Chromatic properties of astigmatic eyes

Abstract

Background: Chromatic differences in power, refractive compensation, position and magnification have been described in the literature for Gaussian eyes.

Aim: This article explores these definitions and defines chromatic properties for eyes that have astigmatic and decentred or tilted elements.

Setting: Linear optics.

Methods: The optical model is linear optics and makes use of the ray transference T.

Results: Results are presented as either 2 × 2 matrices or 2 × 1 vectors. The dependence of the chromatic properties on the position of an object and the limiting aperture is explored and results are presented as independent of, or dependent on, object and aperture position. Apertures undergo both longitudinal and transverse shifts in position. The results are general and apertures may include pupils or pinholes, either surgically inserted inside the eye or held in front of the eye. Numerical examples are provided for Le Grand’s four-surface eye and an arbitrary astigmatic heterocentric four-surface eye.

Conclusion: Aperture-independent chromatic properties include chromatic difference in power and refractive compensation, both given as 2 × 2 matrices. Aperture-dependent chromatic properties are all dependent on longitudinal shifts in the plane of the limiting aperture. In addition, chromatic difference in position and inclination depend on both object and transverse aperture position. Chromatic difference in image size or angular spread depends on object position and is independent of transverse aperture position. These four aperture-dependent chromatic properties are given as 2 × 1 vectors. Chromatic magnifications are independent of object and transverse aperture position and are given as 2 × 2 matrices.