Full text of article: Russian language.

Abstract:
Optical element design containing two groups of optical surfaces is presented. The first group produces cylindrical beam from the light source spherical beam. The second one generates required irradiance distribution from incident cylindrical beam. The method for optical elements design to generate required irradiance distribution is presented. Two optical elements producing uniform irradiance distribution in rectangular regions with sizes17x4 meters and 17x2 meters are computed. Energy efficiency of computed optical elements exceeds 83 % and non-uniformity of generated irradiance distribution is less than 9 %.

Key words:
design of optical elements, irradiance distribution, light emitting diode, total internal reflection, collimating.

References:

1. Pengfei, P. On a Monge-Ampere equation arising in geometric optics / P. Pengfei, W. Xu-Jia // J. Differential Geom. – 1998. – Vol. 48(2). – P. 205-223.
2. Knowles, I. Radially symmetric solutions of a Monge-Ampere equation arising in the reflector mapping problem / I. Knowles [et al.] //Proceedings of the UAB International Conference on Differential Equations and Mathematical Physics, Lecture Notes in Math, 1987. – P. 361-374.
3. Oliker, V.I. Geometry and Nonlinear Partial Differential Equations / V.I. Oliker, A. Treibergs. – AMS Bookstore, 1992. – P. 154.
4. Elmer, W.B. Optical design of reflectors. P. 2 / W.B. Elmer // Applied Optics. – 1978. – Vol. 17(7). – P. 977–979.
5. Elmer, W.B. The Optical Design of Reflectors / W.B. El­mer. – N.Y.: Willey, 1980. – 290 p.
6. Kusch, O. Computer-aided optical design of illumination and irradiating devices / O. Kusch – Moscow: “ASLAN” Publishing House, 1993. – 192 p.
7. Hicks, R.A. Designing a mirror to realize a given projection / R.A. Hicks // J. Opt. Soc. Am. A. – 2005. – Vol. 22(2). – P. 323-330.
8. Doskolovich, L.L. Calculating the surface shape of mirrors for shaping an image in the form of a line / L.L. Doskolovich, S.I. Kharitonov // J. Opt. Tech. – 2005. – Vol. 72(4). – P. 318-321. – (in Russian).
9. Doskolovich, L.L. Designing a mirror to form a lineshaped directivity diagram / L.L. Doskolovich, N.L. Kazanskiy, S. Bernard // J. Mod. Opt. – 2007. – Vol. 54(4). – P. 589-597.
10. Doskolovich, L.L. Designing radially symmetric refractive surfaces with regard for Fresnel losses / L.L. Doskolovich, M.A. Moiseev // Computer Optics. – 2008. – Vol. 32(1). – P. 201-203. – (in Russian).
11. Bortz, J. Optimal design of a nonimaging projection lens for use with an LED source and a rectangular target / J. Bortz, N. Shatz, D. Pitou // Proc. SPIE. – 2000. – Vol. 4092. – P. 130-138.
12. Ries, H. Tailoring freeform lenses for illumination / H. Ri­es, J. Muschaweck // Proc. SPIE. – 2001. – Vol. 4442. – P. 43-50.
13. Ries, H. Tailored freeform optical surfaces / H. Ries, J. Mu­schaweck, // J. Opt. Soc. Am. A. – 2002. – Vol. 19(3). – P. 590-595.
14. Jacobson, B.A. Lens for uniform LED illumination: an example of automated optimization using Monte Carlo ray-tracing of an LED source / B.A. Jacobson, R.D. Gendelbach // Proc. SPIE. – 2001. – Vol. 4446. – P. 130-138.
15. Parkyn, B. Free-form illumination lens designed by a pseudo-rectangular lawnmower algorithm / B. Parkyn, D. Pelka // Proc. SPIE. – 2006. – Vol. 6338.
16. Belousov, A.A. A gradient method for solving problem of focusing light from extended source to the 2D region / A.A. Belousov, L.L. Doskolovich // Computer Optics . – 2007. – Vol. 31(3). – P. 20-26. – (in Russian).
17. Belousov, A.A. A gradient method of eikonal calculating for focusing in the prescribed region / A.A. Belousov, L.L. Doskolovich, S.I. Kharitonov // Avtometria. – 2007. – Vol. 1. – P. 98-106. – (in Russian).
18. Belousov, A.A. A gradient method of designing optical elements for forming a specified irradiance on a curved surface / A.A. Belousov, L.L. Doskolovich, S.I. Kharitonov // J. Opt. Tech. – 2008. – Vol. 75(3). – P. 161-165. – (in Russian).
19. Yi, D. Freeform LED lens for uniform illumination / D. Yi, G. Pei-fu, L. Xu, Zh. Zhen-rong // Optics Express. – 2008. – Vol. 16(17). – P. 12958-12966.
20. Moiseev, M.A. Gradient computation of refracting spline-surface on condition of producing of required irradiance distribution / M.A. Moiseev, L.L. Doskolovich // Computer Optics. – 2009. - Vol. 33(1). - P. 37-42. – (in Russian).
21. Moiseev, M.A. Computation of refracting optical element producing required irradiance distribution for extended light source / M.A. Moiseev, L.L. Doskolovich // Computer Optics. – 2010. – Vol. 34(2). – P. 194-200. – (in Russian).
22. Moiseev, M.A. Computation of refractive optical element producing line-shaped directivity diagram / M.A. Moiseev, L.L. Doskolovich // Computer Optics. – 2008. – Vol. 32(4). – P. 366-369. – (in Russian).
23. Moiseev, M.A. Calculations for refracting optical elements for forming directional patterns in the form of a rectangle / M.A. Moiseev, L.L. Doskolovich // J. of Opt. Tech., – 2009. – Vol. 76(7). – P. 430-434. – (in Russian).
24. Ershova, V.V. Impulse functions. Functions of complex variable. Operator calculus / V.V. Ershova. – Minsk: “Vyshejshaja shkola” Publisher, 1976. – 255 p. – (in Russian).
25. Boor, C. De A Practical Guide to Splines / Carl De Boor. – N.Y.: Springer, 2001. – 346 p.
26. Bonnans, J.-F. Numerical optimization, theoretical and numerical aspects (Secondary Edition) / J.-F. Bonnans [et al.] - N.Y.: Springer, 2006. – 490 p.
27. http://www.lambdares.com/software_products/tracepro/.

---

© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; E-mail: ko@smr.ru; Phones: +7 (846) 332-56-22, Fax: +7 (846) 332-56-20