攜行相位的光跡追蹤法

對於描述古典光學系統，光跡追蹤法有著非常準確的預測。然而一旦應用到波動性很強的現象時，光跡追蹤往往會得到錯誤的結果。在本論文中，我們從光跡的概念上繼續衍生出波動相位的物理量，並且勾勒一個適用於大尺度繞射的模型。所謂的大尺度繞射，是產生繞射的結構遠比繞射波長要大數萬倍，以論文中所提供的實驗而言，是由氦氖雷射通過一片蔡司鏡片之後所形成的干涉現象。模型於底片處重建了成千上萬的干涉條紋，這些條紋可以視為透鏡的光學指紋。這個模型同時也會產生大約三十個左右的特徵紋路，稱為「摩爾紋」；對於判斷每個模型參數，摩爾紋非常有用，同樣地摩爾紋也適用於判斷模型中一處特定的波函數計算。另外，相較於以格林函數處理波動問題，由於文中所介紹的方法最多只需要一重積分——積分型式取決於光程轉換為相位的細節——因此這也是一種快速演算法。

關鍵字

光跡追蹤；波動方程式；有限元素法；同調光源；一次光學

並列摘要

It is classically accurate to apply a traditional ray-tracing schema to an optical system. However, calculations generally go wrong when a ray-based analysis is imposed to cooperate with a wavelike stage. In this report, we extend the concept of rays to include wave phase quantities and derive a model to investigate a large scale interference scenario, in which the fringes come from a He-Ne laser conducting interference on a piece of Zeiss® eyeglass. This model reconstructs thousands of distinct fringes, considered the optical fingerprint of the lens, over the digital film. It in addition outputs about 30 characteristic patterns, called Moiré patterns, which are valuable when judging all the parameters of the model and a specific rule of wave function arithmetic. It is also a fast algorithm compared to a Green's function approach for that it requires a single integration at most, or no integration, depending on the conversion of optical path length to wave phase.

並列關鍵字

ray-tracing ； wave equation ； finite element method ； coherent light source ； primary optics

參考文獻

[1] G. Können, Polarized light in nature. Cambridge University Press Archives, 1985.

[2] R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, vol. 2. Addison-Wesley, 1964.

[3] D. J. Griffiths, Introduction to Electrodynamics. Addison-Wesley, 3rd ed., 1999.

[4] J. D. Jackson, Classical Electrodynamics. John Wiley & Sons, Inc., 3rd ed., 1998.

[5] D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics. John Wiley & Sons, Inc., 8th ed., 2007.

國際替代計量

攜行相位的光跡追蹤法

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