脂肪射线:高斯束物理光学和几何光学的综合

A. W. Greynolds
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引用次数: 1

摘要

光学系统主要是通过跟踪光束束来设计和分析的。这些射线实际上是通过系统传播的几何波前上的离散点。局部场振幅与波前曲率半径或与邻近射线点的距离成反比。由于根据定义,几何光学中不包括衍射效应,因此能量密度在焦点处或在焦散上是无限大的。如果将这些射线扩展成物理光学光束,这些光束至少是简化(傍轴或抛物线)波动方程的解,则可以消除这些奇点。这样,每个单独的场在任何地方都是有限的和连续的,它们的叠加就代表了系统中像差、干涉、遮挡和衍射的累积效应。这种对无限小几何射线的“增肥”类似于物理光学傅里叶变换解中使用的无限平面波的“减薄”。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fat Rays: A Synthesis of Physical and Geometrical Optics with Gaussian Beamlets
Optical systems are primarily designed and analyzed by tracing bundles of rays. These rays are actually discrete points on the geometrical wavefront propagating through the system. The local field amplitude is inversely proportional to the radius of curvature of the wavefront or the distance from a neighboring ray point. Since by definition diffraction effects are excluded from geometrical optics, the energy density is infinite at focus or, in general, on a caustic. These singularities can be removed if the rays are expanded into physical-optics beamlets which are solutions to at least the reduced (paraxial or parabolic) wave equation. The individual fields would then be finite and continuous everywhere, and their superposition would represent the cumulative effects of aberrations, interference, obscurations, and diffraction in the system. This "fattening" of the infinitesimal geometrical rays is analogous to "thinning" the infinite plane waves used in the Fourier transform solutions of physical optics.
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