一种用于角膜重建的改进低阶方法。

Bioengineering Institute, Faculty of Engineering, University of Auckland, Auckland, New Zealand.

Optom Vis Sci. 2008 Mar;85(3):211-7. doi: 10.1097/OPX.0b013e318164ee9b.

PURPOSE

An iterative and cubic arc-step method for corneal reconstruction developed previously, was retested including improved skew-ray compensation. The method was compared with a similar method described by Klein, and also with a least squares based approach using Zernike polynomials.

METHODS

Images of an asphere, a cornea after photorefractive keratectomy (PRK), an ellipsoid and radially keratotomized (RK) cornea were generated. Three reconstruction methods were applied: (i) the cubic method (without skew-ray compensation; with old and improved compensation), (ii) the method due to Klein and (iii) a least squares approach based on Zernike polynomials (order taken up to 25). Errors were recorded for all conditions tested.

RESULTS

The root mean square errors for the improved method were well below micron level, and consistently lower than the method of Klein. The Zernike-based method produced lowest errors for aspheric and ellipsoidal surfaces, when order was > or =(10, 8) respectively. However, the improved method produced the lowest errors for the PRK and RK examples. In this case, the Zernike-based method produced submicron errors for orders > or =14 (both surfaces), but errors comparable with the arc-step methods could not be achieved for polynomial orders < or =25. The improved method completed in three to four iterations (abs. height error <1 x 10(-7) mm) in all cases.

CONCLUSIONS

Compensation for skew-rays was incorporated in a straightforward way, yielding an efficient and effective low-order method. The Zernike method produced the lowest root mean square errors for asphere and ellipsoid, provided order was > or =(10, 8). However, the arc-step methods (the cubic and Klein methods) were more accurate for RK and PRK surfaces, at least for Zernike orders < or =25. The results suggest that low order methods provide a good solution to the reconstruction of corneal shape, at least for Placido disk videokeratography applications.

目的

对之前开发的用于角膜重建的迭代三次弧步长法进行重新测试，包括改进的斜光线补偿。将该方法与克莱因描述的类似方法以及使用泽尼克多项式的基于最小二乘法的方法进行比较。

方法

生成了非球面、准分子激光原位角膜磨镶术（PRK）后角膜、椭球体和放射状角膜切开术（RK）角膜的图像。应用了三种重建方法：（i）三次方法（无斜光线补偿；有旧的和改进的补偿），（ii）克莱因方法，以及（iii）基于泽尼克多项式的最小二乘法（阶数取到25）。记录了所有测试条件下的误差。

结果

改进方法的均方根误差远低于微米水平，并且始终低于克莱因方法。基于泽尼克的方法在非球面和椭球体表面分别在阶数≥10和≥8时产生最低误差。然而，改进方法在PRK和RK示例中产生最低误差。在这种情况下，基于泽尼克的方法在阶数≥14时（两种表面）产生亚微米误差，但对于阶数≤25的多项式无法达到与弧步长法相当的误差。改进方法在所有情况下三到四次迭代即可完成（绝对高度误差<1×10⁻⁷毫米）。

结论

以直接的方式纳入了斜光线补偿，产生了一种高效且有效的低阶方法。如果阶数≥10和≥8，泽尼克方法在非球面和椭球体上产生最低的均方根误差。然而，弧步长法（三次方法和克莱因方法）在RK和PRK表面上更准确，至少对于泽尼克阶数≤25是这样。结果表明，低阶方法为角膜形状重建提供了一个很好的解决方案，至少对于普拉西多盘式角膜地形图应用是这样。