Dependence of optical properties of heterocentric astigmatic systems on internal elements, with application to the human eye

Abstract

For applications in eye surgery, optometry and vision science there is considerable interest in the sensitivity of optical properties of the eye to properties of particular elements within the eye. The purpose of this paper is to describe a general approach to obtaining relationships for the dependence of properties of heterocentric astigmatic systems on particular parameters within the system. The analysis is in terms of linear optics and the 5×5 augmented symplectic matrix called the transference. Exact expressions are obtained for the dependence on width of gaps and on curvature and tilt of refracting surfaces within the system. The dependence is affine in the case of the fundamental properties of the system but more complicated in the case of other properties. The approach described here has the potential to contribute to the solution of problems of relevance in vision.

Keywords:

• Heterocentricity
• astigmatism
• sensitivity
• transference
• linear optics
• vision

ACKNOWLEDGEMENTS

I thank the National Research Foundation for support. T. Evans kindly drew my attention to errors in the originals of equations (38) and (39). I thank her and R.D. van Gool for comments on the manuscript.