Original Research
Generalized magnification in visual optics. Part 2: Magnification as affine transformation
Submitted: 12 December 2010 | Published: 12 December 2010
About the author(s)
W. F. Harris, Department of Optometry, University of Johannesburg, South AfricaFull Text:
PDF (1MB)Abstract
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)
Keywords
Metrics
Total abstract views: 3087Total article views: 4569