Research Notes

Inner-product spaces for quantitative analysis of eyes and other optical systems

William F. Harris, Tanya Evans, Radboud D. van Gool
African Vision and Eye Health | Vol 75, No 1 | a348 | DOI: https://doi.org/10.4102/aveh.v75i1.348 | © 2016 William F. Harris, Tanya Evans, Radboud D. van Gool | This work is licensed under CC Attribution 4.0
Submitted: 14 January 2016 | Published: 26 September 2016

About the author(s)

William F. Harris, Department of Optometry, University of Johannesburg, South Africa
Tanya Evans, Department of Optometry, University of Johannesburg, South Africa
Radboud D. van Gool, Department of Optometry, University of Johannesburg, South Africa


Share this article

Bookmark and Share

Abstract

Because dioptric power matrices of thin systems constitute a (three-dimensional) inner-product space, it is possible to define distances and angles in the space and so do quantitative analyses on dioptric power for thin systems. That includes astigmatic corneal powers and refractive errors. The purpose of this study is to generalise to thick systems. The paper begins with the ray transference of a system. Two 10-dimensional inner-product spaces are devised for the holistic quantitative analysis of the linear optical character of optical systems. One is based on the point characteristic and the other on the angle characteristic; the first has distances with the physical dimension L−1 and the second has the physical dimension L. A numerical example calculates the locations, distances from the origin and angles subtended at the origin in the 10-dimensional space for two arbitrary astigmatic eyes.


Keywords

ray transference; inner-product space; linear optics; astigmatism

Metrics

Total abstract views: 2678
Total article views: 3724

 

Crossref Citations

1. Linear optics of the eye and optical systems: a review of methods and applications
Tanya Evans, Alan Rubin
BMJ Open Ophthalmology  vol: 7  issue: 1  first page: e000932  year: 2022  
doi: 10.1136/bmjophth-2021-000932