Haze of surface random systems: An approximate analytic approach

Abstract

Approximate analytic expressions for haze (and gloss) of Gaussian randomly rough surfaces for various types of correlation functions are derived within phase-perturbation theory. The approximations depend on the angle of incidence, polarization of the incident light, the surface roughness, $\ensuremath{\sigma}$, and the average of the power spectrum taken over a small angular interval about the specular direction. In particular it is demonstrated that haze (gloss) increase (decrease) with $\ensuremath{\sigma}/\ensuremath{\lambda}$ as $\text{exp}[\ensuremath{-}A{(\ensuremath{\sigma}/\ensuremath{\lambda})}^{2}]$ and decreases (increase) with $a/\ensuremath{\lambda}$, where $a$ is the correlation length of the surface roughness, in a way that depends on the specific form of the correlation function being considered. These approximations are compared to what can be obtained from a rigorous Monte Carlo simulation approach, and a good agreement is found over large regions of parameter space. Some experimental results for the angular distribution of the transmitted light through polymer films and their haze are presented and compared to the analytic approximations derived in this paper. A satisfactory agreement is found. In the literature haze of blown polyethylene films has been related to surface roughness. Few authors have quantified the roughness and others have pointed to the difficulty in finding the correct roughness measure.