Optics of the average normal cornea from general and canonical representations of its surface topography
Optics of the average normal cornea from general and canonical representations of its surface topography
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DOI：
10.1364/josaa.23.000219
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发表时间：
2006-02-01
影响因子：
1.9
通讯作者：
Hernández, JL
中科院分区：
文献类型：
--
作者：
Navarro, R;González, L;Hernández, JL
通常，角膜地形图的分析涉及将原始数据拟合到包括规则基础表面的参数几何模型，加上某种多项式展开以调整更不规则的残余分量。到目前为止，这些参数化模型一直以其规范形式使用，忽略了观察（角膜曲率）坐标系与角膜对称轴不同。在这里，我们建议，而不是使用的标准形式时，地形图是指固有的角膜坐标系，由其主轴的对称。这个想法是使用椭圆体的一般表达式来拟合仪器给出的原始数据来实现的。然后，定义正常角膜的固有笛卡尔坐标系的椭圆体的三个正交半轴的位置和方向可以通过标准线性代数传递到规范形式来识别。该模型首先通过实验验证，与以前的标准模型相比，获得了显著更低的均方根拟合误差值：球形，圆锥形和双圆锥形。然后通过Zernike多项式展开调整拟合残差。分析了123个角膜的形貌，获得了它们的曲率半径、圆锥常数、Zernike系数以及椭圆体光轴的方向和位置。与使用标准模型得到的结果进行了比较。一般椭球模型提供了更多的二次曲线常数的负值和较低的顶点半径（更长的形状）比标准模型应用于相同的数据。如果使用标准模型分析数据，则所得角膜的平均形状与先前的研究一致，但当使用椭圆体模型时，我们发现了新的有趣特征：平均角膜是一个更长的椭圆体（顶焦度50 D），光轴方向约为鼻侧2.3度，残差项显示出三个显著高于零的Zernike系数（三阶三叶形和四阶和六阶球形）。这三个非零泽尼克系数是负责大多数高阶像差的平均角膜。最后，我们提出并实现了一个简单的方法，用于三维注册的角膜地形图，通过从一般的标准形式的椭球。(c)2006年美国光学学会。
Generally, the analysis of corneal topography involves fitting the raw data to a parametric geometric model that includes a regular basis surface, plus some sort of polynomial expansion to adjust the more irregular residual component. So far, these parametric models have been used in their canonical form, ignoring that the observation (keratometric) coordinate system is different from corneal axes of symmetry. Here we propose, instead, to use the canonical form when the topography is referenced to the intrinsic corneal system of coordinates, defined by its principal axes of symmetry. This idea is implemented using the general expression of an ellipsoid to fit the raw data given by the instrument. Then, the position and orientation of the three orthogonal semiaxes of the ellipsoid, which define the intrinsic Cartesian system of coordinates for normal corneas, can be identified by passing to the canonical form, by standard linear algebra, This model has been first validated experimentally obtaining significantly lower values for rms fitting error as compared with previous standard models: spherical, conical, and biconical. The fitting residual was then adjusted by a Zernike polynomial expansion. The topographies of 123 corneas were analyzed obtaining their radii of curvature, conic constants, Zernike coefficients, and the direction and position of the optical axis of the ellipsoid. The results were compared with those obtained using the standard models. The general ellipsoid model provides more negative values for the conic constants and lower apex radii (more prolate shapes) than the standard models applied to the same data. If the data are analyzed using standard models, the resulting mean shape of the cornea is consistent with previous studies, but when using the ellipsoid model we find new interesting features: The mean cornea is a more prolate ellipsoid (apical power 50 D), the direction of the optical axis is about 2.3 degrees nasal, and the residual term shows three Zernike coefficients significantly higher than zero (third-order trefoil and fourth-and sixth-order spherical). These three nonzero Zernike coefficients are responsible for most of the higher-order aberrations of the average cornea. Finally, we propose and implement a simple method for three-dimensional registration of corneal topographies, passing from the general to the canonical form of the ellipsoid. (c) 2006 Optical Society of America.