以改良式基因演算法的交配機制設計繞射光學元件之研究

Abstract

在本篇論文中，我們以基因演法算來設計繞射光學元件。在所使用的演算法中，為了深入瞭解交配機制，我們排除突變機制的影響，並且提出了一種新式的交配運算子。在設計此新式的交配運算子時，我們利用了繞射光學元件具有明確目標光場圖形的性質，因此，我們亦將其命名為「目標圖形導向交配運算子」。藉由利用目標光場圖形，此運算子能夠刺激整個族群，提供演化時的動力。 在本論文中，我們探討了該運算子的特性。藉由使用不同的初始族群，我們驗證了該演算法對初始條件的強韌性。我們觀察到繞射效率及均方根誤差的快速收斂性質；同時，我們也發現在訊雜比的演化需要較多的世代數。另外，在演化結束後，我們發現在整個族群的個體表現上，繞射效率與訊雜比無法達到同時優化，而必須在其中一者有所犧牲。 我們將所提出的方法應用於二階、多階及連續相位調變繞射光學元件的設計上。我們也針對了以本方法所設計出來的結果，與其他演算法的結果進行比較。例如，與疊代傅立葉轉換演算法與簡單型基因演算法的結果比較。在與使用不同突變率之簡單型基因演算法的比較上，我們提出的演算法可以在 5,000 世代時達到相似的結果，這相當於只需要簡單型基因演算法 20 分之 1 的世代數。而在與疊代傅立葉轉換演算法的比較上，本方法所得結果的繞射效率與均方根誤差與其相似，並且訊雜比可以達到 2 倍以上。

In this thesis, a method is proposed to design the diffractive optical elements (DOEs), in which the genetic algorithm (GA) is used with a novel crossover operator. The mutation mechanism is excluded from the method. The novel crossover operator is derived by taking advantage of the existence of the well-defined target in the DOE design and it is therefore entitled the TArget-oriented CrossOver (TACO) operator. By utilizing the target property in the DOE design, the TACO operator stimulates the evolution of solution toward the global maximum in the solution space. The properties of the TACO operator are studied. The robustness against different intial populations is verified. The fast convergence of efficiency and root-mean-square error (RMSERR) is observed. On the other hand, the growth of signal-to-noise ratio (SNR) is relatively slow. The trade-off between the efficiency and the SNR of the final population is also observed. The proposed method is applied to the design of the binary, multi-level, and continuous phase DOEs. The performance is compared with that of other optimization algorithms, such as the iterative Fourier transform algorithm (IFTA) and the simple genetic algorithm (SGA). Compared with the SGA using different mutation rates, the proposed method yields comparable results within a total of 5,000 generations, only 1/20 of that used in the SGA. Also, the efficiency and the RMSERR of the result yielded by the proposed algorithm are comparable to the IFTA, while the SNR is twice as high as that of the IFTA.