We numerically investigate the light-absorption behavior of thinfilm silicon for normal-incident light, using surface textures to enhance absorption. We consider a variety of texture designs, such as simple periodic gratings and commercial random textures, and examine arbitrary irregular periodic textures designed by multi-parameter optimization. Deep and high-index-contrast textures exhibit strong anisotropic scattering that is outside the regime of validity of the Lambertian models commonly used to describe texture-induced absorption enhancement for normal incidence. Over a 900-1100 nm wavelength range, our optimized surface texture in two dimensions (2D) enhances absorption by a factor of 2.7 pi n, considerably larger than the original pi n Lambertian result and exceeding by almost 50% a recent generalization of Lambertian model for periodic structures in finite spectral range. However, the pi n Lambertian limit still applies for isotropic incident light, and our structure obeys this limit when averaged over all the angles. Therefore, our design can be thought of optimizing the angle/enhancement tradeoff for periodic textures. (C) 2011 Optical Society of America