Corneal Topography Algorithm using Pseudo Random Encoding and Zernike Polynomial Fitting

Abstract

Abstract: : Purpose: We developed an algorithm that directly determines Zernike coefficients describing corneal anterior surface derived from the reflection image of a stimulus with pseudo random encoding. The performance of this algorithm is evaluated using numerical and experimental data. Methods: Unlike the ring topographer that employs a Placido disk system, we use a topographer that uses a color-coded stimulus pattern. One-to-one correspondence between points on the recorded Purkinje image and points on the source pattern can be uniquely determined using pseudo random array. A surface reconstruction procedure, that includes tracing rays from image points to stimulus points and fitting of surface normals, calculates the Zernike coefficients representing the surface. The algorithm is applied to numerically generated spherical surfaces to test whether the reconstruction recovers the correct curvature. Reflection patterns from spherical balls were used to study the effect of alignment. Measurements on human eyes were done to determine the repeatability of the procedure. Results: The numerical tests show an accuracy of about 0.8 µm in determining the radius of curvature of the cornea. When the position of the surface apex is aligned with respect to the topographer optical axis, the measured Zernike tilt terms, Z^-1₁ and Z¹₁ , have very small absolute values. This is useful as a guide to locate a reference position for the corneal surface. On the other hand, the Zernike power terms, Z⁰₂, have negligible differences when the same surface is placed at different locations within 0.5 mm from the reference position. The measured values for corneal apex radius of curvature have a standard deviation of about 50 µm. Conclusions: A method is now available to calculate Zernike coefficients describing corneal shape without the intermediate step of determining corneal height maps. This creates new possibilities for calculating the contribution of the cornea to the wavefront aberration of the eye.

Keywords: topography • optical properties • cornea: basic science