Modeling the performance of an integrating-cavity absorption meter: theory and calculations for a spherical cavity.

A mathematical model for photon behavior within a spherical integrating-cavity absorption meter (ICAM) that does not depend on the assumption of a homogeneous energy density within the cavity has been developed. Explicit expressions for the proportion of emitted or reflected photons that survive a single transit across the cavity, the average number of collisions with the wall per photon, and the average path length per photon, are derived for an absorbing nonscattering medium. Monte Carlo modeling shows that operation of the ICAM is essentially unaffected by scattering, in agreement with the experimental observations of Fry et al. [Appl. Opt. 31, 2055 (1992)]. Calculations for the performance of the absorption meter as a function of the cavity diameter, the absorption coefficient of the medium, and the reflectivity of the cavity are presented.