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 radiation leaving an arbitrary point on the wall of a spherical cavity with diffuse reflectivity is obtained. 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. The results are applied to the Earth Radiation Budget Experiment (ERBE) integrating sphere. It is shown that by using appropriate interpretation and processing, a high-accuracy shortwave calibration of the ERBE sensors can be achieved.