Optical reflection and transmission through a flat system with a thick fluctuating layer

In the theoretical description of reflection and transmission coefficients through a system with a layer much thicker than the wavelength the fluctuations of the thickness Δd/d and the spectrometer resolution Δλ/λ must be taken into consideration. The connection between the measured averaged values and the reflection and transmission coefficients from the front and back sides into the substrate is given by a Fourier sum. The total averages correspond to the summation over all light intensities caused by multiple incoherent internal reflections inside the substrate layer. As a special result of this analysis the measurement of the absorption in a thin layer by only reflection measurement will be demonstrated in a following paper. For smaller fluctuations the distribution function or better its Fourier components can also be measured by the analysis of the remaining interference effects.