Line of sight of a heterocentric astigmatic eye William F Harris, Radboud DHM van Gool and Tanya Evans Department of Optometry, University of Johannesburg, Johannesburg, South Africa Citation information: Harris WF, van Gool RDHM & Evans T. Line of sight of a heterocentric astigmatic eye. Ophthalmic Physiol Opt 2013, 33, 57– 66. doi: 10.1111/opo.12007 Keywords: astigmatism, corneal sighting centre, heterocentricity, line of sight, sighting axis, transference Correspondence: William F Harris E-mail address: wharris@uj.ac.za Received: 17 July 2012; Accepted: 7 November 2012 Abstract Background: The line of sight and the corneal sighting centre are important refer- ences for clinical work in optometry and ophthalmology. Their locations are not fixed but may vary with displacement of the pupil and other changes in the eye. Purpose: To derive equations for the dependence of the locations on properties of an eye which may be heterocentric and astigmatic. Methods: The optical model used is linear optics. It allows for the refracting sur- faces of the eye to be astigmatic and tilted or decentred. Because the approach is general it applies not only to the natural eye but also to a pseudophakic eye and to the compound system of eye and any optical instrument in front of it. The analysis begins with the line of sight defined in terms of the foveal chief ray. Results: Equations are derived for the position and inclination of the line of sight at incidence onto the eye. They allow one to locate the line of sight and corneal sighting centre given the structure (curvatures, tilts, spacings of refracting sur- faces) of the eye. The results can be generalized in several ways including applica- tion in the case of extra-foveal fixation and when there is a lens or other optical instrument in front of the eye. The calculation is illustrated in the Appendix for a model eye with four separated, astigmatic and tilted refracting surfaces. Conclusions: The equations allow routine calculation of the line of sight for an eye of known structure and of the eye combined with an optical device such as a spectacle lens. They also allow exploration of the dependence of the line of sight on the location of the centre of the pupil and on other properties in the eye. There is a dependence of the line of sight on the frequency (or vacuum wavelength) of light but this may not be of clinical significance. Introduction Among the several axes defined for the eye the line of sight has been described as ‘the most important axis from the point of view of visual function, including refraction proce- dures’. 1 However the line of sight is not fixed for any eye because the centre of the pupil can vary. 1–3 Indeed displace- ment of the pupil centre is but one of many changes, inside and outside the eye, that may alter the line of sight. Actu- ally, even for a fixed eye, there is strictly no unique line of sight but one for each frequency or vacuum wavelength of light. (These statements will be justified below.) However, how significant are these effects? Despite the importance of the concept the literature seems to have no clear answers. Our purpose here is to develop a framework for finding answers. More particularly we shall make use of the power- ful methodology of linear optics to derive an equation for the line of sight as a function of properties of the eye with or without an optical device in front of it. The methodology used in this note is the same as that used in several recent papers 4–10 to which the reader is referred for more details than are given here. The equations derived below allow one to examine the sensitivity of the line of sight to displacement of the centre of the pupil, to accommodation, to decentration of an intraocular lens, to frequency and so on. Linear optics and the concept of the ray transference allow one to approach the problem in a very general manner; we are not limited to particular mod- els of the eye and can handle eyes with multiple, separated, decentred and nonaligned astigmatic elements. Further- Ophthalmic & Physiological Optics 33 (2013) 57–66 © 2012 The College of Optometrists 57 Ophthalmic & Physiological Optics ISSN 0275-5408