An artifact in fits to conic-based surfaces

TL;DR

This paper reveals that in fitting conic-based surfaces in Physiological Optics, the parameters of radius and asphericity are strongly correlated due to the geometry of ellipses, affecting measurement accuracy.

Contribution

It demonstrates that the correlation between radius and asphericity variations is inherent to elliptical geometry, not dependent on specific devices or fitting methods.

Findings

Correlation observed in experimental and simulated data

Effect is due to elliptical geometry, not device-specific

Impacts accuracy of corneal and lens surface measurements

Abstract

It is common in Physiological Optics to fit the corneal and the lens surfaces to conic-based surfaces (usually ellipse-based surfaces), obtaining their characteristic radius of curvature and asphericity. Here we show that the variation in radius and asphericity due to experimental noise is strongly correlated. This correlation is seen both in experimental data of the corneal topographer Pentacam and in simulations. We also show that the effect is a characteristic of the geometry of ellipses, and not restricted to any experimental device or fitting procedure.