Generalized magnification in visual optics. Part 2: Magnification as affine transformation
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...
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| Format: | Article |
| Language: | English |
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AOSIS
2010-12-01
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| Series: | African Vision and Eye Health |
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| Online Access: | https://avehjournal.org/index.php/aveh/article/view/142 |
| _version_ | 1818062566669156352 |
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| author | W. F. Harris |
| author_facet | W. F. Harris |
| author_sort | W. F. Harris |
| collection | DOAJ |
| description | 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) |
| first_indexed | 2024-12-10T14:06:15Z |
| format | Article |
| id | doaj.art-283ee9f9c68b482e8d6a3441512ca40c |
| institution | Directory Open Access Journal |
| issn | 2413-3183 2410-1516 |
| language | English |
| last_indexed | 2024-12-10T14:06:15Z |
| publishDate | 2010-12-01 |
| publisher | AOSIS |
| record_format | Article |
| series | African Vision and Eye Health |
| spelling | doaj.art-283ee9f9c68b482e8d6a3441512ca40c2022-12-22T01:45:39ZengAOSISAfrican Vision and Eye Health2413-31832410-15162010-12-0169416617210.4102/aveh.v69i4.142111Generalized magnification in visual optics. Part 2: Magnification as affine transformationW. F. Harris0Department of Optometry, University of JohannesburgIn 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)https://avehjournal.org/index.php/aveh/article/view/142Linear magnification, affine magnificationtransverse translationastigmatism |
| spellingShingle | W. F. Harris Generalized magnification in visual optics. Part 2: Magnification as affine transformation African Vision and Eye Health Linear magnification, affine magnification transverse translation astigmatism |
| title | Generalized magnification in visual optics. Part 2: Magnification as affine transformation |
| title_full | Generalized magnification in visual optics. Part 2: Magnification as affine transformation |
| title_fullStr | Generalized magnification in visual optics. Part 2: Magnification as affine transformation |
| title_full_unstemmed | Generalized magnification in visual optics. Part 2: Magnification as affine transformation |
| title_short | Generalized magnification in visual optics. Part 2: Magnification as affine transformation |
| title_sort | generalized magnification in visual optics part 2 magnification as affine transformation |
| topic | Linear magnification, affine magnification transverse translation astigmatism |
| url | https://avehjournal.org/index.php/aveh/article/view/142 |
| work_keys_str_mv | AT wfharris generalizedmagnificationinvisualopticspart2magnificationasaffinetransformation |