Measurements and an adjoining corneal zone: Effects on the power matrix of a regular astigmatic cornea

A circular zone around the corneal cap is magnified in order to observe the regularity on this anterior surface element of an eye and measure its principal refractive powers. Experiment confirms that powers on smaller zones on the same cornea are augmented for slightly larger zones. This article aims to perturb powers from the smaller zone to associate its exact and paraxial measurements with a central neighbouring zone small enough to reflect paraxial rays. Readings estimated for this slightly larger zone are propagated to their own 2 × 2 matrix which can be expressed as components that systematically supplement a matrix from the smaller zone. Orders of perturbation parameters distinguish a matrix from the smaller central zone from the other power components and their natures. Matrix components with interesting structures represent the sensitivity of the power matrix to changes in principal powers only or to principal meridians only or to both. An analytic method for bounds estimated around a host of clinical standard measurements to be propagated to their dioptric power matrices is established to also facilitate calculations for quality in clinical measurements. A numerical example supports the techniques discussed.