Correcting for non-uniform detector response in bidirectional reflectance distribution function measurements

Abstract Systems for measuring the bidirectional reflectance distribution function (BRDF) are intended to be able to measure a variety of sample scattering distributions—from close-to-specular to diffuse, from polarised to unpolarised. Measuring the BRDF involves taking the ratio of measurements of both the amount of light incident on the sample and the amount of light that is reflected by the sample. Detectors used in these systems have a finite sized aperture, and so the different sample scattering distributions will have different distributions of light falling on the detector, and this distribution will also be different from the distribution of light during the incident beam measurement. An ideal detector with a perfectly uniform response is unlikely in reality. For BRDF measurements, it is generally assumed that the response of the detector is the same for both the incident and scattered beams, so even for imperfect detectors, the response of the detector will drop out when the ratio is taken. However, if for some reason the response of the detector differs between the two ratioed quantities, then it will induce an error in the measured ratio. A difference in the response of the detector in the MSL goniospectrophotometer between the collimated and polarised incident beam and the diffuse and unpolarised scattered beam has been identified. Having identified this issue, two different approaches have been taken to avoid the error in our measurements. Firstly, a correction factor was calculated from a detailed model of the detector, using ray tracing. Secondly, a new detector with an integrating sphere in the position of the photodiode was designed to avoid the differing response. To validate these approaches, we compared measurements made using the new sphere detector with corrected measurements made using the original detector, and demonstrate that these agree within the limits of uncertainty.