Journal of the European Optical Society - Rapid publications, Vol 7 (2012)

Differential optics for illumination design in the presence of caustics

P. Ott, L. Yu


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.

© The Authors. All rights reserved. [DOI: 10.2971/jeos.2012.12018]

Full Text: PDF

Citation Details

Cite this article


J. M. Howard, "Optical design using computer graphics," Appl. Optics 40, 3225-3231 (2001).

J. M. Howard, "SLIDERS: the next generation of automated optical design tools has arrived," Proc. SPIE 5174, 19-25 (2003).

E. D. Evans, and S. A. Collins, "Expressions for tracing rayassociated electromagnetic fields through optical systems," J. Opt. Soc. Am. A 8, 841-849 (1991).

V. Greco, and G. Giusfredi, "Reflection and refraction of narrow Gaussian beams with general astigmatism at tilted optical surfaces: a derivation toward lens design," Appl. Optics 46, 513-521 (2007).

H. Ries, and J. Muschaweck, "Tailord freeform optical surfaces," J. Opt. Soc. Am. A 19, 590-595 (2002).

W. Klein, Asphrische Flchen in optischen Systemen zur Korrektion verschiedener Bildfehler, in Jahrbuch fr Optik und Feinmechanik 1992 (Schiele & Schn, Berlin, 1992).

G. D. Wasserman, and E. Wolf, "On the theory of aplanatic aspheric systems," Proc. Phys. Soc. B 64, 2-8 (1949).

W. A. Parkyn, "Illumination lenses designed by extrincis differential geometry," SPIE 3482, 389-396 (1998).