Total corneal power estimation: ray tracing method versus gaussian optics formula

Abstract

Purpose: To evaluate with the use of corneal topographic data the differences between total corneal power calculated using ray tracing (TCP) and the Gaussian formula (GEP) in normal eyes, eyes that previously underwent laser in situ keratomileusis/photorefractive keratectomy (LASIK/PRK), and theoretical models.

Methods: TCP and GEP using mean instantaneous curvature were calculated over the central 4-mm zone in 94 normal eyes, 61 myopic-LASIK/PRK eyes, and 9 hyperopic-LASIK/PRK eyes. A corneal model was constructed to assess the incident angles at the posterior corneal surface for both refracted rays and parallel rays. Corneal models with varying parameters were also constructed to investigate the differences between mean TCP and GEP (4-mm zone), and an optical design software validation was performed.

Results: The TCP values tended to be less than GEP in normal and myopic-LASIK/PRK eyes, with the opposite relationship in some hyperopic-LASIK/PRK eyes having the highest anterior surface curvature. The difference between TCP and GEP was a function of anterior surface instantaneous radii of curvature and posterior/anterior ratio in postrefractive surgery eyes but not in normal eyes. In model corneas, posterior incident angles with parallel rays were greater than those with refracted rays, producing an overestimation of negative effective posterior corneal power; differences in magnitude between TCP and GEP increased with decreasing ratio of posterior/anterior radii of curvature, consistent with clinical results.

Conclusions: In eyes after refractive surgery, calculating posterior corneal power using the Gaussian formula and its paraxial assumptions introduces errors in the calculation of total corneal power. This may generate errors in intraocular lens power calculation when using the Gaussian formula after refractive surgery.