Original Research

Ray transference of a system with radial gradi- ent index

W. F. Harris
African Vision and Eye Health | South African Optometrist: Vol 71, No 2 | a70 | DOI: https://doi.org/10.4102/aveh.v71i2.70 | © 2012 W. F. Harris | This work is licensed under CC Attribution 4.0
Submitted: 09 December 2012 | Published: 09 December 2012

About the author(s)

W. F. Harris, Department of Optometry, University of Johannesburg, South Africa

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The ray transference is central to the understanding of the first-order optical character of an optical system including the visual optical system of the eye.  It can be calculated for dioptric and catadioptric systems from a knowledge of curvatures, tilts and spacing of surfaces in the system provided the material between successive surfaces has a uniform index of refraction.  However the index of the natural lens of the eye is not uniform but varies with position.  There is a need, therefore, for a method of calculating the transference of systems containing such gradient-index elements.  As a first step this paper shows that the transference of elements in which the index varies radially can be obtained directly from published formulae.  The transferences of radial-gradient systems are examined.  Expressions are derived for several properties including the power, the front- and back-surface powers and the locations of the cardinal points.  Equations are obtained for rays through such systems and for the locations of images of object points through them.  Numerical examples are presented in the appen-dix. (S Afr Optom 2012 71(2) 57-63)


gradient index, transference; cardinal points; stigmatic system.


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