Expressions for the reflectance of finite, perfect diffuse, and perfect specular samples measured in an integrating sphere with finite ports and a uniform, perfectly diffuse reflecting wall, are derived by solving a set of linear equations. The derivation is easy compared with the long computations necessary when using an integral equation approach.
Expressions are given both for the comparison and the substitution method of measurement, with curved or flat sample and standard. For finite, flat, diffuse, and specular samples, computed examples indicate the range of sample sizes within which previous approximate expressions may be used, without introducing significant errors.
BJARNE J. HISDAL, "Reflectance of Perfect Diffuse and Specular Samples in the Integrating Sphere," J. Opt. Soc. Am. 55, 1122-1125 (1965)