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Abel transform to calculate the gradient of optical elements with spherically symmetric distribution of the refractive index

V.V. Kotlyar1,2 A.S. Melekhin2
1 Image Processing Systems Institute of RAS
2 Samara State Aerospace University

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Pages: 48 - 52.

Abstract:
The Abel integral transform in the framework of ray optics was used to derive and solve the integral equations for the well-known lenses with a spherically symmetric distribution of the refractive index: the Maxwell’s fisheye lens and the Eaton-Lipman lens. In addition, this work presents a solution to the problem of generating a gradient optical element with a spherically symmetric distribution of the refractive index, which focuses a plane light beam into a radially symmetric region with a given intensity distribution, located at a certain distance from the element in a plane perpendicular to the optical axis of the incident beam.

Keywords:
Abel transform, refractive index, integral equation, Maxwell’s fisheye lens, Eaton-Lipman lens, gradient optical element.

Citation:
Kotlyar VV, Melekhin AS. Abel transform to calculate the gradient of optical elements with spherically symmetric distribution of the refractive index. Computer Optics 2002; 24: 48-52.

References:
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