Langenbucher Achim, Szentmáry Nóra, Cayless Alan, Hoffmann Peter, Wendelstein Jascha
Department of Experimental Ophthalmology, Saarland University, Homburg/Saar, Germany.
Dr. Rolf M. Schwiete Centre for Limbal Stem Cell and Aniridia Research, Saarland University, Homburg/Saar, Germany.
Ophthalmic Physiol Opt. 2025 Sep;45(6):1270-1281. doi: 10.1111/opo.13539. Epub 2025 Jun 19.
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.
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.
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.
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.
研究用于光线追踪的不同角膜表面模型的性能。比较基于几何表面和多项式拟合的模型，并讨论差异。
对于此模拟研究，生成了五种特征性的通用表面配置：(A) 完美双圆锥面，(B) 带有白噪声的偏心双圆锥面，(C) 具有旁中心凹陷以模拟近视性准分子激光原位角膜磨镶术后情况的双圆锥面，(D) 具有随机点状不规则性的双圆锥面，以及 (E) 具有中周部隆起以模拟角膜扩张情况的旋转对称圆锥面。拟合了浮动最佳拟合球面（BFS）、圆锥面（BFC）、双圆锥面（BFBC）、BFS 之上的条纹泽尼克面（BFSZ）、条纹泽尼克面（BFZ）和高斯过程表面模型（BFGP），并分析了均方根拟合误差。
表面 A 和 B 能被 BFBC、BFSZ、BFZ 和 BFGP 很好地描述，但不能被 BFS 和 BFC 很好地描述。表面 C 不能被 BFS、BFC 和 BFBC 很好地表示，但能被 BFSZ 和 BFZ 合理地表示，被 BFGP 很好地表示。表面 D 和 E 的表示效果较差，尤其是被 BFS、BFC 和 BFBC 表示时，但被 BFSZ 和 BFZ 表示时也较差，被 BFGP 很好地表示。即使对于表面 B而言，两种泽尼克表示形式BFSZ和BFZ之间也没有系统差异。
用封闭表面模型表示角膜点云数据在光线追踪中起关键作用。简单的表面模型如BFS、BFC或BFBC易于处理，但不能完全表示角膜屈光手术后局部不规则或角膜扩张的临床情况。
