The synthetic aperture radar imaging of fractal rough surface is studied. The natural surface can be very accurately described in terms of fractal geometry. Such a two-dimensional fractional Brownian motion (FBM) stochastic process provides a very sound description of natural surface. The samples of band-limited FBM process are realized by using physical Weierstrass-Mandelbrot function. The parameters of fractal rough surface are discussed and how to choose the value is analyzed. The roughness is mostly determined by the Hurst coefficient or the fractal dimension. In the actual simulation, a fractal rough surface can be seen as the superposition of finite sinusoidal tones, and any scattering measurement is limited to a finite set of scales. In this paper, the surface is described with two-scale model, i. e., locally approximated by plane facets with dimension smaller than that of resolution cells, but much larger than wavelength. Because this paper focuses on the texture of the synthetic aperture radar (SAR) image and the overall image texture is related to the macroscopic scale, the microscopic roughness superimposed on the facets is neglected. For the macroscopic scale scattering problem, a facet Kirchhoff approach is proposed. The fractal rough surface consists of many triangle facets, and the scatter field of each facet can be obtained by the facet Kirchhoff approach. The principle of dimension selection is studied. The dimension of facet must follow the principle that the surface profile is not damaged. At the same time, the facet dimension should be as large as possible in order to increase the efficiency of imaging. After establishing the fractal geometry model and obtaining the field from each facet, the SAR image can be realized through Rang-Doppler method in the stripmap mode. The results show that in the SAR image, the effects of fractal parameters on the rough surface can be obviously observed. The peaks and ravines of rough surface are obviously observed at low fractal dimension or high Hurst coefficient. However, when the fractal dimension gets higher or Hurst coefficient gets higher, the peaks and ravines disappear because the surface becomes rougher and diffuse scattering is enhanced. The effect of fractal parameter on the SAR image can be specifically expressed with entropy and angle second moment. With the increase of fractal dimension D, the texture of SAR image behaves more randomly and disorderly. So the entropy of SAR image becomes larger and the angle second moment of SAR image becomes smaller. The texture of SAR image is also related to the squint angle and frequency of incidence wave. The relative roughness will become larger when the squint angle and frequency of incidence wave become larger. The research on a complete fractal surface SAR imaging system consists of establishing the environmental model, developing the electromagnetic scattering model, and using the SAR imaging technique. The achievements show the characteristics of fractal rough surface SAR image, which have a theoretical support for natural environment remote sensing and the environment parameters inversion.
