Deciphering the performance of different surface models for corneal topography.

Purpose: To study the performance of different corneal surface models to be used for ray tracing. Models based on geometric surfaces and polynomial fits were compared and the differences discussed.

Methods: For this simulation study, five characteristic generic surface configurations were generated: (A) perfect biconic, (B) decentred biconic with white noise, (C) biconic with paracentral hollow simulating the situation after myopic LASIK, (D) biconic with random dot irregularities and (E) rotationally symmetric conic with mid-peripheral bump simulating the situation of corneal ectasia. A floating best fit sphere (BFS), conic (BFC), biconic (BFBC), fringe Zernike on top of a BFS (BFSZ), fringe Zernike (BFZ) and Gaussian process surface model (BFGP) were fitted and the root-mean-squared fit error was analysed.

Results: Surfaces A and B were well described by BFBC, BFSZ, BFZ and BFGP, but not by BFS and BFC. Surface C was not well represented by BFS, BFC and BFBC, but reasonably with BFSZ and BFZ and quite well with BFGP. Surfaces D and E were poorly represented, especially with BFS, BFC and BFBC, but also with BFSZ and BFZ and quite well with BFGP. There was no systematic difference between the two Zernike representations BFSZ and BFZ, even for surface B.

Conclusions: Representing corneal point cloud data with a closed surface model plays a key role in ray tracing. Simple surface models such as BFS, BFC or BFBC are easy to handle but do not fully represent clinical situations with local irregularities after corneal refractive surgery or with ectasia.