Line of sight of a heterocentric astigmatic eye

The line of sight and the corneal sighting centre are important references 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.

To derive equations for the dependence of the locations on properties of an eye which may be heterocentric and astigmatic.

The optical model used is linear optics. It allows for the refracting surfaces 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.

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 surfaces) of the eye. The results can be generalized in several ways including application 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.

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.