中文摘要：

目的本文试以数学方法归纳分析角膜地形图内的光学数据，初步推算验证正常人眼角膜的椭球形态的数学表达。方法对每位研究对象进行Orbscan Ⅱ角膜地形图系统检测，采集角膜顶点和0°、30°、60°、90°、120°、150°、180°、210°、240°、270°、300°、330°子午线上距角膜顶点分别为1．5、2．5、3．5、4．5mm处点的角膜前表面、后表面的曲率半径及角膜厚度的数据，用三维坐标和椭圆二次曲线方程分别推算角膜前、后表面的空间数学表达式及其形状系数；并验证由较平坦子午线到较陡峭子午线角膜曲率分布Toric光学面特性。结果本研究样本显示的正常人角膜空间形态的数学表达式为，角膜前表面的椭球方程式：x^2／8．053^2＋y^2／7．973^2＋（z-8．226）^2／8．226^2=1，角膜后表面椭球方程式：x^2／6．836^2＋y^2／6．745^2＋（z-8．080）^2／7．527^2=1；角膜前表面形状系数：陡峭子午线e^2=1-（15．61z-y^2）／z^2，平坦子午线e^2=1-（15．61z-x^2）／z^2，角膜后表面形状系数：陡峭子午线e^2=1-[12．254（z-0．553）-y^2]／（z-0．553）^2，平坦子午线e^2=1-[12．254（z-0．553）-x^2]／（z-0．553）^2；斜轴子午线角膜曲率分布符合正弦规律F′Fa＋（Fb-Fa）·Sin^2α。结论正常人角膜前后表面的空间形态基本符合椭球面，而且角膜曲率具有从平坦子午线向陡峭子午线正弦相关的变化规律。

英文摘要：

Objective To detect the initial characters of the corneal shape that has been evaluated using a mathematical analysis. Methods Subjects were measured with Orbscan Ⅱ corneal topography system. Anterior and posterior corneal radius of curvature and thickness of the points located 1.5 mm, 2. 5 mm, 3.5 mm and 4.5 mm away from the corneal apex on certain meridians, including 0°, 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°, 270°, 300°and 330°meridians, were measured. The mathematical formula of space-form of the cornea as well as the shape factor （SF） were demonstrated. Distributions of corneal curvature between the two principal meridians were discussed. Results Mathematical model of anterior and posterior corneal surface were x^2/8. 0532 ＋ y^2/7. 9732 ＋ （z - 8. 226 ） 2/8. 2262 = 1, x^2/6. 8362 ＋ y^2/6. 7452 ＋ （z-8.080）2/7. 5272 = 1 respectively. The SF models of the steepest and flattest meridians on anterior corneal surface were e^2 = 1 - （ 15.61z - y^2 ）/z^2 and e^2 = 1 - （ 15.61z - x^2 ）/z^2 respectively; the same parameters in the posterior corneal surface were e^2 = 1 - [ 12. 254 （z - 0. 553 ） - y^2 ] / （ z - 0. 553 ） 2 and e^2 = 1 - [ 12. 254 （ z - 0. 553 ） - x^2 ] / （z - 0. 553 ） 2 respectively. The curvature of oblique meridian was described with the formula F′ = Fa ＋ （ Fb - Fa ） - Sin2α. Conclusions Anterior and posterior corneal surfaces are both toric similar to ellipsoidals. The distributions of corneal curvature between the two principal meridians have something to do with the law of Sine.