Geometric-optics design of diffractive  optical elements to focus into a plane line
A.Y. Dmitriev
, L.L. Doskolovich, S.I. Kharitonov

Image Processing Systems Institute of the RAS,
S. P. Korolyov Samara State Aerospace University

Full text of article: Russian language.

Abstract:
We derive general non-paraxial analytical representation of the eikonal function for design of diffractive optical element (DOE) to focus into a arbitrary oriented plane line. The eikonal is given in special curvilinear coordinates. The calculation of the eikonal on condition of focusing into a line with prescribed intensity distribution is reduced to solving of a first-order differential equation solved for the derivative. We design DOEs to generate a line-segment focus. The simulation data shows that the DOE produces high performance focal lines.

Key words: eikonal, diffractive optical element, curvilinear coordinates, intensity, light field, line density.

References:

  1. Methods for Computer Design of Diffractive Optical Elements. Edited by Victor A. Soifer // A Wiley Interscience Publication, John Wiley & Sons, Inc., New York, 2002, 764 p.
  2. Diffractive Computer Optics / edited by V.A. Soifer – Moscow: Fizmatlit, 2007. Chapter 3. – (in Russian)
  3. Doskolovich L.L., Kazanskiy N.L., Soifer V.A., Kharitonov S.I., Perlo P. A DOE to form a line-shaped directivity diagram // Journal of Modern Optics, 2004, Vol. 51, № 13, pp. 1999-2005.
  4. V. Soifer, V. Kotlyar, L. Doskolovich. Iterative Methods for Diffractive Optical Elements Computation // Taylor&Francis LTD, 1997, 244 p.
  5. Danilov V.A. Theory of coherent focusers / B.E. Kinber, A.E. Shilov // Computer optics. - Moscow, 1987. - Vol. 1, №1. - pp. 40-52.
  6. Goncharsky A.V. Solving the inverse problem of focusing the laser light into an arbitrary curve / A.V. Goncharsky et al. // Dokl. USSR Acad Sci. 1983. Vol. 273, №3. pp. 605-608. – (in Russian)
  7. Goncharsky A.V. Planar focusing elements of visible range / A.V. Goncharsky et al. // J. Quant. Electron, 1986, Vol.13, № 3. – pp. 660-662. – (in Russian)
  8. Soifer V.A., Golub M.A. Diffractive micro-optical elements with non-point response // Proceedings SPIE. - 1992. - Vol.1751. - P.140-154.
  9. Doskolovich L.L. Comparative analysis of different focusators into segment / L.L. Doskolovich N.L. Kazanskiy, V.A. Soifer // Optics and Laser Technology. - 1995. - Vol.27, №4. - P.207-213.
  10. Goncharsky A.V. Mathematical models in the design of flat optics elements // Computer optics - Moscow, 1989. - Vol. 1, №1. - pp. 13-20
  11. Dmitriev A.Yu. Geometric-optics design of focusators into a line in noparaxial case / A.Yu. Dmitriev, L.L. Doskolovich, S.I. Kharitonov // Computer optics, 2008, Vol.32, №4, pp. 343-347. – (in Russian)
  12. Dmitriev A.Yu. Geometric-optics design of optical elements into a line in noparaxial case / A.Yu. Dmitriev, L.L. Doskolovich, S.I. Kharitonov, M.A. Moiseev // Computer optics, 2009, Vol.33, №2, pp. 122-128. – (in Russian)
  13. Born M. Principles of optics / M. Born, E. Wolf – Мoscow: Nauka, 1973.
  14. Belousov A. A. A gradient method of designing optical elements for forming into 2-D domain in case of distant radiation source / A. A. Belousov, L. L. Doskolovich // Computer optics, 2007, Vol. 31, №3, pp. 20-26. – (in Russian)
  15. 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, and S. I. Kharitonov // Journal of Optical Technology, Vol. 75, Issue 3, 2008, pp. 161-165
  16. A. A. Belousov Gradient method of calculating the eikonal for focusing in a given region / A. A. Belousov, L. L. Doskolovich, and S. I. Kharitonov // Avtometriya Vol. 43, №1, 2007, pp. 98-106 – (in Russian)
  17. Young C., Wells D. Ray Tracing Creations, 2d Ed. London. Waite Group Press, 1994.

© 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