Geodesic
The inverse problem of synthesis of optical elements for laser radiation
Numerical methods and programming, Tome 7 (2006) no. 1, pp. 138-162.

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The problems of formation of laser radiation are of great importance for a wide range of applications: telecommunications, laser metal processing, holography, etc. This paper addresses the formation of rectangular laser beams with uniform intensity distribution. Such problems prove to be beyond the limited capabilities of common optical elements. Thus, the problem considered is reduced to computing the phase function of a flat optical element that forms the required image. Elements with smooth phase functions are shown to have important advantages from the viewpoint of practical implementation. We formulate the problem of the domain-to-domain formation of laser radiation in the approximation of geometric optics. This nonlinear problem is reduced to nonlinear Monge-Ampere equation and is shown to have a solution which is not unique. An efficient numerical algorithm is proposed.
Keywords: Monge-Ampere equation, laser metal processing, optical elements, laser radiation, phase functions. 
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     author = {A. A. Goncharsky and D. V. Tunitsky},
     title = {The inverse problem of synthesis of optical elements for laser radiation},
     journal = {Numerical methods and programming},
     pages = {138--162},
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     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2006_7_1_a17/}
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A. A. Goncharsky; D. V. Tunitsky. The inverse problem of synthesis of optical elements for laser radiation. Numerical methods and programming, Tome 7 (2006) no. 1, pp. 138-162. http://geodesic.mathdoc.fr/item/VMP_2006_7_1_a17/