The shadow function for rough surfaces

摘要

For many remote sensing applications it is beneficial to know how the amount of shadows on a surface depends on illumination. Many natural surfaces (planetary surfaces being an example) may be successfully described by a fractal model. While the fractal shadowing function can be easily calculated experimentally, to date no rigorous analytical model of self-shadowing on a fractal surface exists. In this paper we offer an integral form of the shadowing function for fractal surfaces with different fractal and roughness parameters. The analysis is based on working out the covariance matrix for an arbitrarily long sequence of heights in a fractal profile.