非均勻相位繞射元件之最佳化函數之研究

A Study of the Optimization Function for Phase-Only Diffractive Optical Elements with Unevenly-Spaced Phase Levels

李永桐(Yung Tung Li)

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(2006年)

https://doi.org/10.6841/NTUT.2006.00279

摘要

本論文主要在探討以繞射面的效能參數(振幅均方根差,繞射效率,訊雜比等)做為選擇最佳相位的依據，再採取順向遞迴量化(forward iterative quantization, or FIQ)和反向遞迴量化(backward iterative quantization, or BIQ)兩種量化方法來設計4階非均勻相位的繞射元件。模擬結果將和以元件面的量化誤差做為最佳量化相位選擇方法做比較，以上的方法所採用的為遞迴傅立葉演算法(iterative Fourier-transform algorithm, or IFTA)。
在模擬過程中，共執行3015次的最佳化的遞迴運算(包括30組初始相位、7個量化Q值、5種遞迴相位量化方法及3種最佳化參數)。根據模擬的結果，BIQ4可得到最高的繞射效率及訊雜比。其中繞射效率最大值為83.58%發生於對均方根差優化的BIQ4(DOE#2，Q=30)，訊雜比最大值為1.3121發生於對均方根差優化的BIQ4(DOE#18，Q=15)。特別的是本篇所提出的最佳化參數設計繞射元件，在所有的遞迴量化方法可得到比傳統元件相位量化方法(即量化誤差)較高的繞射效率及訊雜比。

關鍵字

繞射光學元件 ； 量化誤差 ； 相位量化。

並列摘要

The objective of this thesis is to study the use of the performance parameters in the diffractive plane, such as the root-mean squared error, the diffractive efficiency, and the signal-to-noise ratio, to optimize the quantization phase levels of unevenly-spaced diffractive optical elements (DOEs). These parameters were conducted in two iterative quantization methods: forward iterative quantization (FIQ) and backward iterative quantization (BIQ) methods. This approach was compared with the previous method in which the uneven phase levels was optimized based on the quantization error in the DOE plane. All these approaches were adopted into the iterative Fourier transform algorithm (IFTA).
In the simulations, 3150 DOEs were designed: 30 initial phase arrays, 7 quantization increments, 5 iterative methods, and 3 performance parameters. According to the simulation results, BIQ4 method resulted in the highest diffraction efficiency and the signal-to-noise ratio. The largest efficiency of BIQ4 were 83.58% (DOE#2，Q=30) was obtained by using BIQ4 method with phase optimization of the root-mean-squared error (at Q=30). The largest signal-to-noise ratio of 1.3121 was also obtained by using the same approach (at Q=15). Especially, all the iterative quantization methods with the proposed optimization parameters designed DOEs with higher diffraction efficiency and the signal-to-noise ratio than them using the traditional quantization MSE.

並列關鍵字

Diffraction optical elements ； MSE (mean-squared error) ； phase quantization。

參考文獻

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