a normalized two-dimensional band-limited Weierstrass fractal function is presented for modeling the rough surface
and an analytic solution of the scattering field from two-dimensional band-limited Weierstrass fractal surface is derived based on Kirchhoff theory.The scattering field
the average scattering coefficient and the variance of scattering intensity are given to study the influence of fractal dimension and other related parameters on the scattering field by theoretical analysis and numerical calculations.