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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.

Differential optics for illumination design in the presence of caustics