Abstract
Usually nodal, principal and focal points are defined independently and thought of as distinct structures with no simple relationship among them. By adopting a holistic approach, in which these threetypes of cardinal points are treated as particular cases of a larger class of special points, this paper develops a method of constructing the locations of the cardinal points of a system graphically directly from the transference. The method provides a useful way of visualising the relationship of the locations of the cardinal points and of how they are affected by changes in the system or when a second optical system is placed in front of the first. Thepaper illustrates the graphical procedure by apply-ing it in several situations of interest in optometryand ophthalmology, including the effect of a contact lens or refractive surgery on a reduced eye and the effect of accommodation, a spectacle lens and an afocal telescope on the Gullstrand-Emsleyschematic eye. (S Afr Optom 2011 70(1) 3-13)
Highlights
The purpose of this paper is to show how one can obtain the locations of cardinal and other special points by graphical construction directly from the transference of the dioptric system in question
A key issue here is the unification of focal, nodal and principal points under the general heading of special points. This leads to a pair of straight lines, called the locator lines, superimposed on a sketch of the system from which one can obtain the positions of the individual cardinal points by construction
This provides for holistic visualization of the locations of individual cardinal points and of how they are altered by accommodation, refractive surgery and by contact and spectacle lenses and telescopes in front of the eye
Summary
The purpose of this paper is to show how one can obtain the locations of cardinal and other special points by graphical construction directly from the transference of the dioptric system in question. A key issue here is the unification of focal, nodal and principal points under the general heading of special points. This leads to a pair of straight lines, called the locator lines, superimposed on a sketch of the system from which one can obtain the positions of the individual cardinal points by construction. Changes in an eye or lenses placed in front of the eye change the locator lines and so change the locations of the cardinal points This provides for holistic visualization of the locations of individual cardinal points and of how they are altered by accommodation, refractive surgery and by contact and spectacle lenses and telescopes in front of the eye
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