臺灣博碩士論文加值系統

同調性是光的基本特性之一，其描述的是在不同位置、不同時間所觀測到的兩個光場的相位的相似性，不同程度的同調性在不同領域有重要應用，例如，高同調程度的雷射光源能夠製造散斑，部分同調光源較不容易受到大氣擾動的影響，適合用於通訊。有鑒於光源發光機制中固有的隨機性，使用隨機過程的數學方法模擬光場，將比傳統波動光學的架構裡僅僅將光場視為決定性訊號更為精確。另外，傅立葉光學是處理光學訊號的重要領域，其應用遍及成像光學，再加上同調理論，便發展出一門充滿潛力的領域——相位光學。
本篇論文的目的是希望透過一系列地介紹上述領域，能夠綜觀地串聯起傅立葉光學、隨機過程、同調理論乃至相位光學的整體圖像。

Coherence is one of the most important properties of light, which describes the correlation of the phase of two different fields separated by space and time. Light sources with different degree of coherence are applied to different situations. For examples, lasers with high degree of coherence can be used to produce speckles; partial coherent lights are less affected by atmospheric turbulence, and hence are useful in communications. In view of the inherent randomness of spontaneous emission, it would be more accurate to model lights by means of random processes than deterministic signals, which are assumed in the configuration under wave optics. Besides, Fourier optics provides an essential theory for signal processing. Combining Fourier optics and coherence theory would lead to a promising realm, which is called Phase-space optics.
The goal of this thesis is not only to introduce the foregoing knowledge in turns, but also to give the big picture of coherence theory and related subjects.

一、緒論(p.1)
二、傅立葉光學(p.3)
2.1 傅立葉轉換(p.3)
2.1.1 定義(p.3)
2.1.2 存在條件(p.5)
2.1.3 由向量投影解釋傅立葉轉換(p.5)
2.2 線性位移不變系統(p.8)
2.2.1 線性(p.8)
2.2.2 位移不變性(p.9)
2.2.3 線性位移不變系統(p.10)
2.2.4 討論(p.12)
2.3 摺積與相關函數(p.13)
2.3.1 摺積(p.13)
2.3.1.1 定義(p.13)
2.3.1.2 討論(p.16)
2.3.2 相關函數(p.16)
2.3.2.1 定義(p.17)
2.3.2.2 基本性質(p.19)
2.4光學傳遞系統與繞射公式(p.20)
2.4.1 角頻譜(p.21)
2.4.2 瑞利－索末菲繞射(p.23)
2.4.3 菲涅耳繞射公式(p.24)
2.4.4 夫朗和斐繞射(p.26)
2.5 干涉與繞射(p.26)
2.5.1 干涉(p.27)
2.5.2 繞射(p.29)
2.6 章節總結(p.32)
三、隨機過程(p.33)
3.1 隨機變數(p.33)
3.1.1 定義(p.33)
3.1.2 期望值與動差(p.38)
3.1.3 兩個隨機變數(p.41)
3.2 隨機向量(p.45)
3.3 隨機過程(p.47)
3.3.1 定義(p.47)
3.3.2 相關函數(p.54)
3.3.3 平穩性與遍歷性(p.56)
3.3.4 功率頻譜密度(p.63)
3.4 章節總結(p.65)
四、同調理論(p.67)
4.1 以隨機過程詮釋光場(p.67)
4.2 時間同調性、空間同調性及同調函數(p.70)
4.2.1 時間同調性(p.71)
4.2.2 空間同調性(p.74)
4.2.3 以向量和詮釋交互強度函數(p.80)
4.3 van Cittert-Zernike theorem(p.84)
4.4 章節總結(p.90)
五、相位光學(p.92)
5.1 文獻回顧(p.94)
5.1.1 〈Radiometry and Coherence〉(p.94)
5.1.1.1 座標轉換(p.95)
5.1.1.2 廣義輻射亮度與韋格納分佈函數 (p.96)
5.1.1.3 章節總結(p.97)
5.1.2〈Wigner Distributions and How They Relate to the Light Field〉(p.98)
5.1.2.1 引述〈Radiometry and Coherence〉(p.98)
5.1.2.2 光場(Light Field)與韋格納分佈函數(p.100)
5.1.2.3 章節總結(p.103)
5.1.3〈Validity of Wigner Distribution Function for Ray-based Imaging〉(p.104)
5.1.3.1 韋格納分佈函數之詮釋(p.104)
5.1.3.2 韋格納分佈函數之基本性質(p.104)
5.1.3.3 近軸近似(p.105)
5.2 質疑：對於韋格納分佈函數之普遍理解(p.106)
5.2.1 座標轉換之物理意義(p.106)
5.2.2〈Radiometry and Coherence〉公式推導之缺失(p.109)
六、總結與未來展望(p.111)
6.1 總結(p.111)
6.2 未來展望(p.112)
引用(p.113)

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