Numerical modeling of an integrating sphere radiation source

Integrating spheres are often used as calibration sources providing uniform radiance within a solid angle and/or uniform irradiance at a distance. The best performance in such a system can be achieved if one is able to evaluate as well as predict the important characteristics of the sphere system’s output, such as the spatial and angular distributions of radiance over the exit port, or the distribution of irradiance at the external plane of calibration. We have developed the algorithms and specialized software based on Monte Carlo techniques to solve the problem of radiation transfer inside an integrating sphere containing several point sources and conical annular baffle. The new algorithm employs backward ray tracing coupled with the “shadow rays” technique. As a timesaving procedure, the axial symmetry of the sphere and the superposition principle are used to substitute the sum of single source radiation fields rotated through a specific angle, for the radiation field of the complete multiple source sphere. The random (due to the stochastic character of the Monte Carlo method) component of uncertainty for the radiance or irradiance results is less than 0.1%. The results of numerical experiments are used to establish the performance variation as a function of the reflectance and specularity of the sphere wall, the number of radiation sources, the type of baffle used, and the angular distribution of their radiant intensity.