多波長聚焦相位元件設計之研究

A study of the design of focusing phase element for multiple wavelengths

陳智權(Chih-Chuan Chen)

指導教授 ： 劉宗平

元智大學/工程學院/電機工程學系/碩士(2006年)

摘要

在此研究中，針對以光軸為旋轉對稱的系統，提出一個與一般不同的光學濾波相位元件之設計方法。此種元件的設計方法，它是建立在相位恢復和迭代算法結合的一般性理論的基礎之上。所建議的光學濾波相位元件可用來濾波，以及將某些特定波長的光學元件濾波聚焦在焦平面上的光軸處。設計的過程對應於在光學中進行逆向求解，所設計的光學濾波相位元件是一種非週期性揭面式的深度分布。數值結果證明所建構的光學濾波相位，可以進行多波長濾波，並將某些特定波長在預定的位置處聚焦得很好。本文將詳細探討所設計的光學濾波相位元件，例如透射槽中的頻寬、焦面上聚焦點的光班斑以及相位元件的量化程度之影響等；這些性質符合微型光學中的各種應用，面對多波長照射的旋轉對稱系統，引用楊顧算法來處理此型問題。

關鍵字

濾波相位元件 ； 楊顧算法 ； 相位恢復 ； 迭代算法

並列摘要

In this research, we put forward one and generally different optical filtered phase(OFPEs) design method of elements. This kind of component design method, sets up the foundation of the general theory combined with iteration algorithm in phase-retrieval. The OFPEs are desirable to filtering the optical waves with the specified wavelengths and focusing them on a axial position of the focal plane. The design procedure corresponds to solving an inverse source problem in optics. The designed OFPEs have aperiodically surface-relief depth distributions. Numerical results demonstrate that the constructed OFPEs can conduct multiple wavelengths filtering at the predetermined wavelengths well. The performances of the designed OFPEs are explored in detail, such as the frequency line-widths in the transmission spectrum, the spot sizes of the focusing point on the focal plane, and the influences of phase quantized levels of the OFPEs, etc. The nature accords with various kinds of application in micro-optics. Yang-Gu algorithm is generalized to tackling problems in the rotationally symmetric system with the multiple-wavelength illumination.

並列關鍵字

filtered phase elements ； Yang-Gu algorithm ； phase-retrieval ； iteration algorithm

參考文獻

（2）Chung Ping Liu, Kuei Jen Lee, and Cheng-Hao Ko,

phase elements," Optics & Laser Technology (2006).

(accepted)

Jie-yao Zhuang, and Okan K. Ersoy, "Gerchberg-Saxton

and Yang-Gu algorithms for phase retrieval in an