Original Research

Generalized magnification in visual optics. Part 1: Magnification as linear transformation

W. F. Harris
African Vision and Eye Health | South African Optometrist: Vol 69, No 3 | a134 | DOI: https://doi.org/10.4102/aveh.v69i3.134 | © 2010 W. F. Harris | This work is licensed under CC Attribution 4.0
Submitted: 11 December 2010 | Published: 12 December 2010

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

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In Gaussian optics magnification is a scalar; the interpretation is obvious.  In linear optics, the simplest optics of astigmatic systems, the generalization is a  2 2×  real matrix and, in general, is much
harder to interpret.  This generalized magnification may imply magnification in the familiar sense that differs from one meridian to another, shear distortion, rotation, reflection, inversion, magnification in the familiar sense or combinations of these effects.  The purpose of this paper is to illustrate generalized magnification and to provide a comprehensive interpretation.  Because the treatment is abstract it
can be applied to blur and size magnification and to any magnification that can be represented by a  2 X 2  matrix. (S Afr Optom 2010 69(3) 109-122)


Generalized magnification; astigmatism; rotation; reflection; inversion; linear magnification


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