An Analytical Thermal Emission Model on the Effect of Multiple Scattering for 3-D Structural Pixel and the Model Validation
两组分非同温像元热辐射中多次散射影响的解析模型和验证

For a remote sensing pixel with 3D surface, the directionality of thermal emission depends on the component parameters of the pixel, such as component temperatures, component emissivities and structural parameters. The contribution of the multiple scattering between components to the directional thermal emission is mainly affected by the 3D structure of pixel. In this paper, we present an analytical model to describe the multiple scattering between components and its contribution to the pixel's emission. The modeling work is based on the conceptual geometric-optical thermal emission model. For the non-isothermal pixel with random distributed components, at the pixel's scale, the openness coefficient and viewing factor is defined, the effect of multiple scattering between components is modeled with the principle of multiple bouncing. Then the directional thermal emission of pixel is derived based on the areal weighted emission of components by taking the ambient radiation into account. The model is validated using measurement data indoor. The two experimental data sets are on different observing object (samples of pingpong spheres and simulated trees made of cotton). Each set of measurement data includes directional thermal emission of pixel, the emission of components, the ambient thermal radiance, and the structural parameters of the pixel. These measured data of components are as input of the model, the brightness temperature of the pixel is calculated. The model predicted brightness temperatures and their comparison with the measured brightness temperature in pixel scale are presented in the paper. The directionality of the effect of multiple scattering is also discussed. The result demonstrates that in pixel scale the analytical model prediction fits the measurement well. Note that in the multiple scattering effect model, when the samples on the background are very close to each other and the viewing facrot VF 2-2can not be ignored, our modeling methodology can still apply. But the results formula will then be very complicated. In such case, a two layer multiple bouncing model would be more appropriate.