Calculation of power and field of view of keratoprostheses

Abstract

Purpose: To demonstrate a mathematical algorithm for calculating the refractive power of keratoprostheses and to estimate vignetting effects.

Methods: A paraxial calculation scheme based on vergence transformation is developed for determination of the front surface radius or front surface refractive power of a Boston type I or II keratoprosthesis based on the design data of the manufacturer. A concept for derivation of lateral magnification (ratio of image size to slope of the incident ray) is presented based on 2 × 2 matrix representation of the eye. For estimation of vignetting effects, numerical ray tracing was used and the maximum half field angle and half luminance half field angle was extracted.

Results: Simulation calculations were performed in MATLAB. The front surface radius or refractive power is given in explicit form as a function of axial length, target refraction, as well as the principal design data of the keratoprosthesis such as posterior refractive power, length, or refractive index. With variation of the back surface radius it was shown that lateral magnification can be modulated e.g. to match the magnification of the fellow eye. The Boston type I does not restrict the field angle substantially, whereas type II shows significant vignetting effects.

Conclusion: We present a strategy on the calculation of keratoprostheses and variation of the design (e.g. back surface curvature) to help to avoid aniseikonia in case of binocular vision (e.g. one phakic eye and one with keratoprosthesis).