Abstract

The luminance of a source is the key to any calculation in illumination analysis. The lambertian source is remembered to have several characteristic attributes. The illuminance at a detector element through an apertur limiting hole is shown to be independent of position and geometry of the source. This law can be extended to non-lambertian sources, when the hole is made arbitrariliy small. As a consequence the concept of 'pseudo luminance' of the hole is introduced. Inserting an optical system between hole and source leads to the final configuration under investigation. The hole is now to be understood as the pupil of the optical system including everything up to and inclusive the source. The identity of pseudo-luminance at the pupil and the original luminance of the source is of fundamental importance. Calculating the illumination at a detector element means integrating a luminance-function over the pupil. The discontinuity of this integrand at the edge of the pupil (zero outside) has strong consequencies to the performance of any quadrature-algorithm under use. Classical methods are not satisfactory for general cases where non-convex pupil areas are involved. A special numerical quadrature-scheme is outlined.

© 1990 Optical Society of America