(44-6) 04 * << * >> * Russian * English * Content * All Issues
  
Analytical design of refractive optical elements generating a prescribed two-dimensional intensity distribution
  E.V. Byzov 1, L.L. Doskolovich 1,2, S.V. Kravchenko 1, N.L. Kazanskiy 1,2
1 IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
     443001, Samara, Russia, Molodogvardeyskaya 151,
    2 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34
  PDF, 1320 kB
DOI: 10.18287/2412-6179-CO-818
Pages: 883-892.
Full text of article: Russian language.
 
Abstract:
A new source-target  mapping for the design of refractive optical elements generating prescribed 2D  intensity distributions is proposed. The calculation of the optical element is  reduced to the solution of ordinary explicit differential equations. The  simulation results presented demonstrate high performance of the proposed  method. While generating uniform rectangular intensity distributions with  angular dimensions varying from 80°×1° to 40°×20°, the normalized  root-mean-square deviations between the generated and required distributions do  not exceed 15 %.
Keywords:
Freeform surface, LED optics, refractive optics, nonimaging optics, intensity distribution, computation methods.
Citation:
  Byzov EV, Doskolovich LL, Kravchenko SV, Kazanskiy NL. Analytical design of refractive optical elements generating a prescribed two-dimensional intensity distribution. Computer Optics 2020; 44(6): 883-892. DOI: 10.18287/2412-6179-CO-818.
Acknowledgements:
  This work was financially supported by the Russian Science Foundation (Project No. 18-19-00326).
References:
- Scuello M, Abramov I, Gordon J, Weintraub S. Museum lighting: Why are some illuminants preferred? J Opt Soc Am A 2004; 21(2): 306-311.
   
  - Li Z, Yu S, Lin L, Tang  Y, Ding X, Yuan W, Yu B. Energy feedback freeform lenses for uniform illumination  of extended light source LEDs. Appl Opt 2016; 55: 10375-10381..
   
  - Zhao  S, Wang K, Chen F, Qin Z, Liu S. Integral freeform illumination lens design of  LED based pico-projector. Appl Opt 2013; 52: 2985-2993.
     
  - Moiseev  MA, Doskolovich LL. Design of refractive spline surface for generating required  irradiance distribution with large angular dimension. J Mod Opt 2010; 57(7):  536-544.
     
  - Ries  H, Winston R. Tailored edge-ray reflectors for illumination. J Opt Soc Am A  1994; 11: 1260-1264.
     
  - Chaves  J. Introduction to nonimaging optics. 2nd ed. CRC Press; 2016.
     
  - Wu  R, Huang CY, Zhu X, Cheng H-N, Liang R. Direct three-dimensional design of  compact and ultra-efficient freeform lenses for extended light sources. Optica  2016; 3: 840-843.
     
  - Wu  R, Hua H, Benítez P, Miñano JC. Direct design of aspherical lenses for extended  non-Lambertian sources in two-dimensional geometry. Opt Lett 2015; 40:  3037-3040.
     
  - Hu  S, Du K, Mei T, Wan L, Zhu N. Ultra-compact LED lens with double freeform  surfaces for uniform illumination. Opt Express 2015; 23: 20350-20355.
     
  - Li  X, Ge P, Wang H. Prescribed intensity in 3D rotational geometry for extended  sources by using a conversion function in 2D design. Appl Opt 2017; 56:  1795-1798.
     
  - Li  X, Ge P, Wang H. An efficient design method for LED surface sources in  three-dimensional rotational geometry using projected angle difference.  Lighting Res Technol 2019; 51(3): 457-464.
     
  - Byzov  EV, Kravchenko SV, Moiseev MA, Bezus EA, Doskolovich LL. Optimization method  for designing double-surface refractive optical elements for an extended light  source. Opt Express 2020; 28: 24431-24443.
     
  - Guan  P, Wang X-J. On a Monge-Ampere equation arising in geometric optics. J Differ  Geom 1998; 48(2): 205-223.
     
  - Oliker  VI. Geometric and variational methods in optical design of reflecting surfaces  with prescribed irradiance properties. Proc SPIE 2005; 5942: 594207.
     
  - Parkyn WA. Illumination lenses designed by  extrinsic differential geometry. Proc SPIE 1988; 3482: 389-396.
     
  - Kirkilionis  M, Kromker S, Rannacher R, Tomi F. Trends in nonlinear analysis. Berlin: Springer; 2003:  193-224.
     
  - Elmer  W, Cooke F. Optical design of reflectors. Part 2. Appl Opt 1978; 17(7):  977-979.
     
  - Moiseev  MA, Doskolovich LL. Design of TIR optics generating the prescribed irradiance  distribution in the circle region. J Opt Soc Am A 2012; 29(9): 1758-1763.
     
  - Doskolovich  LL, Kazanskiy NL, Kharitonov SI, Perlo P, Bernard S. Designing reflectors to  generate a line-shaped directivity diagram. J Mod Opt 2005; 52(11): 1529-1536.
     
  - Doskolovich  LL, Kazanskiy NL, Bernard S. Designing a mirror to form a line-shaped  directivity diagram. J Mod Opt 2007; 54(4): 589-597.
     
  - Dmitriev  AYu, Doskolovich LL. Design of refracting surface to generate a line-segment  directivity diagram. Computer Optics 2010; 34(4): 476-480.
     
  - Doskolovich  LL, Dmitriev AY, Bezus EA, Moiseev MA. Analytical design of freeform optical  elements generating an arbitrary-shape curve. Appl Opt 2013; 52(12): 2521-2526.
     
  - Doskolovich  LL, Bezus EA, Moiseev MA, Bykov DA, Kazanskiy NL. Analytical source-target  mapping method for the design of freeform mirrors generating prescribed 2D  intensity distributions. Opt Express 2016; 24: 10962-10971.
     
  - Wu  R, Xu L, Liu P, Zhang Y, Zheng Z, Li H, Liu X. Freeform illumination design: a  nonlinear boundary problem for the elliptic Monge–Ampére equation. Opt Lett  2013; 38: 229-231.
     
  - Wu  R, Li K, Liu P, Zheng Z, Li H, Liu X. Conceptual design of dedicated road  lighting for city park and housing estate. Appl Opt 2013; 52: 5272-5278.
     
  - Wu  R, Benítez P, Zhang Y, Miñano JC. Influence of the characteristics of a light  source and target on the Monge–Ampére equation method in freeform optics  design. Opt Lett 2014; 39: 634-637.
     
  - Doskolovich  LL, Bykov DA, Mingazov AA, Bezus EA. Optimal mass transportation and linear  assignment problems in the design of freeform refractive optical elements  generating far-field irradiance distributions. Opt Express 2019; 27:  13083-13097.
     
  - Mingazov  AA, Bykov DA, Bezus EA, Doskolovich LL. On the use of the supporting quadric  method in the problem of designing double freeform surfaces for collimated beam  shaping. Opt Express 2020; 28: 22642-22657.
     
  - Doskolovich  LL, Andreev ES, Kharitonov SI, Kazansky NL. Reconstruction of an optical  surface from a given source-target map, J Opt Soc Am A 2016; 33: 1504-1508.
     
  - Fournier  FR, Cassarly WJ, Rolland JP. Fast freeform reflector generation using  source-target maps. Opt Express 2010; 18: 5295-5304.
     
  - Wang  L, Qian K, Luo Y. Discontinuous free-form lens design for prescribed  irradiance, Appl Opt 2007; 46: 3716-3723.
     
  - Ding  Y, Liu X, Zheng Z, Gu P. Freeform LED lens for uniform illumination. Opt  Express 2008; 16: 12958-12966.
     
  - Wu  R, Li H, Zheng Z, Liu X. Freeform lens arrays for off-axis illumination in an  optical lithography system. Appl Opt 2011; 50: 725-732.
     
  - Bruneton  A, Bäuerle A, Wester R, Stollenwerk J, Loosen P. High resolution irradiance  tailoring using multiple freeform surfaces, Opt Express 2013; 21(9):  10563-10571.
     
  - Bösel  C, Gross H. Ray mapping approach for the efficient design of continuous  freeform surfaces. Opt Express 2016; 24(13): 14271-14282.
     
  - Schwartzburg  Y, Testuz R, Tagliasacchi A, Pauly M. High-contrast computational caustic  design. ACM Trans Graph 2014; 33(4): 1-11.
     
  - Feng  Z, Froese BD, Liang R. Freeform illumination optics construction following an  optimal transport map. Appl Opt 2016; 55(16): 4301-4306.
     
  - Lin  C, Fang Y, Su W. Design of LED free-form lens for sensor systems, Sens Mater  2020; 32(6): 2177-2185.
     
  - Desnijder  K, Hanselaer P, Meuret Y. Flexible design method for freeform lenses with an  arbitrary lens contour. Opt Lett 2017; 42(24): 5238-5241.
     
  - Prautzsch  H, Boehm W, Paluszny M. Bézier and B-spline techniques. Berlin,  Heidelberg:  Springer-Verlag; 2002. 
 
  - TracePro – software for design and analysis of illumination  and optical systems. Source: <https://www.lambdares.com/tracepro/>.
   
  
  © 2009, IPSI RAS
  151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: ko@smr.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20