Current research / employment

Short abstract about IMPRS PhD project:

Background and Goals:

The aim of the study is to provide a mathematical model eye for individualized intraocular lens (IOL) design. Analytical formulas, which are based on Gaussian optics, have been the standard solution for IOL power determination in cataract surgery for more than two decades. They are popular worldwide because of their simple implementation and clinically satisfactory results. In addition, wavefront analysis for human eyes has been widely performed in ophthalmology since 1990s, which can provide solutions to problems that the standard power calculation of refractive components cannot explain. Thus, for the customized treatment of an individual eye, we need to employ wavefront analysis into the IOL design. This is impossible by simply using analytical formulas since they are based on Gaussian optics. Here, an anatomic accurate model eye is proposed by using the ray tracing method for customized IOL calculation.

Material and methods:

A free form surface representation (bi-cubic spline incorporated with a smoothing procedure) is proposed for describing the refractive surfaces of human eye. First, we tested this strategy on the most important refractive surface: the anterior corneal surface. Standard strategies, such as quadratic function and high order polynomials were also implemented for comparison purpose. Corneal topography extracted from a TMS-2N corneal topographer (Tomey, Nagoya, Japan) were used as original data. After validation of the bi-cubic spline function for refractive surface representation against the standard methods, this free form strategy was implemented for both corneal surfaces and IOL surfaces for building up a four-surface model eye. Corneal tomography extracted from an AS-OCT (SS-1000 CASIA, Tomey, Nagoya, Japan) and the eye’s axial length from the IOLMaster (Carl Zeiss Meditec, Jena, Germany) were used as original data. The optimized IOL was then obtained by an inverse calculation. After that, a forward ray tracing and a backward ray tracing procedure was applied for evaluation of the optical outcome of the IOL design.


In the first study with corneal topography, the free form surface representation strategy shows best performance with respect to the smallest fitting error to the original data. A quadratic function always gives a fitting error for more than several microns in a 6 mm corneal zone. High of polynomials (Taylor polynomial) can also achieve a micron scale fitting error, but the order selection for such polynomials behaves adaptive to the corneal shape.

With corneal tomography and axial length data, a four-surface model eye with free form surface was built up. For comparison, four cases were simulated: 1) quadratic cornea + quadratic IOL; 2) spline cornea + quadratic IOL; 3) spline cornea + spline IOL (model proposing); and 4) spherical cornea + spherical IOL (analytical formula derived). Case 3 showed an equally small focus to the spherical model (case 4); while additionally a great advantage in wavefront correction was observed. Case 1 showed a manipulated perfect result by ignoring the high order portion in corneal height profile, and case 2 showed the importance of considering the high order portion of corneal height profile according to the results of forward/backward ray tracing.


A free form surface representation (bi-cubic spline function) can give a more realistic corneal description than the standard method. An anatomically accurate model eye is the basic requirement for a reliable wavefront correction. For this, the free form representation is a proper choice. Compared to traditional analytical formulas, which solely calculate the IOL power, the new numerical model eye which is based on the ray tracing method can not only give out an equally sharp focus (correct power value), but also can eliminate the wavefront error which is inevitable for an improved and customized treatment of the human eye.

Publications Z. Zhu, E. Janunts, T. Eppig, T. Sauer, A. Langenbucher, Iteratively re-weighted bi-cubic spline representation of corneal topography and its comparison to the standard methods, Z.Med.Phys, doi: 10.1016/j.zemedi., 2010.07.002, article in press, (2010)