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Calculation of generalized Fish-Eye lenses of Maxwell and Eaton-Lippmann

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

 PDF, 374 kB

Pages: 53 - 57.

Abstract:
Integral equations for the rays in two gradient lenses with a spherically symmetric dependence of the refractive index on coordinates are derived and solved using the Abel transform. The first lens shaped as a half-sphere with a spherically symmetric distribution of the refractive index focuses a flat beam of rays that falls perpendicular on the flat surface of the half-sphere to a point lying on the axis of the incident beam and at a certain distance from the half-sphere. Such a lens appeared to be a generalization of the well-known Maxwell’s fisheye lens. The second lens is a generalization of the well-known Eaton-Lipman lens and it reflects (or deflects) any ray at a given angle. The generalized Eaton-Lipman lens forms an incident parallel beam of rays into conical waves, that is, it is a gradient axicon. In addition, an integral equation was derived and solved for calculating a gradient, spherically symmetric focusator, shaped as a half-sphere, which focuses a parallel beam of rays falling perpendicular to its flat surface into a radially symmetric region of a plane with a given intensity distribution, located perpendicular to the beam axis at a certain distance from the half-sphere.

Keywords:
Fish-Eye lense, Eaton-Lipman lens, Maxwell’s lens, half-sphere, gradient axicon, focusator.

Citation:
Kotlyar VV, Melekhin FS. Calculation of generalized Fish-Eye lenses of Maxwell and Eaton-Lippmann. Computer Optics 2002; 24: 53-57.

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