Explicit solution of the spectral radiance in integrating spheres with application to the Earth Radiation Budget Experiment ground calibration

An explicit solution of the spectral radiance leaving an arbitrary point on the wall of a spherical cavity with diffuse reflectivity is obtained. The solution is applicable to spheres with an arbitrary number of openings of any size and shape, an arbitrary number of light sources with possibly nondiffuse characteristics, a nonuniform sphere-wall temperature distribution, nonuniform and nondiffuse sphere-wall emissivity, and nonuniform but diffuse spherewall spectral reflectivity. A general measurement equation is obtained that describes the output of a sensor measuring the sphere output within a given field of view and with specified angular and spectral responses measuring the sphere output. The results are applied to the Earth Radiation Budget Experiment (ERBE) integrating sphere. The sphere-wall radiance uniformity, loading effects, and nonuniform wall temperature effects are investigated. It is shown that by using appropriate interpretation and processing, a high-accuracy shortwave calibration of the ERBE sensors can be achieved.