模擬退火法於設計繞射光學元件之研究

Study of Simulated Annealing Algorithm for Design of Diffractvie Optical Elements

許顧輝(Ku-Hui Hsu)

指導教授 ： 徐巍峰

國立臺北科技大學/機電學院/光電工程系所/碩士(2005年)

https://doi.org/10.6841/NTUT.2005.00023

摘要

本篇論文主要探討使用模擬退火演算法來設計純相位式繞射光學元件時在演算法上所會碰到的問題 ，在此我們所使用的退火計劃均為快速模擬退火(fast simulated annealing)。在應用其演算法時將會遭遇到的問題包括有初溫、冰點溫度的設定及穩定態的決定等，為此，我們將模擬不同的系統參數以釐清其與所設計出元件性能高低之關係，並且研究這些參數的設定如何影響演算法的收斂性質。另外，在過去前人的論文當中，使用模擬退火演算法處理類似的問題時均是採用單點擾動的鄰近解搜尋方式，像這樣的方式有著難於被人發覺的缺點，即其所搜尋之解空間受到限制。故我們在此篇論文中提出多點擾動的鄰近解搜尋方式來改善這個缺點，由數據及圖表中也確實觀察到不但有改善這個缺點的情形，更加快了演算法之收斂速度。

關鍵字

繞射光學元件 ； 模擬退火法 ； 單點擾動 ； 多點擾動

並列摘要

In this thesis, we discussed several issues regarding the designs of the 4-level phase-only diffractive optical elements (DOEs) using the simulated annealing (SA) method. The SA scheme adopted here was the fast simulated annealing. The concerned issues include the effects of the initial and freezing temperatures, the stable state, and the number of perturbations. The simulation results of 4-level DOEs that were designed using various temperatures and stable states were presented and analyzed. Moreover, we discuss the relationship between annealing parameters and convergent properties. In the currently-presented papers about DOEs designed using the SA method, researchers adopted a conventional SA scheme in which a single perturbation is conducted in each iteration. This results on a limited search in a local area of the solution space. In this study, we proposed a modified SA scheme in which multiple perturbations were conducted to relax the local search on the conventional method. According to the simulation results, the case of multiple perturbation effectively extended the limited search area in the solution space, which in turns increased the convergence speed.

並列關鍵字

diffractive optical elements ； simulated annealing ； single perturbation ； multiple perturbations

參考文獻

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