Optical systems protected by plane-parallel entrance windows from external environmental conditions were studied to determine the radiant fluxes passing through their circular apertures from wide-angle on-axis and off-axis point sources. The study was performed for the case when the windows, the internal environments, and the external environments of these optical systems were considered as three different homogeneous isotropic and attenuating media. All considerations were made for ideal plane-parallel windows illuminated by an arbitrary radiation field applying the multiple-reflection theory. As a result of this study a multi-domain integral equation method based on a mathematical formula expressed by a series of multiple-reflected fluxes of radiation within the plane-parallel window was proposed. The applicability of the method was tested using computer simulations for an isotropic point source and a small area Lambertian source represented by a point-source model. The computed results were validated by the optical software for layout and optimization program from Lambda Research Corporation (USA). The selected results were illustrated graphically and analyzed. The numerical simulations have shown high accuracy and efficiency in the calculations for arbitrary emitting point sources. The potential applications of the presented method include optical sensing and metrology of noncollimated radiation from the various on-axis and off-axis point sources.
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