韋格納分佈函數應用於光學系統之研究

以計算效率的角度而言，利用幾何光學模型，並以光線追跡評估光學系統特性是一項重要且方便的手段，然而，光的物理特性僅有在巨觀尺度下滿足直線傳播的特性。為了克服此弱點，我們選擇了韋格納分布函數為工具，透過統計光學與傅氏光學理論，連結了此項函數模型與光場技術的關係；證明韋格納分布函數在巨觀條件下與光場等價，同時考慮到繞射效應。接著，我們分析韋格納分布函數的傅立葉對偶函數-模糊函數在光學系統中的意義，建立模糊函數與光學傳遞函數之關係，並與韋格納分布函數整合。論文最後，我們將韋格納分布函數，應用於擴展景深系統。

關鍵字

韋格納分布函數；統計光學；富氏光學；模糊函數

並列摘要

In viewpoint of computational efficiency, ray tracing based on geometric model is a convenient but effective way to analyze the performance of an optical system. However, neglect of diffraction effect may leads to the error of optical modeling-. In order to overcome this defect, we use the Wigner distribution function (WDF) as a tool, based on statistics and Fourier optics, to address the correspondence between WDF and light field technique. On account of macroscopic conditions, WDF could be proved equivalent to light field including diffraction effect. After discussing the WDF, we examine the physical significance of its Fourier dual – Ambiguity function (AF) associated with optical transfer function. The connection between AF and WDF in optical system will be given. Finally, we employ WDF analyses in extending depth of field (EDoF) system.

並列關鍵字

Wigner Distribution Function ； statistical optics ； fourier optics ； Ambiguity Function

參考文獻

[1] A. Ashok and M. Neifeld, “Compressive light field imaging,” Proc. SPIE 7690, 76900Q, 2010.

[2] M. J. Bastiaans. “The Wigner distribution function applied to optical signals and systems,” Opt. Commun., 25(1):26-30, Apr. 1978.

[4] Z. Zhang, M. Levoy, “Wigner distributions and how they relate to the light field,” IEEE International Conference on Computational Photography, 2009.

[6] E. R. Dowski, Jr. and W. T. Cathey, “Extended depth of field through wave-front coding,” Applied Optics, 34(11):1859-1866, Apr. 1995.

[7] J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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韋格納分佈函數應用於光學系統之研究

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