The radiance distribution on the wall of an integrating sphere having a centrally located sample is analyzed. The radiance of the sphere wall is found as a function of the angular position inside the sphere. The analysis assumes mixed reflectance for the samples. It takes into account the effect of (1) the size of the sample relative to the sphere, (2) the average diffuse reflectance of the sphere wall, (3) the reflectance of the back face of the sample, and (4) the angle of incidence of the reference beam incident on the sample. The analysis considers the effect of the radiant exchange between the sample, its back, and the sphere wall. It allows also for the shadow of the sample on the sphere wall. The radiance distribution inside the sphere is found in case the reference beam does not hit the sample directly upon its entry into the sphere (this is useful in the absolute-reflectance-measurement technique). It is also derived when the sample is in the way of the reference beam. The expressions found for the radiance distribution allow accurate estimation of the errors due to the effect of centrally located samples in integrating sphere in reflectance measurements. The effects of the different factors involved in the interaction between the sample and the sphere wall can be seen from radiance-distribution expressions and would be of use in design of integrating-sphere reflectance-measurement systems. An example of the estimation of errors due to the effect of a centrally located sample inside an integrating sphere, in the measurement of mixed reflectance, is demonstrated.
HEMMAT H. SAFWAT, "Effect of Centrally Located Samples in the Integrating Sphere," J. Opt. Soc. Am. 60, 534-541 (1970)