We demonstrate a method of calculating the spectral function of a composite from measured reflectivity data. To solve this inverse problem it is necessary for the reflectivity data to be taken through a strong, high Q, resonance. By analyzing the reststrahlen region of different fill fraction KCl-diamond composites at three different temperatures, we find accurate spectral functions that are independent of temperature with the low temperature data giving the best resolution. These spectral functions are then used to successfully predict the optical response of RbCl-diamond composites.