雙波長純相位式繞射元件之研究

Implementation of Two-Wavelength Phase-Only Diffractive Optical Elements

戴嘉呈(Jia-Cheng Dai)

指導教授 ： 徐巍峰

國立臺北科技大學/電資學院/光電工程系研究所/碩士(2008年)

https://doi.org/10.6841/NTUT.2008.00065

摘要

本篇論文主要是透過遞迴傅立葉演算法(IFTA)與模擬退火演算法(SA)來實現具有雙波長分工作用的純相位繞射元件的設計。該元件設計的功用是使兩道不同波長的入射光源，經過繞射元件後，在觀察平面上分別照射出個別的目標圖形，之後我們將所設計的繞射元件圖形輸入至液晶空間光調變器(LC-SLM)中，並利用它來重建繞射圖形。
本篇論文的IFTA方法是採用H. Dammann 所設計的分色光柵的設計概念，並導入減緩相位變化與附加權值來優化程式。我們提出適合的雙波長演算流程去尋找不同波長所對應的元件相位分佈，其結果是結合不同重建場的單一繞射元件，可達成不同波長分光的效果。此外為了使用LC-SLM顯示其重建結果，必須將元件相位分佈轉換成0~255階的灰階變化，並額外加上不同波長對應的比例，我們即可獲得適合於LC-SLM的繞射元件。
最後我們配合LC-SLM不同波長對應的相位調變，將輸入的元件圖形分別利用不同波長的雷射照射於LC-SLM上，實際進行光學重建的動作，成功的重建出期望的圖形。

關鍵字

雙波長 ； 遞迴傅立葉演算法 ； 模擬退火演算法 ； 液晶空間光調變器 ； 繞射光學元件

並列摘要

The objective is to design phase-only diffractive optical elements (DOEs) for double-wavelength multiplexing by using the iterative Fourier transform algorithm (IFTA) and the simulated annealing algorithm (SA). This purpose of the designed DOEs is to separate two wavelengths and for each to generate individual diffractive pattern. After we obtained the double-wavelength DOEs were input to a liquid crystal spatial light modulator (LC-SLM) to reconstruct different intensity patterns when it is illuminated by the specified wavelengths.
When using IFTA in this thesis, we adopted Dammann’s design, put forward retard phase variation, and added the weighting coefficients for improving the DOE design. We proposed an adaptive two-wavelength algorithm to search the phase field that corresponds to individual wavelength. The results were obtained for a single DOE component that to combine different diffractive fields and it achieved the two-wavelength reconstruction.
Furthermore, because we want to use a LC-SLM to display DOE to reconstruct the diffractive images, the phase distributions, ranging from 0 to 2π of the phase-only DOE were converted into grayscaled integers, ranging form 0 to 255. The grayscaled matrices of DOEs were exported to the LC-SLM for the double-wavelength exertions.
At last, we successfully used the LC-SLM which replaced the DOEs to reconstruct different anticipative patterns when it is illuminated by two wavelengths.

並列關鍵字

two-wavelength ； iterative Fourier transform algorithm ； simulated annealing algorithm ； liquid crystal spatial light modulator ； diffractive optical element

參考文獻

[31] 施嘉博，LC-R2500液晶空間光調變器之測定研究，碩士論文，國立台北科技大學光電工程研究所，台北，2008。

[3] J. H. Holland, Adaptation in natural and artificial systems, Ann Arbor, MI: The University of Michigan Press, 1975, pp. 1-120.

[4] W. Feller, An Introduction to Probability Theory and Its Applications, vol. 1, 3rd Ed., New York: Wesley, 1950.

[5] J. S. Liu, A. J. Caley, and M. R. Taghizadeh, “Diffractive optical elements for beam shaping of monochromatic spatially incoherent light,” Appl. Opt., vol 45, no. 33, 2006, pp. 8440-8447.

[6] C.-C. Lee, Y.-C. Chang, C.-M. Wang, J.-Y Chang., and G.-C. Chi “Silicon-based transmissive diffractive optical element,“ Opt. Lett., vol. 28, no. 14, 2003, pp. 1260-1262.