Influence of the acceptance angle on the evaluation of reflectance data of randomly rough surfaces using scalar diffraction theory

Apart from coherent reflectance, which corresponds to specular reflection, the values obtained by real spectrophotometers also include contribution from incoherent reflectance, which represents light scattered by the samples and registered by the detector due to its finite acceptance angle. This work aims to investigate the influence of this second part on reflectance spectra measured for samples with randomly rough surfaces. Three silicon samples with roughened surfaces are investigated. The reflectance is measured using a commercial spectrophotometer with acceptance angles restricted by apertures placed in the incident and reflected beam. The proposed method is based on the simultaneous processing of spectral dependencies of reflectance measured with differently-sized apertures. The utilized theoretical approach is based on the scalar diffraction theory. Because the dependencies on both wavelength and acceptance angle are considered, a model providing correct predictions for these dependencies should also correctly describe how is the total reflectance separated into its coherent and incoherent parts. It is shown that the theoretical predictions for incoherent reflectance are consistent with the changes in the diameter of the apertures. It was possible to determine the RMS value of the heights as well as the estimate for the autocorrelation length and additional parameter controlling the course of the autocorrelation function. A short discussion comparing our results with those achieved using methods employed in earlier works is also provided.