A response function is derived for the description of photo-induced birefringence and dichroism in case of materials where the underlying process is photo-isomerization. Our result explains the usefulness of the theoretical formulae derived earlier by Kakichashvili for photo-anisotropic materials of another kind, which are widely used in polarization holographic models. The expression proposed by us depends on the exposure time for a given intensity, and describes the saturation of the anisotropy with time and intensity. The material constants introduced in our approach are expressed by proper microscopic quantities. The results are verified by numerical simulation and also by experiments.