Design of refractive optical elements with two free-form surfaces for generation of prescribed illuminance distribution
S.V. Kravchenko, M.A. Moiseev, L.L. Doskolovich

Image Processing Systems Institute, Russian Academy of Sciences,
Samara State Aerospace University

Full text of article: Russian language.

Abstract:
New optimization method for design of refractive optical elements with two free-form surfaces is presented. Algorithm of design consists of two parts: generation of initial approximation and the further optimization of outer surface parameters from condition of producing prescribed illuminance distribution. As an example the optical element generating uniformly illuminated rectangular region with angular sizes 60° × 40° with extended 1x1 mm Lambertian light source is computed. The light efficacy of optical element is about 88,5% and the relative root-mean-square error of generated illuminance distribution is less than 8,5 %.

Key words:
light emitting diode, free-form surface, optimization method, illuminance distribution, non-imaging optics, optical surface design.

References:

  1. Guan, P. On a Monge-Ampere equation arising in geometric optics / P. Guan, X.-J. Wang // Journal of Differential Geometry. – 1998. – Vol. 48, Issue 2. – P. 205-223. – ISSN 0022-040X.
  2. Elmer, W.B. Optical design of reflectors. Part 2 / W.B. El­mer // Applied Optics. – 1978. – Vol. 17, Issue 7. – P. 977-979. – ISSN 0003-6935.
  3. Oliker, V.I. Radially symmetric solutions of a Monge-Ampere equation arising in the reflector mapping problem / V.I. Oliker, P. Waltman // Proceedings of the UAB International Conference on Differential Equations and Mathematical Physics, Lecture Notes in Math, 1987. – P. 361-374.
  4. 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).
  5. Kravchenko, S.V. Design of axis-symmetrical optical element with two aspherical surfaces for generation of prescribed irradiance distribution / S.V. Kravchenko, M.A. Moi­seev, L.L. Doskolovich, N.L. Kazanskiy // Computer Optics. – 2011. – Vol. 35(4). – P. 467-472. – (In Russian).
  6. Moiseev, M.A. Fast and robust technique for design of axisymmetric TIR optics in case of an extended light source / Mikhail A. Moiseev, Leonid L. Doskolovich, Kseniya V. Bo­risova, Egor V. Byzov // Journal of Modern Optics. – 2013. – Vol. 60, Issue 14. – P. 1100-1106.
  7. Chen, H.-C. Rectangular illumination using a secondary optics with cylindrical lens for LED street light / H.-C. Chen, J.-Y. Lin, H.-Y. Chiu // Optics Express. – 2013.– Vol. 21, Issue 3. – P. 3201-3212.
  8. Lin, K.Ch. Weighted least-square design of freeform lens for multiple point sources / K.Ch. Lin // Optical Engineering. – 2012. – Vol. 51, Issue 4 – P. 043002.
  9. Moiseev, M.A. Design of refractive spline surface for generating required irradiance distribution with large angular dimension / M.A. Moiseev, L.L. Doskolovich // Journal of Modern Optics. ? 2010. ? Vol. 57(7). – P. 536-544. ? ISSN 0950-0340.
  10. Moiseev, M.A. Design of 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. – ISSN 0134-2452. – (In Russian).
  11. Michaelis, D. Cartesian oval representation of freeform optics inillumination systems / D. Michaelis, P. Schreiber, A. Bräuer // Optics Letters. – 2011. – Vol. 36(6). – P. 918-920.
  12. Benitez, P. Simultaneous multiple surface optical design method in three dimensions / P. Benitez, J.C. Minano, J. Blen, R. Mohe­dano, J. Chaves, O. Dross, M. Hernandez, W. Falicoff // Optical Engineering. – 2004. – Vol. 43, Issue 7. – P. 1489-1502.
  13. Bauerle, A. Algorithm for irradiance tailoring using multiple freeform optical surfaces / A. Bauerle, A. Bruneton, R. Wes­ter, J. Stollenwerk, P. Loosen // Optics Express. – 2012. – Vol. 20, Issue 13. – P. 14477-14485.
  14. Bruneton, A. High resolution irradiance tailoring using multiple freeform surfaces / A. Bruneton, A. Bäuerle, R. Wester, J. Stollenwerk, P. Loosen // Optics Express. – 2013. – Vol. 21(9). – P. 10563-10571.
  15. Feng, Z. Beam shaping system design using double freeform optical surfaces / Z. Feng, L. Huang, M. Gong, G. Jin // Optics Express. – 2013. – Vol. 21(12). – P. 14728-14735.
  16. Duerr, F. Tailored free-form optics with movement to integrate tracking in concentrating photovoltaics / F. Duerr, Y. Meuret, H. Thienpont // Optics Express. – 2013. – Vol. 21(S3). – P. A401-A411.
  17. http://en.wikipedia.org/wiki/Bicubic_interpolation.
  18. http://www.lambdares.com/tracepro.
  19. Born, M. Principles of optics / M. Born, E. Wolf. – Cambridge: Cambridge University Press, 2003. – 952 p.
  20. http://www.mathworks.com/products/matlab/.

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