We report a study of the optical properties of silicon moth-eye structures using a custom-made fully automated broadband spectroscopic reflectometry system (goniometer). This measurement system is able to measure specular reflectance as a function of wavelength, polar incidence angle and azimuth orientation angle, from normal to near-parallel polar incidence angle. The system uses a linear polarized broadband super-continuum laser light source. It is shown that a moth-eye structure composed of a regular array of protruding silicon rods, with finite sidewall angle reduces reflectance and sensitivity to incident wavelength in comparison to truly cylindrical rods with perpendicular sidewalls. It is also shown that moth-eye structures have omnidirectional reflectance properties in response to azimuth orientation of the sample. The importance of applying the reflectometer setup to study the optical properties of solar cell antireflective structures is highlighted.