Four-parameter model for polarization-resolved rough-surface BRDF

Ingmar G E Renhorn,Glenn D Boreman,David Bergström,Tomas Hallberg

doi:10.1364/oe.19.001027

Abstract

A modeling procedure is demonstrated, which allows representation of polarization-resolved BRDF data using only four parameters: the real and imaginary parts of an effective refractive index with an added parameter taking grazing incidence absorption into account and an angular-scattering parameter determined from the BRDF measurement of a chosen angle of incidence, preferably close to normal incidence. These parameters allow accurate predictions of s- and p-polarized BRDF for a painted rough surface, over three decades of variation in BRDF magnitude. To characterize any particular surface of interest, the measurements required to determine these four parameters are the directional hemispherical reflectance (DHR) for s- and p-polarized input radiation and the BRDF at a selected angle of incidence. The DHR data describes the angular and polarization dependence, as well as providing the overall normalization constraint. The resulting model conserves energy and fulfills the reciprocity criteria.

Highlights

Polarimetric imaging is of growing interest in the remote sensing community
The predictive capability of polarimetric Bidirectional Reflectance Distribution Functions are limited and more work is needed on developing an understanding of various types of surfaces
BRDF measurements were made at 0.5 degree increments of scattering angle in the plane of incidence (β = 0), over a range from 80 to 80 degrees

Summary

Introduction

Polarimetric imaging is of growing interest in the remote sensing community. The utility of the technique has mainly been in areas where flat surfaces of manmade materials are involved such as surfaces in the urban environment or anomaly detection of targets such as surface laid mines. One class of semi-empirical models is based on geometrical optics and statistical description of surface facet slope distributions These types of models can be represented by the Torrance-Sparrow [1] model from 1967, and they require limitations on roughness relative to the wavelength and generally require masking and shadowing functions. The Fresnel equation is invoked using half the angle between incident and reflected beam direction Dielectric surfaces in this model are typically assumed to have a complex index of refraction n~1.65 based on past measurements. There exist models for polarimetric BRDF in the literature, for instance [7,8] These models are generally quite complex, and rather limited in applicability with respect to scattering angles and surface roughness. Future tests will show the generality in the present approach with respect to the physical phenomena in the material represented by the effective complex index of refraction and the effective roughness parameter

Theory

Experimental results

Discussion and conclusions