Estimation of gloss from rough surface parameters

TL;DR

This paper derives an approximate formula for surface gloss based on rough surface parameters using phase perturbation theory, validated by Monte Carlo simulations, to improve material characterization in optics.

Contribution

It introduces a new approximate expression for gloss that relates it to surface roughness and correlation functions, validated through simulations.

Findings

Gloss depends exponentially on surface roughness and momentum transfer.

The approximation shows good agreement with simulations across various parameters.

The method provides a practical way to estimate gloss from surface measurements.

Abstract

Gloss is a quantity used in the optical industry to quantify and categorize materials according to how well they scatter light specularly. With the aid of phase perturbation theory, we derive an approximate expression for this quantity for a one-dimensional randomly rough surface. It is demonstrated that gloss depends in an exponential way on two dimensionless quantities that are associated with the surface randomness: the root-mean-square roughness times the perpendicular momentum transfer for the specular direction, and a correlation function dependent factor times a lateral momentum variable associated with the collection angle. Rigorous Monte Carlo simulations are used to access the quality of this approximation, and good agreement is observed over large regions of parameter space.