Shealy David L, Hoffnagle John A
University of Alabama at Birmingham, Department of Physics, Birmingham, AL 35216-1170, USA.
J Opt Soc Am A Opt Image Sci Vis. 2008 Sep;25(9):2370-82. doi: 10.1364/josaa.25.002370.
A simple expression is given for the k-function associated with the general solution of Stavroudis to the eikonal equation for refraction or reflection of a plane wave from an arbitrary surface. Using this result, we specialize the solution to derive analytic expressions for the wavefront and caustic surfaces after refraction of a plane wave from any rotationally symmetric surface. The method is applied to evaluating and comparing the wavefront and caustic surfaces formed both by a planospherical lens and a planoaspheric lens used for laser beam shaping, which provides understanding of how the irradiance is redistributed over a beam as the wavefront folds back on itself within the focal region.
给出了一个简单的表达式，用于表示与斯塔夫鲁迪斯对平面波从任意表面折射或反射的程函方程的通解相关的k函数。利用这一结果，我们对该解进行特殊化处理，以推导平面波从任何旋转对称表面折射后的波前和焦散面的解析表达式。该方法用于评估和比较用于激光束整形的平凸透镜和平非球面透镜所形成的波前和焦散面，这有助于理解当波前在焦区内自身折返时，辐照度是如何在光束上重新分布的。
