Point-source integrating-cavity absorption meter: theoretical principles and numerical modeling

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Abstract
A mathematical model has been developed for photon behavior within a spherical integrating-cavity absorption meter with a point light source at the center of the cavity. Explicit expressions for the average number of collisions with the wall per photon, the average path length per photon, and the transmittance of the cavity containing a water sample relative to that containing pure water are derived for an absorbing nonscattering medium. Monte Carlo modeling shows that the operation of the point-source integrating-cavity absorption meter is essentially unaffected by scattering. Calculations of the performance of the absorption meter as a function of the cavity diameter, absorption coefficient of the medium, and the reflectivity of cavity are presented.