波前像差引导的激光眼屈光手术中角膜切削模型

Mathematical models for wavefront-guided refractive corneal surgery

基于改变角膜厚度可以改变眼屈光系统波前像差的原理 ,提出了一种矫正眼波前像差的角膜切削模型 .首先给出理想参考平面波前和实际波前之间的位置关系 ,用一个通用的数学模型表示了波前像差 ;其次用Zernike多项式系列来描述眼像差结构 ,将波前像差表示成带权重的Zernike多项式系列累加和的形式 ;最后将眼波前像差转换为光程差的形式 ,用光程差表示了角膜切削厚度 ,并进一步得出角膜切削厚度同波前像差之间转换的数学模型 (像差矫正模型 ) .该像差矫正模型在理论上能矫正包括低阶像差 (近视、远视、散光 )和高阶像差在内的 35项像差 .

Based on the relationship between the change of the cornea thickness and optical aberrations, a mathematical model for the correction of wavefront aberration is presented. Positions of the ideal reference plane-wave and the wavefront are given. The meaning of wavefront aberration is illustrated using a general mathematical model. Basic functions of Zernike are used for describing the aberration structure. The wavefront aberration of an eye is described mathematically as the weighted sum of these Zernike basis functions. The ocular wavefront aberration is transformed into optical path-length difference and the cornea ablation profile is expressed mathematically using this optical path-length difference. Furthermore, a mathematical model for the transfer of wavefront aberration into a corneal ablation profile is given. This corneal ablation model can be used for the correction of both lower-order aberrations(myopia, hyperopia or astigmatism) and higher-order aberrations. Aberrations that can be corrected using this corneal ablation model are theoretically up to seventh order (35 terms).