Abstract
Alternatively to using time-consuming Monte-Carlo simulations the irradiation at a target plane can also be calculated by differential optics methods. In the case of caustics, these methods yield to infinite irradiance and its results are not directly comparable to those of Monte-Carlo simulations. In this paper, a differential based algorithm for an on axis point source and a rotationally symmetric optical system is presented, which yields to the same results as a Monte-Carlo simulation. However, the differential optical methods are about three orders of magnitude faster than the latter one, thus allowing fast trial and error design of such kind of illumination systems. An applet is presented that uses sliders to change the shape of the lens and other properties of the illumination system whereas the irradiance profile is nearly immediately perceived. For beginners in the field, this does not only accelerate the design process itself but also the learning process is improved considerably. Some extensions and special cases are shortly discussed.
Highlights
Design of illumination systems incorporates regularly MonteCarlo simulations tracing of the order of a million of optical rays
Targeting for a specified irradiance distribution, an approach by trail and error is impeding for beginners. For these simple illumination systems of standard optical elements there is, in contradiction to imaging optical systems, a lack of textbooks which allow to get a feeling of the effect of such systems
The author of this paper suggests that a comparable introductionary subject in illumination design is the analysis of the irradiance profile of a point source collimated by a spherical lens
Summary
Design of illumination systems incorporates regularly MonteCarlo simulations tracing of the order of a million of optical rays. The author himself has teached students and other newcomers in illumination design by using educational licenses of complex commercial software based on Monte Carlo methods from the scratch This kind of teaching, supported by standard illumination ray tracing, is threatened by a number of facts, one of them is that students get disappointed by the high latency between input (e.g. change of the lens parameters) and output, i.e. the irradiance profile. The irradiance profile at a distance of 2000 mm from the lens is seeked (or just consider a scaled version of this example) An application of such a scaled version would be the starting design (based on a point source) of a spot light with a (obviously truncated) lambertian LED and a single spherical lens. From this figure the typical problems associated with this method described up to here are obvious:
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