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Abel transform in the problems of design of gradient optical elements

V.V Kotlyar1,2, A.S. Melekhin2

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

 PDF, 312 kB

Pages: 29-36.

Full text of article: Russian language.

Abstract:
The paper considers different types of direct and inverse Abel transforms applied to the problems of calculating the dependence of the refractive index on coordinates for the generalized spherical Luneberg lens and for the cylindrical Mikaelyan lens. The relation is shown between the Morgan and Fletcher integral equations, from which the solution for the generalized Luneberg lens follows. The derivative of the Abel transform is used to obtain a solution for the ordinary Luneberg lens. Integral equations are also developed for the generalized cylindrical Mikaelyan lens and the cylindrical generalized axicon.

Keywords:
Abel transform, gradient optical element, spherical Luneberg lens, cylindrical Mikaelyan lens, Morgan and Fletcher integral equations, cylindrical generalized axicon.

Citation:
Kotlyar VV, Melekhin AS. Abel transform in the problems of design of gradient optical elements. Computer Optics 2001; 22: 29-36.

References:
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