Mathematical model of a Placido disk keratometer and its implications for recovery of corneal topography

The purpose of this paper is to illustrate the importance of radial contours in the target pattern of a Placido disk keratometer. We do so by presenting an example of a corneal surface which cannot be determined solely by the use of Placido ring images, but rather which requires radial contours for its determination. In order to prove our assertions, we derive partial differential equations (called the corneal transform), which relate the ring targets to their images.