A gradient method for solving problem of focusing light from extended source to the 2D region

А.А. Belousov, L.L. Doskolovich# Image Processing Systems Institute оf the RAS, Samara, Russia,

Samara State Aerospace University (SSAU), Samara, Russia

А.А. Belousov, L.L. Doskolovich

Samara State Aerospace University (SSAU), Samara, Russia

Full text of article: Russian language.

Abstract:

A computational method for refracting surfaces is considered to form required illuminance distributions from extended light sources. The method is based on surface representation by means of distribution of the light field eikonal in adjacent plane and approximation of a radiation source by the set of points. The eikonal is defined as a polynomial. Calculation of a refracting surface is based on the gradient minimization of an error functional that represents the difference between calculated and required field illuminance. For the gradient of the error functional, an analytical expression is obtained. The refracting surface is calculated to form continuous illuminance distribution of an area.

Key words:

Illumination design, nonimaging optics, geometric optical design, optimization.

Citation:

Belousov AA, Doskolovich LL. A gradient method for solving problem of focusing light from extended source to the 2D region [In Russian]. Computer Optics 2007; 31(3): 20-26.

References:

- Guan P, Wang X. On a Monge-Ampere equation arising in geometric optics. J. of Differential Geometry 1998; 48: 205-223.

- Oliker V. Mathematical aspects of design of beam shaping surfaces in geometrical optics in Trends in Nonlinear Analysis. Springer, Berlin, 2003; 193–224.

- Glimm T, Oliker V. Optical Design of Two-reflector Systems, the Monge-Kantorovich Mass Transfer Problem and Fermat’s Principle. Indiana University Mathematics Journal 2004; 53: 1255-1277.

- Volkov AV, Golovashkin DL, Doskolovich LL, Kazanskiy NL, Kotlyar VV, Pavelyev VS, Skidanov RV, Soifer VA (ed.), Solovjev VS, Usplenyev GV, Kharitonov SI, Khonina SN. Methods of Computer Optics [In Russian]. Moscow: “Fizmatlit” Publisher, 2003; 688 p.

- Soifer VA (ed.), Doskolovich LL, Golovashkin DL, Kharitonov SI, Khonina SN, Kotlyar VV, Paveliev VS, Skidanov RV, Soloviev VS, Volkov AV, Uspleniev GV. Methods For Computer Design of Diffractive Optical Elements. A Wiley-Interscience Publication John Wiley & Sons, Inc., 2002; 765 p.

- Danilov VA, Popov VV, Prokhorov AM, Sagatelyan DM, Sisakyan EV, Sisakyan IN, Soifer VA. Optical elements focusing coherent radiation into arbitrary focal curve [In Russian]. Preprint 69. Moscow: FIAN (Lebedev Physical Institute of the U.S.S.R. Academy of Sciences), 1983; 41 p.

- Goncharsky AV, Danilov VA, Popov VV, Prokhorov AM, Sisakyan IN, Soifer VA, Stepanov VV. Solution of the inverse problem of focusing of laser radiation into an arbitrary curve [In Russian]. Proceedings of the Academy of Sciences of the USSR 1983; 273(3): 605-608.

- Danilov VA, Popov VV, Prokhorov AM, Sagatelyan DM, Sisakyan IN, Soifer VA. Synthesis of optical elements forming an arbitrary focal curve [In Russian]. Technical Physics Letters 1982; 8(13): 810-815.

- Goncharsky AV, Popov VV, Stepanov VV. Introduction to Computer Optics [In Russian]. Lomonosov Moscow State University Publisher, 1991; 309 p.

- Danilov VA, Kinber BE, Shilov AE. Theory of coherent focusers [In Russian]. Computer Optics 1987; 1: 40-52.

- Elmer WB. The Optical Design of Reflectors. 2nd Edition Wiley, New York, 1985.

- Feuermann D, Gordon JM, Ries H. Nonimaging optical designs for maximum power density remote irradiation. Applied Optics 1998; 37; 1835-1844.

- Feuermann D, Gordon JM. Optical performance of axisymmetric edge-ray concentrators and illuminators. Applied Optics 1998; 37; 1905-1912.

- Gordon JM, Rabl A. Reflectors for uniform far-field irradiance: fundamental limits and example of an axisymmetric solution. Applied Optics 1998; 37: 44-47.

- Ries H, Muschaweck J. Tailored freeform optical surfaces. J. Opt. Soc. Am. A 2002; 19: 590-595.

- Andrew R. Hicks Designing a mirror to realize a given projection. J. Opt. Soc. Am. A 2005; 22: 323-330.

- Born M, Volf E. Principles of Optics [In Russian]. Moscow: “Nauka” Publisher, 1970.

- Belousov AA, Doskolovich LL, Kharitonov SI. A gradient method of computation of eikonal function for focusing in prescribed region [In Russian]. Optoelectronics, Instrumentation and Data Processing 2007; 43(3).

- Dresel Thomas, Beyerlein Mathias, Schwider Johannes. Design of computer-generated beam-shapingholograms by iterative finite-element mesh adaption. Applied Optics 1996; 35: 6865-6874.

- http://www.lambdares.com/products/tracepro/index.phtml.

© 2009, ИСОИ РАН

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