Replacement of ensemble averaging by the use of a broadband source in scattering of light from a one-dimensional randomly rough interface between two dielectric media

TL;DR

This paper demonstrates that using a broadband Gaussian beam on a single realization of a rough interface can replicate ensemble-averaged scattering results, simplifying analysis in light scattering studies.

Contribution

It introduces a method to replace ensemble averaging with broadband illumination in modeling light scattering from rough interfaces.

Findings

Broadband illumination closely matches ensemble-averaged scattering results.

Single realization experiments can replace multiple realizations in scattering analysis.

Phase perturbation theory supports the equivalence between broadband and ensemble averaging.

Abstract

By the use of phase perturbation theory we show that if a single realization of a one-dimensional randomly rough interface between two dielectric media is illuminated at normal incidence from either medium by a broadband Gaussian beam, it produces a scattered field whose differential reflection coefficient closely matches the result produced by averaging the differential reflection coefficient produced by a monochromatic incident beam over the ensemble of realizations of the interface profile function.