Original Research

Aperture referral in dioptric systems with stigmatic elements

W. F. Harris
African Vision and Eye Health | South African Optometrist: Vol 71, No 1 | a60 | DOI: https://doi.org/10.4102/aveh.v71i1.60 | © 2012 W. F. Harris | This work is licensed under CC Attribution 4.0
Submitted: 08 December 2012 | Published: 09 December 2012

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W. F. Harris, Department of Optometry, University of Johannesburg, South Africa

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A previous paper develops the general theory of aperture referral in linear optics and shows how several ostensibly distinct concepts, including the blur patch on the retina, the effective corneal

patch, the projective field and the field of view, are now unified as particular applications of the general theory.  The theory allows for astigmatism and heterocentricity.  Symplecticity and the generality of the approach, however, make it difficult to gain insight and mean that the material is not accessible to readers unfamiliar with matrices and linear algebra. The purpose of this paper is to examine whatis, perhaps, the most important special case, that in which astigmatism is ignored.  Symplecticity and, hence, the mathematics become greatly simplified. The mathematics reduces largely to elementary vector algebra and, in some places, simple scalar algebra and yet retains the mathematical form of the general approach.  As a result the paper allows insight into and provides a stepping stone to the general theory.  Under referral an aperture under-goes simple scalar magnification and transverse
translation.  The paper pays particular attention to referral to transverse planes in the neighbourhood of a focal point where the magnification may be positive, zero or negative.  Circular apertures are treated as special cases of elliptical apertures and the meaning of referred apertures of negative radius is explained briefly. (S Afr Optom 2012 71(1) 3-11)


aperture referral; stigmatic systems; blur patch; effective corneal patch; field of view; projective field


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