The human cornea is not a surface with simple geometric shape especially after refractive surgery. Thus, conventional topographical instruments of the corneal curvature can not measure the correct values on the peripheral cornea. This is because the assumptions made in current topographical instruments are based on that the human cornea is composed of spherical surfaces. The peripheral cornea is not only important for shape formation after refractive surgery, but also important for the high contrast resolution of vision. This paper presents a new algorithm, which do not depend on the assumption of the corneal shape. The mathematical equations are based on polynomial equations and geometric optics of the measurements. By adjusting the coefficients, the polynomial equations can approach the curves of complicated shapes. The equations based on polynomial modeling are nonlinear, thus the Newton method is applied to simplify the equations. To implement experiments for the new algorithm, a setup is built at the Ohio State University. Topographical images are captured from simulated corneal surfaces and the image is processed using C programming. The curvature information is acquired through numerical analysis of polynomial equations. Spherical surfaces and aspherical surfaces are tested on this setup as well as on Topographical Modeling System and EyeSys Corneal Analysis System. The results show that the polynomial modeling can measure the radius of curvature for spherical or aspherical surfaces within 0.05 mm of error. Results also show that the aspherical surfaces measured on Topographical Modeling System and EyeSys Corneal Analysis System have about 0.3 mm of error at the periphery of 3.0 mm from optical axis. However, the polynomial modeling seems to have larger standard deviation. To improve the polynomial modeling, future studies are suggested in the dissertation.
Cynthia J. Roberts,
"New algorithm for topographical measurements of the corneal curvature", Proc. SPIE 2393, Ophthalmic Technologies V, (22 May 1995); doi: 10.1117/12.209834; https://doi.org/10.1117/12.209834