Optical measurements of nanostructured GaSb prepared by sputtering is presented. The optical response is studied by Mueller Matrix Ellipsometry~(MME) in the visible range ($430$--$850 \mbox{nm}$), and by spectroscopic ellipsometry in the range $0.6$--$6.5 \mbox{eV}$. The nano-structured surfaces reported in this work, consist of densely packed GaSb cones approximately $50 \mbox{nm}$ high, on bulk GaSb. The nanostructured surfaces are here shown to considerably modify the optical response of the surface, hence giving a strong sensitivity to the far field spectroscopic (Mueller matrix) ellipsometric measurements. The off-specular scattering and the depolarization is found to be low. The anisotropic response is particularly emphasized by studying nano-structured GaSb cones approximately $45$ degrees tilted with respect to the surface normal. In the latter case, one observes upon rotating the sample around the surface normal, that the Mueller matrix elements $m_{13}$ and $m_{14}$ oscillate as a function of the rotation angle. Finally, Mueller matrix techniques have been applied to the measured data, in order to analyze the acquired Mueller matrix in terms of physical realisability and noise.