Design considerations regarding ellipsoidal mirror based reflectometers

Michael R Benson,Michael A Marciniak

doi:10.1364/oe.21.027519

Abstract

Hemi-ellipsoidal mirrors are used in reflection-based measurements due to their ability to collect light scattered from one focal point at the other. In this paper, a radiometric model of this energy transfer is derived for arbitrary mirror and detector geometries. This model is used to examine the imaging characteristics of the mirror away from focus for both diffuse and specular light. The radiometric model is applied to several detector geometries for measuring the Directional Hemispherical Reflectance for both diffuse and specular samples. The angular absorption characteristics of the detector are then applied to the measurement to address measurement accuracy for diffuse and specular samples. Examining different detector configurations shows the effectiveness of flat detectors at angles ranging from normal to 50°, and that multifaceted detectors can function from normal incidence to grazing angles.

Highlights

Directional Hemispherical Reflectance (DHR) is a metric used to describe the ratio of light reflected from a surface to the light incident at a given angle of incidence
All of the light scattered by the sample is reflected by the mirror to the second focal point, where the detector measures the total light reflected from the sample
For the case of normal incidence, the detector could accurately measure a sample with δ = 0.050 with less than a 1% error

Summary

Introduction

Directional Hemispherical Reflectance (DHR) is a metric used to describe the ratio of light reflected from a surface to the light incident at a given angle of incidence. Because this metric requires measuring the total amount of light reflected, the measurement instrument must be able to capture all light reflected over the front hemisphere of the sample. All of the light scattered by the sample is reflected by the mirror to the second focal point, where the detector measures the total light reflected from the sample

Image formation

Image distortion

Size of the detector

Coupling light into the detector

Findings

Conclusion