Light scattering from multilayer optics: comparison of theory and experiment

Abstract

Measurements of angular scattering due to surface roughness were taken from a 24-layer dielectric mirror and compared to theory. In addition, the top surface roughness of the multilayer stack is analyzed from Talystep profilometer measurements. These roughness data are used to obtain a roughness spectral density function to be used in a vector multilayer scattering theory. The theory uses three multilayer stack models to incorporate possible effects of different degrees of correlation between interfaces of the stack. It was found that the angular scattering calculated using the experimentally obtained roughness spectral density function agreed remarkably well with the measured angular scattering data. This is especially true if care is taken to differentiate between particulate and roughness scattering. For the sake of comparison, the angular scattering from an aluminum film is also given, and differences from scattering from the multilayer mirror are noted.

Surface Roughness Studies with DALLAS-Detector Array for Laser Light Angular Scattering

“…Experiments involving measured and calculated scattering distributions have been done for optical surfaces by Elson, Bennett, and Rahn [30,31]. Their work differs from ours in that the theory they used is more straightforward.…”

Multiscale Surface Roughness and Backscattering

“…Such surfaces can be treated in the same way as multilayer stacks [8]. The initial surface is described with a profile z 1 (x).…”

“…It is natural to assume that the initial and final surfaces are partially correlated. As more changes take place, more additive components appear and the final surface profile is [8] z n (x) = z 1 …”

“…The final surface correlation function is then obtained as a sum of the original surface correlation and the autocorrelation of the random changes [8]. Conventional finish analysis uses a sum of exponentials and Gaussians to describe the final surface autocorrelation function [1] …”

“…However, even this method is usually applied assuming that the surface roughness can be described with the two classical constant parameters, rms height and correlation length. The problem of surfaces having both small and large scale roughness characteristics has been studied in several cases [1,3,6,8], but the use of the IEM equations for calculating the surface backscattering coefficients for surfaces having multiscale roughness requires further consideration. This problem is also studied in this paper for cases having small dielectric constant values, such as sea ice [3].…”