Full text of article: Russian language.
Abstract:
The calculation of the  eikonal from the condition of focusing into a line with designed energy  distribution reduces to a first-order differential equation solved for the  derivative. We design a DOE and  non-diffractive refractive optical elements to produce a line-segment focus and  a circular-arc focus. The simulation shows that the optical elements produce  high-quality focal lines.
Key words:
eikonal, optical  element, curvilinear coordinates, intensity, light field, line density.
References:
  - Danilov V.A. Optical elements to focus into an arbitrary focal line, / V.A. Danilov et al.  // preprint, №69 – Moscow:  Lebedev Physical Institute, 1983, p. 41. – (in Russian)
- Goncharsky A.V. Inverse problem of coherent optics, focusing into a line / A.V.  Goncharsky, V.V. Stepanov // J.  Calculat. Math. And Math.  Phy. 1986. Vol. 26, №.1, pp. 80-91. – (in Russian) 
- 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)
- Danilov V.A. Theory of coherent focusers / B.E. Kinber, A.E. Shilov // Computer optics. - Moscow, Pergamon Press,  1989. - Vol. 1, №1. - pp. 29-38. 
- Goncharsky A.V. Mathematical models in the design of flat optics elements // Computer  optics - Moscow,  Pergamon Press, 1989. - Vol. 1, №1. - pp. 13-20
- Methods of  Computer Optics (Secondary Edition) / edited by V.A. Soifer – Moscow: Fizmatlit, 2003. – 688 с. – (in Russian). 
- Diffractive Computer  Optics / edited by V.A. Soifer – Moscow:  Fizmatlit, 2007.  Chapter 3. – (in  Russian)
- 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, Vol.32, №4, pp. 343-347. – (in Russian)
- Korn G., Korn T. Reference-book on mathematics. Мoscow: Nauka, 1970. – (in Russian)
- Fedoryuk M.V. Asymptotic: Integrals and series. – Мoscow: Nauka. Phys.-math. lit., 1987. Chapter 2. – (in Russian)
-   http://www.lambdares.com/products/tracepro/index.phtml.
  
  
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