Design of refractive optical element producing required irradiance distribution for extended light source
M.A. Moiseev, L.L. Doskolovich

Image Processing Systems Institute of the RAS,
Samara State Aerospace University

Full text of article: Russian language.

Abstract:
A method for design of refractive optical element producing the prescribed irradiance distribution with large angular dimensions from extended light source is presented. The method is based on the gradient optimization of the refractive surface represented as a bicubic spline in spherical coordinates. The optical elements that produce uniform irradiance distribution in the elliptic and rectangular regions for point and extended light sources are computed. The energy efficiency of the optical elements is more than 73 %; the non-uniformity of the generated irradiance distribution is less than 7.5 %. The ratio of the illuminated region size to the thickness of the optical system is about 6.5. This value is twice as large as that for the optical elements presented in available publications.

Key words:
optical element design, uniform irradiance, light-emitting diode, gradient method.

References:

  1. Muschaweck, J. Tailored LED lowbeam headlamps / J. Muschaweck // Laser+Photonik, 2004. – P. 26–28.
  2. Benitez, P. Etendue Preserving Mixing and Projection Optics for High Brightness LEDs Applied to Automotive Headlamps / P. Benitez, J. Chaves, A. Cvetkovic, O. Dross, J.C. Minano, R. Mohedano // Proc. SPIE, 2006. – Vol. 6342(2).
  3. Benitez, P. Etendue-preserving mixing and projection optics for high-luminance LEDs, applied to automotive headlamps / P. Benitez, J. Chaves, A. Cvetkovic, O. Dross, J.C. Minano, R. Mohedano // Optics Express, 2006. – Vol. 14(26). – P. 13014–13020. – ISSN: 1094-4087.
  4. Sung-Il, Ch. Microlens array diffuser for a light-emitting diode backlight system / L. Baik-Kyu, H. Sh. Dong, K. Jin-Jong, Y. Jun-Bo, K. Hongki, Ch. Sung-Il // Optics Letters, 2006. – Vol. 31(20). – P. 3016–3018. – ISSN: 0146-9592.
  5. Jui-Wen, P. Homogenized LED-illumination using microlens arrays for a pocket-sized projector / W. Chih-Ming, L. Hsiao-Chin, Ch. Jeng-Yang, P. Jui-Wen, S. Wen-Shin // Optics Express, 2007. – Vol. 15(17). – P. 10483–10491. – ISSN: 1094-4087.
  6. 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. – ISSN 0022-040X.
  7. Oliker, V. Determining the intensities produced by reflected and refracted wave fronts in geometrical optics / E. Newman, V.I. Oliker // J. Opt. Soc. Am. A, 1995. – Vol. 12(4). – P. 784–793. – ISSN 1084-7529.
  8. Elmer, W.B. Optical design of reflectors. Part 2 / W.B. Elmer // Applied Optics, 1978. – Vol. 17(7). – P. 977–979. – ISSN 0003-6935.
  9. Elmer, W.B. The Optical Design of Reflectors / W.B. Elmer – N.Y.: Willey, 1980. – 290 pp.
  10. Kusch, O. Computer-aided optical design of illumination and irradiating devices / O. Kusch – M.: "ASLAN" Publishing House, 1993. – 192 pp.
  11. 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. – ISSN 1084-7529.
  12. 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. – ISSN 1070-9762.
  13. Doskolovich, L.L. Designing a mirror to form a lineshaped directivity diagram / L.L. Doskolovich, N.L. Kazansky, S. Bernard // J. Mod. Opt., 2007. – Vol. 54(4). – P. 589–597. – ISSN 0950-0340.
  14. 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). – ISSN 0134-2452.
  15. Doskolovich, L.L. Calculations for refracting optical elements for forming directional patterns in the form of a rectangle / L.L. Doskolovich, M.A. Moiseev // J. Opt.Tech., 2009. – Vol. 76(7). – P. 430–434. – ISSN 0134-2452.
  16. 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.
  17. Ries, H. Tailoring freeform lenses for illumination / J. Muschaweck, H. Ries // Proc. SPIE, 2001. – Vol. 4442. – P. 43–50.
  18. Ries, H. Tailored freeform optical surfaces / J. Muschaweck, H. Ries // J. Opt. Soc. A. A, 2002. – Vol. 19(3). – P. 590–595. – ISSN 1084-7529.
  19. 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.
  20. Parkyn, B. Free-form illumination lens designed by a pseudo-rectangular lawnmower algorithm / B. Parkyn, D. Pelka // Proc. SPIE, 2006. – Vol. 6338.
  21. 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). – ISSN 0134-2452.
  22. 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).  ISSN 0320-7102.
  23. 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. – ISSN 0134-2452.
  24. Yi, D. Freeform LED lens for uniform illumination / G. Pei-fu, L. Xu, D. Yi, Zh. Zhen-rong // Optics Express, 2008. – Vol. 16(17). – P. 12958–12966. – ISSN 1094-4087.
  25. Doskolovich, L.L. Gradient calculation of refracting B-spline surface generating prescribed irradiance distribution / L.L. Doskolovich, M.A. Moiseev // Computer Optics. – 2009. – Vol. 33(1). – P. 37–42. – (in Russian). – ISSN 0134-2452.
  26. Boor, C. De A Practical Guide to Splines / Carl De Boor – N.Y.: Springer, 2001. – 346 pp.
  27. Gill, Ph.E. Practical Optimization / Ph.E. Gill, W. Murray, M.H. Wright – N.Y.: Springer, 1981. – 401 pp.
  28. http://lambdares.com/software_products/tracepro/
  29. http://www.philipslumileds.com/pdfs/DS63.pdf

© 2009, ИСОИ РАН
Россия, 443001, Самара, ул. Молодогвардейская, 151; электронная почта: ko@smr.ru ; тел: +7 (846 2) 332-56-22, факс: +7 (846 2) 332-56-20