 387127DEST_PATH_IMAGE025
可以表示为
Figure 269632DEST_PATH_IMAGE026
 ，式中
Figure 559799DEST_PATH_IMAGE007
为物体的漫反射系数，与物体表面性质有关。
Figure 502347DEST_PATH_IMAGE008
是光源的光强。
Figure 628697DEST_PATH_IMAGE009
为光线入射角，如图2所示。Diffuse reflection occurs when incident light is scattered equally in all directions from a completely matte surface. Assuming that the spatial distribution of diffuse light in the material is uniform, according to Lambert's cosine law, the reflected light intensity is proportional to the cosine of the incident angle. Therefore, the reflected light intensity
Figure 387127DEST_PATH_IMAGE025
It can be expressed as
Figure 269632DEST_PATH_IMAGE026
, where
Figure 559799DEST_PATH_IMAGE007
It is the diffuse reflection coefficient of the object, which is related to the surface properties of the object.
Figure 502347DEST_PATH_IMAGE008
is the light intensity of the light source.
Figure 628697DEST_PATH_IMAGE009
is the incident angle of light, as shown in Figure 2.

1.2 镜面反射模型1.2 Specular reflection model

对于材料的镜面反射模型，学者们提出了基于物理的镜面反射模型（如BRDF）和基于经验的镜面反射模型，由于基于物理的模型计算复杂，实现难度大，且通过调整经验模型的参数，可获得比基于物理的模型更好的效果。本发明采用经验镜面反射模型，可表示为 

Figure 986997DEST_PATH_IMAGE027
，式中
Figure 459567DEST_PATH_IMAGE010
为物体的镜面反射系数，
Figure 494388DEST_PATH_IMAGE028
为视线与反射方向的夹角，如图2所示。
Figure 357302DEST_PATH_IMAGE029
为经验镜面反射模型，描述了镜面反射光的空间分布。参数
Figure 581610DEST_PATH_IMAGE022
为材料镜面反射指数，控制了镜面的光滑程度。如图3所示，当
Figure 597101DEST_PATH_IMAGE022
越大，曲线越陡，表示反射光越集中在反射方向附近，说明表面越光滑。For the specular reflection model of materials, scholars have proposed a specular reflection model based on physics (such as BRDF) and a specular reflection model based on experience. Due to the complex calculation of the physics-based model, it is difficult to realize, and by adjusting the parameters of the empirical model, it can be Get better results than physically based models. The present invention adopts the empirical specular reflection model, which can be expressed as
Figure 986997DEST_PATH_IMAGE027
, where
Figure 459567DEST_PATH_IMAGE010
is the specular reflection coefficient of the object,
Figure 494388DEST_PATH_IMAGE028
is the angle between the line of sight and the reflection direction, as shown in Figure 2.
Figure 357302DEST_PATH_IMAGE029
An empirical specular reflection model that describes the spatial distribution of specularly reflected light. parameter
Figure 581610DEST_PATH_IMAGE022
It is the specular index of the material, which controls the smoothness of the specular surface. As shown in Figure 3, when
Figure 597101DEST_PATH_IMAGE022
The larger the value, the steeper the curve, indicating that the reflected light is more concentrated near the reflection direction, indicating that the surface is smoother.

1.3 材料光散射经验模型1.3 Empirical model of material light scattering

材料的光散射强度为漫反射分量和镜面反射总和。表示为

Figure 819135DEST_PATH_IMAGE030
，定义综合反射率
Figure 418613DEST_PATH_IMAGE013
为当光线以
Figure 118716DEST_PATH_IMAGE031
角入射到某材料表面上时，在
Figure 300298DEST_PATH_IMAGE011
方向上的反射光强与入射光强之比，即
Figure 443966DEST_PATH_IMAGE032
，该式为材料光散射经验模型。其中，是漫反射系数，
Figure 847582DEST_PATH_IMAGE034
为镜面反射系数，
Figure 70622DEST_PATH_IMAGE022
是镜面反射指数。材料光散射经验模型反映了材料的非相干散射特性和相干散射特性，为了保证能量守恒要求。该模型比单纯采用漫反射模型[2]来表示空间目标材料更具有合理性。其中，漫反射系数
Figure 21578DEST_PATH_IMAGE033
、镜面反射系数
Figure 125800DEST_PATH_IMAGE010
、镜面反射指数与材料本身特性有关，即在经验模型的基础上，可以用这三个参数近似表达材料的光散射特性，相对于基于物理模型的BRDF方法，在效果接近的情况下，简化了表示与计算的复杂性，使其更加灵活方便。The light scattering intensity of a material is the sum of the diffuse component and the specular component. Expressed as
Figure 819135DEST_PATH_IMAGE030
, defining the integrated reflectance
Figure 418613DEST_PATH_IMAGE013
for when the light
Figure 118716DEST_PATH_IMAGE031
When the angle is incident on a material surface, the
Figure 300298DEST_PATH_IMAGE011
The ratio of the reflected light intensity to the incident light intensity in the direction is
Figure 443966DEST_PATH_IMAGE032
, which is an empirical model of material light scattering. in, is the diffuse reflection coefficient,
Figure 847582DEST_PATH_IMAGE034
is the specular reflection coefficient,
Figure 70622DEST_PATH_IMAGE022
is the specular index. The material light scattering empirical model reflects the incoherent scattering characteristics and coherent scattering characteristics of the material, in order to ensure the energy conservation requirements . This model is more reasonable than simply using the diffuse reflection model [2] to represent space target materials. Among them, the diffuse reflection coefficient
Figure 21578DEST_PATH_IMAGE033
, Specular reflection coefficient
Figure 125800DEST_PATH_IMAGE010
, specular index It is related to the characteristics of the material itself, that is, on the basis of the empirical model, these three parameters can be used to approximate the light scattering characteristics of the material. Compared with the BRDF method based on the physical model, it simplifies the expression and calculation when the effect is close. complexity, making it more flexible and convenient.

2 复杂空间目标光散射模型2 Light scattering model of complex space target

     假设太阳在空间目标处产生的光照度为

Figure 761586DEST_PATH_IMAGE004
，则入射截面上的面元
Figure 308105DEST_PATH_IMAGE023
（对于空间目标表面面元为
Figure 481597DEST_PATH_IMAGE024
），则该面元接收的光通量为
Figure 679229DEST_PATH_IMAGE036
，当入射光经过截面为
Figure 647185DEST_PATH_IMAGE023
对应的表面
Figure 681000DEST_PATH_IMAGE024
后反射，根据材料的光散射经验模型，其反射光通量为
Figure 127025DEST_PATH_IMAGE037
，空间目标总反射通量为入射截面元反射通量在整个截面上的积分，表示为，其离散形式为
Figure 22748DEST_PATH_IMAGE039
，当取截面面元
Figure 606176DEST_PATH_IMAGE023
为常数时，令
Figure 42842DEST_PATH_IMAGE040
，上式可表示成，令截面平均反射率
Figure 337875DEST_PATH_IMAGE042
，则反射光通量
Figure 346282DEST_PATH_IMAGE043
为，
Figure 88104DEST_PATH_IMAGE044
，该式即为推导的基于截面积分的复杂空间目标光散射模型，式中
Figure 927884DEST_PATH_IMAGE004
为太阳在空间目标处的照度，为已知量；为有效入射截面的面积；
Figure 638668DEST_PATH_IMAGE018
为截面上的平均反射率。Suppose the illuminance produced by the sun at the space target is
Figure 761586DEST_PATH_IMAGE004
, then the surface element on the incident section
Figure 308105DEST_PATH_IMAGE023
(For the spatial object surface surfel is
Figure 481597DEST_PATH_IMAGE024
), then the luminous flux received by the surface element is
Figure 679229DEST_PATH_IMAGE036
, when the incident light passes through a cross section of
Figure 647185DEST_PATH_IMAGE023
corresponding surface
Figure 681000DEST_PATH_IMAGE024
Back reflection, according to the light scattering empirical model of the material, the reflected luminous flux is
Figure 127025DEST_PATH_IMAGE037
, the total reflected flux of the space target is the integral of the reflected flux of the incident section element on the whole section, expressed as , whose discrete form is
Figure 22748DEST_PATH_IMAGE039
, when taking the section surface element
Figure 606176DEST_PATH_IMAGE023
When is a constant, let
Figure 42842DEST_PATH_IMAGE040
, the above formula can be expressed as , so that the cross-sectional average reflectance
Figure 337875DEST_PATH_IMAGE042
, the reflected luminous flux
Figure 346282DEST_PATH_IMAGE043
for,
Figure 88104DEST_PATH_IMAGE044
, which is the deduced light scattering model for complex space objects based on cross-section integrals, where
Figure 927884DEST_PATH_IMAGE004
is the illuminance of the sun at the space target, which is a known quantity; is the area of the effective incident cross-section;
Figure 638668DEST_PATH_IMAGE018
is the average reflectance of the cross section.

2.1 有效入射截面确定2.1 Determination of effective incident cross section

对于无穷远处的点光源，光线可以看成平行光，整个空间目标在入射光线垂直的截面上的平行投影可以看成是空间目标的入射截面。但并非所有照射到目标表面的光线都能反射到在某一观测方向上的观测设备中。因此，定义在入射截面中能反射光线到观测方向的部分为有效入射截面。For a point light source at infinity, the light can be regarded as parallel light, and the parallel projection of the entire space object on the section perpendicular to the incident light can be regarded as the incident section of the space object. But not all the light that strikes the target surface can be reflected to the observation equipment in a certain observation direction. Therefore, the effective incident section is defined as the part that can reflect light to the observation direction in the incident section.

当光源方向

Figure 682716DEST_PATH_IMAGE045
与观测方向
Figure 377003DEST_PATH_IMAGE046
确定时，只有当面元的法线满足与
Figure 95188DEST_PATH_IMAGE048
和
Figure 643981DEST_PATH_IMAGE046
的夹角都小于90度时，该面才能被光线照射，并且能反射光线到观测设备。该判断条件用向量内积可表示为，可以判断空间目标表面微面元
Figure 936740DEST_PATH_IMAGE024
对应的截面
Figure 57011DEST_PATH_IMAGE023
是否为有效入射截面。When the light source direction
Figure 682716DEST_PATH_IMAGE045
and viewing direction
Figure 377003DEST_PATH_IMAGE046
When determined, only when the bin the normal meet with
Figure 95188DEST_PATH_IMAGE048
and
Figure 643981DEST_PATH_IMAGE046
When the included angles are less than 90 degrees, the surface can be illuminated by light and can reflect light to the observation equipment. The judgment condition can be expressed by vector inner product as , it can be judged that the surface micro-facet of the space object
Figure 936740DEST_PATH_IMAGE024
Corresponding section
Figure 57011DEST_PATH_IMAGE023
Whether it is an effective incident cross section.

2.2 

Figure 725890DEST_PATH_IMAGE005
的确定与阴影影响的消除2.2
Figure 725890DEST_PATH_IMAGE005
The determination of and the elimination of shadow effects

平均反射率为有效截面上每一个

Figure 411266DEST_PATH_IMAGE023
对应的目标表面微元的反射率的均值。但是由于目标具有复杂的构型，入射截面上的一个微元
Figure 619799DEST_PATH_IMAGE023
可能是多个目标表面微面元
Figure 721747DEST_PATH_IMAGE024
的投影。而不同
Figure 963372DEST_PATH_IMAGE024
由于材料不同，反射率
Figure 691026DEST_PATH_IMAGE013
也不同，这为
Figure 68917DEST_PATH_IMAGE023
的反射率
Figure 607346DEST_PATH_IMAGE013
的确定造成了困难。average reflectance for each effective section
Figure 411266DEST_PATH_IMAGE023
Corresponding target surface microelements The mean reflectivity of . However, due to the complex configuration of the target, a microelement on the incident section
Figure 619799DEST_PATH_IMAGE023
May be multiple target surface microfacets
Figure 721747DEST_PATH_IMAGE024
projection. but different
Figure 963372DEST_PATH_IMAGE024
Due to the different materials, the reflectivity
Figure 691026DEST_PATH_IMAGE013
is also different, which is
Figure 68917DEST_PATH_IMAGE023
reflectivity
Figure 607346DEST_PATH_IMAGE013
The determination caused difficulties.

 考察光的传播过程可以发现，当一条光线入射到空间目标表面时，在光线传播方向上第一个与光线相交的面为受晒面，其后的面都会由于遮挡产生阴影，即对于一条入射光线，只有距离光源最近的面才对反射能量有贡献，因此，

Figure 759104DEST_PATH_IMAGE024
应取距离光源最近的面元。采取这种策略，既确定了
Figure 103498DEST_PATH_IMAGE023
的反射率
Figure 539158DEST_PATH_IMAGE013
，又有效防止了被遮挡的阴影部分参与计算。Examining the propagation process of light, it can be found that when a ray is incident on the surface of a space object, the first surface that intersects with the ray in the direction of ray propagation is the irradiated surface, and the subsequent surfaces will produce shadows due to occlusion, that is, for an incident For light, only the face closest to the light source contributes to the reflected energy, therefore,
Figure 759104DEST_PATH_IMAGE024
The surface element closest to the light source should be taken. With this strategy, it is determined that
Figure 103498DEST_PATH_IMAGE023
reflectivity
Figure 539158DEST_PATH_IMAGE013
, and effectively prevent the occluded shadow part from participating in the calculation.

3 模型实现3 Model realization

为了最终得到复杂空间目标模型在某个观察方向的反射光通量，关键在于求得复杂空间目标的有效入射截面面积

Figure 45226DEST_PATH_IMAGE050
和平均反射率
Figure 448394DEST_PATH_IMAGE018
。但由于空间目标结构复杂，建立空间目标几何外形的解析数学模型几乎是不可能的，因此，利用解析的方法无法实现
Figure 330900DEST_PATH_IMAGE050
和
Figure 621067DEST_PATH_IMAGE018
的计算。然而，利用计算机图形学的原理与方法，可以方便的求得这两个参数。In order to finally obtain the reflected light flux of the complex space target model in a certain viewing direction, the key is to obtain the effective incident cross-sectional area of the complex space target
Figure 45226DEST_PATH_IMAGE050
and average reflectivity
Figure 448394DEST_PATH_IMAGE018
. However, due to the complex structure of the space target, it is almost impossible to establish an analytical mathematical model of the geometric shape of the space target.
Figure 330900DEST_PATH_IMAGE050
and
Figure 621067DEST_PATH_IMAGE018
calculation. However, using the principles and methods of computer graphics, these two parameters can be easily obtained.

实现的基本原理是：首先根据材料的综合光散射强度，建立材料光散射模型，采用平行投影方法获得空间目标的入射截面，并判断选出有效入射截面，再求得平均反射率和有效入射截面面积，最后建立复杂空间目标光散射模型。在绘制入射截面时，在GPU片元着色器中，进行有效截面判断，剔除不满足的截面点。对满足有效截面条件的点，根据材料的材质属性，在GPU着色器中实现对每一个像素代表的截面元反射率经验模型的计算，形成反射率图。通过统计绘制的有效入射截面上像素的反射率均值得到。根据有效入射截面像素总个数与绘制窗口的面积比例关系，得到有效入射截面面积。具体实现方法与步骤如下（以OpenGL为例）。The basic principle of realization is: first, according to the comprehensive light scattering intensity of the material, establish the light scattering model of the material, use the parallel projection method to obtain the incident section of the space target, and judge and select the effective incident section, and then obtain the average reflectance and effective incident section area, and finally establish the complex space target light scattering model. When drawing the incident section, in the GPU fragment shader, the effective section judgment is performed, and the unsatisfactory section points are eliminated. For the points that meet the effective section conditions, according to the material properties of the material, the calculation of the empirical model of the reflectance of the section element represented by each pixel is realized in the GPU shader to form a reflectance map. Obtained by statistically drawing the average reflectance of pixels on the effective incident section . According to the relationship between the total number of pixels in the effective incident section and the area ratio of the drawing window, the effective incident section area is obtained . The specific implementation method and steps are as follows (taking OpenGL as an example).

1）空间目标几何与材料特性建模1) Modeling of space target geometry and material properties

 利用3DSMax等建模工具，可以构建复杂空间目标的三维精细几何外形，并且还可以为每一种材料设置漫反射和镜面反射参数。计算机图形学中，采用红绿蓝（RGB）三个分量来表示可见光光谱的颜色。材质的表示也采用RGB三个分量。因此，可以将漫反射材质RGB分量设置为（

Figure 110582DEST_PATH_IMAGE033
，
Figure 255256DEST_PATH_IMAGE033
，
Figure 368705DEST_PATH_IMAGE033
），镜面反射材质设置为（，
Figure 705194DEST_PATH_IMAGE010
，
Figure 969954DEST_PATH_IMAGE051
），再设置镜面反射指数后，完成面元的材料属性设置。对于空间目标上具有相同材料的表面，可以设置成统一的材质属性。空间目标上每一类材料设置完材质属性后，就建立具有复杂结构的空间目标几何与材料特性的三维模型。Using modeling tools such as 3DSMax, the three-dimensional fine geometric shape of complex space objects can be constructed, and diffuse reflection and specular reflection parameters can also be set for each material. In computer graphics, the three components of red, green and blue (RGB) are used to represent the colors of the visible light spectrum. The representation of the material also uses three components of RGB. Therefore, the diffuse material RGB components can be set to (
Figure 110582DEST_PATH_IMAGE033
,
Figure 255256DEST_PATH_IMAGE033
,
Figure 368705DEST_PATH_IMAGE033
), with the specular material set to ( ,
Figure 705194DEST_PATH_IMAGE010
,
Figure 969954DEST_PATH_IMAGE051
), and then set the specular index Finally, the material property setting of the surface element is completed. For surfaces with the same material on the spatial object, it can be set to a uniform material property. After the material properties of each type of material on the space object are set, a three-dimensional model of the geometry and material properties of the space object with a complex structure is established.

2）平行投影变换2) Parallel projection transformation

    在OpenGL中，利用函数

Figure 89668DEST_PATH_IMAGE052
完成平行投影变换。函数参数为平行投影的左右、上下和远近裁剪面，利用这些参数来计算投影区域的实际面积
Figure 117666DEST_PATH_IMAGE053
，
Figure 236932DEST_PATH_IMAGE015
  。In OpenGL, using the function
Figure 89668DEST_PATH_IMAGE052
Complete the parallel projection transformation. The function parameters are the left and right, top and bottom, far and near clipping planes of the parallel projection, and these parameters are used to calculate the actual area of the projected area
Figure 117666DEST_PATH_IMAGE053
,
Figure 236932DEST_PATH_IMAGE015
.

3）视口变换3) Viewport transformation

视口变换将投影变换后的坐标变换到屏幕像素坐标。利用函数

Figure 879135DEST_PATH_IMAGE054
实现，参数
Figure 778958DEST_PATH_IMAGE055
为视口左下角坐标，窗口大小(单位为像素)。通常取
Figure 318841DEST_PATH_IMAGE057
。整个显示窗口的像素总数为The viewport transformation transforms the projectively transformed coordinates to screen pixel coordinates. use function
Figure 879135DEST_PATH_IMAGE054
implementation, parameters
Figure 778958DEST_PATH_IMAGE055
is the coordinates of the lower left corner of the viewport, Window size in pixels. usually take
Figure 318841DEST_PATH_IMAGE057
. The total number of pixels in the entire display window is

Figure 627550DEST_PATH_IMAGE058
。
Figure 627550DEST_PATH_IMAGE058
.

4）三维绘制4) 3D rendering

a） 有效截面图的绘制a) Drawing of effective section diagram

为了获得空间目标在入射光线垂直的截面上的垂直投影图像，需要在OpenGL中将视线方向设置为入射光方向；同时，为方便GPU进行有效截面的判断，将光源方向设置为原来探测器观察方向。利用基于GPU的编程技术，在片元着色器中实现对空间目标三维模型的每一个要绘制的像元进行条件(11)的判断，并将满足条件的像元绘制为黑色，将不满足条件的像元绘制成背景颜色（白色），最终形成有效入射截面图像。In order to obtain the vertical projection image of the spatial object on the vertical section of the incident light, the line of sight direction needs to be set as the incident light direction in OpenGL; at the same time, in order to facilitate the GPU to judge the effective section, the light source direction is set to the original detector observation direction . Using GPU-based programming technology, in the fragment shader, the judgment of condition (11) is realized for each pixel to be drawn in the 3D model of the space object, and the pixel that meets the condition is drawn as black, and the pixel that does not meet the condition is drawn The pixels of are drawn in the background color (white), and finally form the effective incident section image.

b）反射率分布图的绘制b) Drawing of reflectance distribution map

由空间目标有效入射截面上每一个像素的反射率构成的二维图像称之为反射率分布图。要得到平均反射率分布图，需要对有效截面上每一个像元的反射率进行计算。在OpenGL中，光源的漫反射光颜色和镜面反射光颜色都设置为（1.0，1.0，1.0），视线方向设置为入射光方向；启用深度测试，保证正确的遮挡关系，以消除阴影的影响。在空间目标三维模型绘制过程中，用模型数据中的漫反射与镜面反射参数为每一个三角形的材质赋值，在OpenGL片元着色器中根据光源属性、材质属性以及几何关系，利用式

Figure 749090DEST_PATH_IMAGE032
(4)，完成对入射截面上每一个像素反射率的计算。模型绘制完毕后，就构成了整个空间目标的反射率分布图。The two-dimensional image composed of the reflectance of each pixel on the effective incident section of the space target is called the reflectance distribution map. To obtain the average reflectance distribution map, it is necessary to calculate the reflectance of each pixel on the effective section. In OpenGL, the diffuse light color and specular light color of the light source are both set to (1.0, 1.0, 1.0), and the line of sight direction is set to the incident light direction; enable the depth test to ensure the correct occlusion relationship to eliminate the influence of shadows. In the process of drawing the 3D model of the space object, use the diffuse reflection and specular reflection parameters in the model data to assign values to the material of each triangle, and use the formula
Figure 749090DEST_PATH_IMAGE032
(4) Completing the calculation of the reflectance of each pixel on the incident section. After the model is drawn, the reflectance distribution map of the entire space target is formed.

c）参数

Figure 56575DEST_PATH_IMAGE059
与
Figure 212749DEST_PATH_IMAGE018
确定c) parameters
Figure 56575DEST_PATH_IMAGE059
and
Figure 212749DEST_PATH_IMAGE018
Sure

经过上述几个步骤后，在二维窗口上得到空间目标的有效入射截面图和反射率图。由于有效截面的获取过程采用的是平行投影，窗口上每一个像元代表的面积相同。因此，通过检测有效入射截面图上有效像素（黑色像素），并进行累加得到有效像素总数为，

Figure 805591DEST_PATH_IMAGE019
乘以每个象素代表的实际面积，就得到复杂空间目标的有效入射截面面积，表示为, 将反射率分布图上每一个像素的反射率求和，并除以
Figure 661868DEST_PATH_IMAGE019
，就可以得到平均反射率
Figure 318240DEST_PATH_IMAGE018
。After the above steps, the effective incidence cross-section diagram and reflectivity diagram of the space target are obtained on the two-dimensional window. Since the acquisition process of the effective cross-section adopts parallel projection, each pixel on the window represents the same area. Therefore, by detecting the effective pixels (black pixels) on the effective incident cross-sectional view and accumulating them, the total number of effective pixels is ,
Figure 805591DEST_PATH_IMAGE019
Multiplied by the actual area represented by each pixel, the effective incident cross-sectional area of the complex space target is obtained, expressed as , sum the reflectance of each pixel on the reflectance distribution map and divide by
Figure 661868DEST_PATH_IMAGE019
, the average reflectance can be obtained
Figure 318240DEST_PATH_IMAGE018
.

4 仿真试验4 Simulation test

4.1 试验数据4.1 Test data

为了验证本文提出的计算复杂空间目标光散射特性的方法的有效性和实际效果，以Quickbird-2卫星为空间目标，以某模拟卫星Sat-1为观测卫星进行试验，轨道根数如表1。QuickBird-2为对地观测卫星，姿态为对地指向，其几何结构较为复杂，外形如图4所示。In order to verify the validity and actual effect of the method proposed in this paper to calculate the light scattering characteristics of complex space objects, the Quickbird-2 satellite is used as the space object, and a simulated satellite Sat-1 is used as the observation satellite to conduct experiments. The orbital elements are shown in Table 1. QuickBird-2 is an earth observation satellite with an attitude pointing to the earth. Its geometric structure is relatively complex, and its shape is shown in Figure 4.

 the

Figure 414372DEST_PATH_IMAGE061
Figure 414372DEST_PATH_IMAGE061

通过轨道计算，得出起始时刻为2008-1-11 00:52:05（UTC），结束时刻为2008-1-11 01:50:36（UTC）共3511秒时间段内，Sat-1可以对Qiuckbird-2卫星实施观测。图5为试验时间段内，目标到观测平台的距离以及太阳方向与观测方向的夹角随时间变化的情况。从图中可以看出，太阳方向与观测方向的夹角在

Figure 63659DEST_PATH_IMAGE062
区间内具有较大的跨度，利用这个时间段内的光照条件进行试验，具有较普遍的代表性。Through orbit calculation, the starting time is 2008-1-11 00:52:05 (UTC), and the ending time is 2008-1-11 01:50:36 (UTC), a total of 3511 seconds, Sat-1 Observations can be made to the Qiuckbird-2 satellite. Figure 5 shows how the distance from the target to the observation platform and the angle between the sun direction and the observation direction change with time during the test period. It can be seen from the figure that the angle between the direction of the sun and the direction of observation is
Figure 63659DEST_PATH_IMAGE062
The interval has a relatively large span, and it is generally representative to use the light conditions in this time period to conduct experiments.

4.2 试验结果4.2 Test results

利用本发明提出的计算复杂空间目标光散射的原理与方法，以10秒为步长，得到了各个时刻有效入射截面图和反射率分布图，并统计了有效截面面积和平均反射率，最终计算了反射光通量。结果如下：Utilize the principle and method for calculating the light scattering of complex space objects proposed by the present invention, and take 10 seconds as the step length, obtain the effective incident cross-sectional diagram and reflectivity distribution diagram at each time, and count the effective cross-sectional area and average reflectivity, and finally calculate reflected luminous flux. The result is as follows:

图6是时间为2008-1-11 01:08:25（距离起始时间1000秒）总入射截面图（a）与有效入射截面图（b）的比较。图7为在试验时间段内有效入射截面与总入射截面面积随时间变化的比较曲线。Figure 6 is a comparison between the total incident cross-section (a) and the effective incident cross-section (b) at 2008-1-11 01:08:25 (1000 seconds from the start time). Fig. 7 is a comparison curve of the effective incident cross-section and the total incident cross-sectional area changing with time during the test period.

有效入射截面与卫星的几何形状以及姿态都密切相关。此外，分析图6和图7，可以看出，有效入射截面明显受到太阳方向与观测方向夹角的影响，有效入射截面总的趋势与太阳方向和观测方向夹角大小的变化相反;在夹角接近180度时，有效入射截面趋于0；而夹角较小时，有效截面超过12平方米，跨度范围较大。这种变化规律与实际情况是相吻合的。此外，通过比较有效入射截面和总入射截面，发现通常有效入射截面要比总入射截面小许多，如图6时刻相差约3倍。因此，不进行有效入射截面的判断，而直接采用总入射截面会给反射能量的计算带来极大的误差。The effective incident cross section is closely related to the geometry and attitude of the satellite. In addition, analyzing Figures 6 and 7, it can be seen that the effective incident section is obviously affected by the angle between the sun direction and the observation direction, and the general trend of the effective incident section is opposite to the change in the angle between the sun direction and the observation direction; When it is close to 180 degrees, the effective incident section tends to 0; when the included angle is small, the effective section exceeds 12 square meters, and the span range is large. This change rule is consistent with the actual situation. In addition, by comparing the effective incident cross section and the total incident cross section, it is found that the effective incident cross section is usually much smaller than the total incident cross section, as shown in Figure 6, the difference is about 3 times. Therefore, directly using the total incident cross section without judging the effective incident cross section will bring great errors to the calculation of the reflected energy.

图8为试验得出的2008-1-11 01:08:25时刻的反射率分布图，颜色越深表示反射率越低。从图中可以看出，由于将视线方向设置在光源方向，空间目标上光线照射不到的阴影部分由OpenGL深度测试，被自动隐藏，不会参与平均反射率的计算。这说明采用基于有效入射截面积分的方法，可以防止阴影产生干扰。Figure 8 is the reflectance distribution map obtained from the test at 01:08:25 on January 11, 2008. The darker the color, the lower the reflectance. It can be seen from the figure that since the line of sight direction is set in the direction of the light source, the shadow part on the space object that cannot be illuminated by light is automatically hidden by the OpenGL depth test, and will not participate in the calculation of the average reflectance. This shows that the method based on the integral of the effective incidence cross section can prevent interference from shadows.

图9为目标平均反射率随时间变化的曲线。从图9可以看出，在3000秒附近，平均反射率有剧烈的抖动，是由于在该时间段内，太阳方向与观测方向夹角接近180度，导致有效入射截面接近0，放大了测量随机误差。另一方面，当太阳方向与观测方向接近180度时，受强烈太阳光线直射的影响，一般设备都无法进行观测。因此，这一区域的得到的数据为无效数据，应将其忽略。这样，该空间目标的平均反射率，在观测方向大约在0.1～0.25之间变化。这种现象说明，随着入射角和观测角的变化，平均反射率也会发生一定的变化。Fig. 9 is a curve of the average reflectance of the target as a function of time. It can be seen from Figure 9 that the average reflectance fluctuates violently around 3000 seconds, which is due to the fact that during this time period, the angle between the sun direction and the observation direction is close to 180 degrees, resulting in an effective incident cross section close to 0, which magnifies the measurement randomness. error. On the other hand, when the direction of the sun is close to 180 degrees to the direction of observation, due to the influence of strong direct sunlight, general equipment cannot perform observations. Therefore, the resulting data for this region is invalid and should be ignored. In this way, the average reflectance of the space object varies between 0.1 and 0.25 in the observation direction. This phenomenon shows that as the incident angle and observation angle change, the average reflectance will also change to a certain extent.

取太阳在空间目标处的照度

Figure 194426DEST_PATH_IMAGE063
为太阳常数1353
Figure 520234DEST_PATH_IMAGE064
，将有效截面与平均反射率代入式
Figure 775766DEST_PATH_IMAGE044
，计算每个步长的反射光通量。其随时间变化曲线如图10所示。Take the illuminance of the sun at the space target
Figure 194426DEST_PATH_IMAGE063
is the solar constant 1353
Figure 520234DEST_PATH_IMAGE064
, substituting the effective cross-section and average reflectivity into the formula
Figure 775766DEST_PATH_IMAGE044
, to calculate the reflected luminous flux for each step. Its time-varying curve is shown in Figure 10.

由式

Figure 291061DEST_PATH_IMAGE003
可知，入射截面和平均反射率对于反射光通量的贡献是相同的。但比较图7、图9发现，有效入射截面主要影响了反射光通量总的变化趋势。这是因为，在观测时间段内，有效入射截面积
Figure 17337DEST_PATH_IMAGE067
的变化要比平均反射率剧烈得多。而有效入射截面受光照条件影响最大。by formula
Figure 291061DEST_PATH_IMAGE003
It can be seen that the incidence cross-section and average reflectivity The contribution to the reflected luminous flux is the same. However, comparing Fig. 7 and Fig. 9, it is found that the effective incident section mainly affects the overall change trend of the reflected luminous flux. This is because, during the observation period, the effective incident cross-sectional area
Figure 17337DEST_PATH_IMAGE067
The variation of the average reflectance much more violent. The effective incident cross section is most affected by the lighting conditions.

对于空间目标的光散射特性的研究，大多数学者都将目标当作简单的几何体。而本发明在根据材料的非相干散射特性和相干散射特性得出的光散射经验公式的基础上，建立了复杂空间目标在有效入射截面上利用截面积和平均反射率表示的光散射模型，并且给出了基于计算机图形学精确获得有效入射截面与平均反射率的方法。最后，计算了在一段可观测时间内Quickbird-2卫星天基观测的有效入射截面、平均反射率以及反射光通量等。For the study of the light scattering characteristics of space targets, most scholars regard the target as a simple geometric body. And the present invention is based on the light scattering empirical formula obtained according to the incoherent scattering characteristic and the coherent scattering characteristic of the material, establishes the light scattering model that the complex space target utilizes cross-sectional area and average reflectivity to represent on the effective incident section, and A method to accurately obtain the effective incident section and average reflectivity based on computer graphics is given. Finally, the effective incident cross-section, average reflectance and reflected luminous flux of Quickbird-2 satellite space-based observation within a period of observable time are calculated.

Claims (9)

1. A light scattering modeling method for a complex space target is characterized by comprising the following steps:
(1) establishing a material light scattering empirical model according to the comprehensive light scattering intensity of the material;
(2) adopting parallel projection transformation to obtain an incident section of the space target, and judging and selecting an effective incident section;
(3) according to the material light scattering empirical model, the average reflectivity is obtained by counting the reflectivity mean value of the pixels on the drawn effective incident section
Figure 764900DEST_PATH_IMAGE002
；
(4) According to the proportional relation between the total number of the effective incidence section pixels and the area of the drawing window, the effective incidence section area is obtained
Figure 769765DEST_PATH_IMAGE004
；
(5) Establishing a complex space target light scattering model
Figure 207700DEST_PATH_IMAGE006
In the formula
Figure 893896DEST_PATH_IMAGE008
Is the illumination of the sun at the spatial target;
Figure 664668DEST_PATH_IMAGE004
is the area of the effective incident cross section;
Figure DEST_PATH_IMAGE009
is the average reflectivity over the cross section.
2. The complex space object light scattering modeling method of claim 1, wherein the integrated light scattering intensity of the material in step (1) is the sum of diffuse reflectance component and specular reflectance, expressed asWherein
Figure 765665DEST_PATH_IMAGE013
Is the diffuse reflection coefficient of the object and is related to the surface property of the object;
Figure 989973DEST_PATH_IMAGE015
is the light intensity of the light source;
Figure 317049DEST_PATH_IMAGE017
is the angle of incidence of the light;
Figure 398138DEST_PATH_IMAGE019
is the specular reflection coefficient of the object and,
Figure 810664DEST_PATH_IMAGE021
is the angle between the line of sight and the direction of reflection.
3. The complex spatial object light scatter modeling method of claim 2, wherein: the empirical model of the light scattering of the material in the step (1) is
Figure 838663DEST_PATH_IMAGE023
Wherein
Figure 82563DEST_PATH_IMAGE025
For the total reflectivity, when the light is reflectedAt an angle of incidence on the surface of a material
Figure 172059DEST_PATH_IMAGE021
The ratio of the reflected light intensity to the incident light intensity in the direction.
4. The complex spatial object light scatter modeling method of claim 3, wherein: the space target incident section in the step (2) is obtained by using a function glOrtho (l, r, b, t, n, f) to complete parallel projection transformation in OpenGL, wherein the function parameters are left, right, upper, lower and far and near cutting surfaces of parallel projection, and the parameters are used for calculating the actual area of a projection area
Figure DEST_PATH_IMAGE027
And transforming the left after projection transformation into screen pixel coordinates by using a function glViewport (x, y, w, h), wherein the parameter (x, y) is the coordinate of the lower left corner of the viewport, the parameter (w, h) is the window size, and if x = y =0, the total number of pixels of the whole display window is equal to
Figure DEST_PATH_IMAGE029
。
5. The complex spatial object light scatter modeling method of claim 4, wherein: in the step (2), when an incident section is drawn, effective section judgment is carried out in a GPU fragment shader, and section points which do not meet judgment conditions are eliminated; and calculating the section element reflectivity empirical model represented by each pixel in the GPU shader according to the material attribute of the material for the points meeting the effective section condition to form a reflectivity distribution diagram.
6. The complex spatial object light scatter modeling method of claim 5, wherein: the effective cross section is a part capable of reflecting light to an observation direction in an incident cross section, when a light source direction L and the observation direction V are determined, when a normal N of a surface element dA meets that the included angles of the L and the V are both smaller than 90 degrees, the surface is irradiated by the light, and the light can be reflected to an observation device, and the judgment condition of the effective cross section is expressed by a vector inner product:
Figure DEST_PATH_IMAGE031
。
7. the complex spatial object light scatter modeling method of claim 6, wherein: the reflectivity distribution graph is a two-dimensional image formed by the reflectivity of each pixel on the effective incident section of the space target, the diffuse reflection and the specular reflection parameters in the model data are used for assigning values to the material of each triangle, and the formula is used in the OpenGL fragment shader according to the light source attribute, the material attribute and the geometric relation
Figure 361338DEST_PATH_IMAGE023
And calculating the reflectivity of each pixel on the incident section, and forming a reflectivity distribution map of the whole space target after the model drawing is finished.
8. The complex spatial object light scatter modeling method of claim 7, wherein: average reflectance in the step (3)
Figure 663006DEST_PATH_IMAGE002
The reflectivity of each pixel on the reflectivity profile is summed and divided by the total number of effective pixels
Figure DEST_PATH_IMAGE033
Thus obtaining the product.
9. The complex space target light scattering modeling method of claim 8, wherein the effective incident cross-sectional area in step (4)
Figure DEST_PATH_IMAGE034
The calculation formula of (a) is as follows:
Figure DEST_PATH_IMAGE036
wherein the total number of effective pixels is
Figure 413794DEST_PATH_IMAGE033
。
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