Original Research

Generalized magnification in visual optics. Part 2: Magnification as affine transformation

W. F. Harris
African Vision and Eye Health | South African Optometrist: Vol 69, No 4 | a142 | DOI: https://doi.org/10.4102/aveh.v69i4.142 | © 2010 W. F. Harris | This work is licensed under CC Attribution 4.0
Submitted: 12 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 astigmatic systems magnification may be different in different directions.  It may also be accompanied by rotation or reflection.  These changes from object to image are examples of generalized magnification.  They are represented by  2 2×  matrices.  Because they are linear transformations they can be called linear magnifications.  Linear magnifications account for a change in appearance without regard to position.  Mathematical structure suggests a natural further generalization to a magnification that is complete in the sense that it accountsfor change in appearance and position.  It is represented by a  3 3×  matrix with a dummy third row. The transformation is called affine in linear algebra which suggests that these generalized magnifica-tions be called affine magnifications.  The purpose of the paper is to define affine magnification in the context of astigmatic optics.  Several examples are presented and illustrated graphically. (S Afr Optom
2010 69(4) 166-172)


Linear magnification, affine magnification; transverse translation; astigmatism


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