Original Research

The log-transference and an average Gaussian eye

W.F. Harris
African Vision and Eye Health | South African Optometrist: Vol 64, No 3 | a225 | DOI: https://doi.org/10.4102/aveh.v64i3.225 | © 2005 W.F. Harris | This work is licensed under CC Attribution 4.0
Submitted: 19 December 2005 | Published: 19 December 2005

About the author(s)

W.F. Harris, Optometric Science Research Group, Department of Optometry, and Department of Mathematics and Statistics, University of Johannesburg, PO Box 524, Auckland Park, 2006 South Africa, South Africa

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Recent research on the logarithm of matrices is likely to have a significant impact on optom-etry.  The purpose of this paper is to draw atten-tion to this research and show application to the calculation of an average centred Gaussian eye in particular.  The paper makes use of Cardoso’s method to obtain an explicit expression for the logarithm of a  transference. The arithmetic aver-age of log-transferences leads to a transference which can be regarded as the transference of the average eye for the set.  A numerical example is presented.


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