Design of an axisymmetric optical element generating a prescribed illuminance distribution and wavefront
Doskolovich L.L., Andreeva K.V., Bykov D.A.

 

IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Molodogvardeyskaya 151, 443001, Samara, Russia,
Samara National Research University, 443086, Russia, Samara, Moskovskoye Shosse 34

 PDF

Abstract:
Design of an axisymmetric refracting optical element to transform an incident beam into an output beam with the prescribed illuminance distribution and prescribed wavefront is considered. The wavefront of the output beam is represented by the eikonal function defined in some plane behind the optical element. The computation of the optical element surface is reduced to the solution of two explicit ordinary differential equations of the first order. As examples, we consider the design of two optical elements to transform a spherical beam from a point Lambert light source into a beam with the uniform illuminance and plane wavefront and a beam with the complex wavefront to focus into an on-axis line.

Keywords:
geometric optics, optical surface design, eikonal.

Citation:
Doskolovich LL, Andreeva KV, Bykov DA. Design of an axisymmetric optical element generating a prescribed illuminance distribution and wavefront. Computer Optics 2018; 42(5): 772-778. DOI: 10.18287/2412-6179-2018-42-5-772-778.

References:

  1. Frieden BR. Lossless conversion of a plane laser wave to a plane wave of uniform irradiance. Appl Opt 1965; 4(11): 1400-1403. DOI: 10.1364/AO.4.001400.
  2. Rhodes PW, Rhodes DL. Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis. Appl Opt 1980; 19(20): 3545-3553. DOI: 10.1364/AO.19.003545.
  3. Hoffnagle JA, Jefferson CM. Design and performance of a refractive optical system that converts a Gaussian to a flattop beam. Appl Opt 2000; 39(30): 5488-5499. DOI: 10.1364/AO.39.005488.
  4. Zhang S, Neil G, Shinn M. Single-element laser beam shaper for uniform flat-top profiles. Opt Express 2003; 11(16): 1942-1948. DOI: 10.1364/OE.11.001942.
  5. Ma H, Lui Z, Jiang P, Xu X, Du S. Improvement of Galilean refractive beam shaping system for accurately generating near diffraction-limited flattop beam with arbitrary beam size. Opt Express 2011; 19(14): 13105-13117. DOI: 10.1364/OE.19.013105.
  6. Duerr F, Thienpont H. Refractive laser beam shaping by means of a functional differential equation based design approach. Opt Express 2014; 22(7): 8001-8011. DOI: 10.1364/OE.22.008001.
  7. Hui X, Liu J, Wan Y, Lin H. Realization of uniform and collimated light distribution in a single freeform-Fresnel double surface LED lens. Appl Opt 2017; 56(15): 4561-4565. DOI: 10.1364/AO.56.004561.
  8. Poleshchyk AG, Nasyrov RK. Aspherical wavefront shaping with combined computer generated holograms. Opt Eng 2013; 52(9): 091709. DOI: 10.1117/1.OE.52.9.091709.
  9. Wyant JC, Bennett VP. Using computer-generated holograms to test aspheric wavefronts. Appl Opt 1972; 11(12): 2833-2839. DOI: 10.1364/AO.11.002833.
  10. Chen S, Zhao C, Dai Y, Li S. Reconfigurable optical null based on counter-rotating Zernike plates for test of aspheres. Opt Express 2014; 22(2): 1381-1386. DOI: 10.1364/OE.22.001381.
  11. Tsai CY. Refractive collimation beam shaper design and sensitivity analysis using a free-form profile construction method. J Opt Soc Am A 2017; 34(7): 1236-1245. DOI: 10.1364/JOSAA.34.001236.
  12. Kravtsov YuA, Orlov YuI. Geometrical optics of inhomogeneous media. Berlin: Springer-Verlag Berlin Heidelberg; 1990. ISBN: 978-3-642-84033-3.
  13. Doskolovich LL, Moiseev MA. Design of radially-sym­metrical refractive surface taking into account Fresnel loss [In Russian]. Computer Optics 2008; 32(2): 201-203.
  14. Kravchenko SV, Moiseev MA, Doskolovich LL, Kazanskiy NL. Design of axis-symmetrical optical element with two aspherical surfaces for generation of prescribed irradiance distribution [In Russian]. Computer Optics 2011; 35(4): 467-472.
  15. 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): 1758-63. DOI: 10.1364/JOSAA.29.001758.
  16. LAMBDA Research Corporation. Source: áhttp://www.lambdares.com/ñ.
  17. Soifer V, Kotlyar V, Doskolovich L. Iterative methods for diffractive optical elements computation. London: Taylor & Francis Ltd; 1997. ISBN: 0-7484-0634-4.
  18. Doskolovich LL, Kazanskiy NL, Soifer VA, Tzaregorodtzev AY. Analysis of quasiperiodic and geometric optical solutions of the problem of focusing into an axial segment. Optik 1995; 101(2): 37-41.
© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: journal@computeroptics.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20