Influence of finite-sized detection solid angle on bidirectional reflectance distribution function measurements

This paper deals with limitations and often overlooked sources of error introduced in compact double-beam goniophotometers. It is shown that relative errors in measured radiance factor, comparable to the total measurement uncertainty, can be introduced if recommended corrections are not carried out. Two different error sources are investigated, both related to the size of the detection solid angle. The first is a geometrical error that occurs when the size of the illuminated area and detector aperture are comparable to the distance between them. The second is a convolution error due to variations in radiant flux over the detector aperture, which is quantified by simulating the full 3D bidirectional reflectance distribution function (BRDF) of a set of samples with different degrees of anisotropic reflectance. The evaluation is performed for a compact double-beam goniophotometer using different detection solid angles, and it is shown that both error sources introduce relative errors of 1%-3%, depending on viewing angle and optical properties of the sample. Commercially available compact goniophotometers, capable of absolute measurements, are becoming more and more common, and the findings in this paper are therefore important for anyone using or planning to use this type of instrument.