A simple matrix technique is presented for modeling integrating-sphere performance. The method is applicable to any sphere configuration, including those with flat areas, specular samples, and baffles, and is especially effective when used in computer simulations of sphere irradiance. The formalism can accommodate the angular sensitivity of any detector or the bidirectional-reflectance distribution function of any sample. Examples of simple analytical solutions are presented, and computer simulation is demonstrated with calculations of the irradiance inhomogeneities caused by underfilling a flat sample. In particular, the simulation shows that, when the input beam does not completely fill a flat sample, the sample is surrounded by a band of reduced irradiance. Outside this dark band, the irradiance is increased slightly. The width of the dark band, but not its depth, increases as the beam size decreases relative to the sample size. The depth depends on sample size and reflectance. Outside the dark-band region, the irradiance shifts due to sample underfilling are much smaller than the easily avoidable, first-order errors caused by neglecting the flat-sample effects.
© 1991 Optical Society of America
Original Manuscript: July 20, 1990
Revised Manuscript: February 18, 1991
Manuscript Accepted: March 25, 1991
Published: September 1, 1991
Herbert L. Tardy, "Matrix method for integrating-sphere calculations," J. Opt. Soc. Am. A 8, 1411-1418 (1991)