## Abstract

A general multidomain integral formula is presented for calculating fluxes of radiation striking a circular disk from various off-axis point source types embedded in an attenuating or nonattenuating medium. This formula is expressed by double line integrals of radiant intensity and sine functions with respect to the polar and horizontal angles determining the angular distribution of the emitted radiation. The formula reduces to single line integral expressions when radiation does not depend on the horizontal angle and is directly applicable for calculating fluxes of revolutional symmetry around the optical axis of the source perpendicular to the disk. The applicability of this reduced formula is tested by computing radiant fluxes from Lambertian and Gaussian point sources using a simple numerical procedure for single integrals. The computed data are illustrated graphically, tabulated, and validated using OSLO. Finally, the accuracy, similarity, and applicability of the results provided by the integral formula and the OSLO program are analyzed. Numerical results have shown the effectiveness of the presented formulas for calculating radiant fluxes from various on- and off-axis point sources passing through a nonattenuating or attenuating homogeneous isotropic media and incident on a circular disk perpendicular to optical axes of these sources. Practical applications of these formulas include optical sensing and metrology, optical coupling, fiber optic for biomedical measurements, and creative lighting design.

© 2013 Optical Society of America

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