臺灣博碩士論文加值系統

本論文探討利用繞射光學理論建構層狀立體影像，而本篇論文中繞射光學理論是採用角頻譜演算法其優勢在於傳遞理論非近似解，計算簡單且有明確物理意義，其傳遞理論以平面波形式傳遞，故具備平面波傳遞相關特性。層狀立體影像的各層影像由一個繞射元件形成，再將繞射元件組成一個大的繞射元件，組合方法採用遮罩式組合法設計層狀立體影像，並利用自行設計之循環遞迴角頻譜演算法消除各層之間的影像串擾，其中循環遞迴角頻譜演算法源自於遞迴角頻譜法並加以改良而成的。
本論文中創建的立體影像截面面積大約為10mm×10mm，其投影成像起始位置為實驗中作為繞射元件的空間光調製器後125mm處，並在起始位置後40mm內創造相互有關係的4層影像，利用相互有關係的4層影像引導光在這40mm內形成連續之立體影像。最後由實驗結果可以看到本論文提出之循環遞迴角頻譜演算法可有效投影出立體影像，並成功消除層狀三維影像中各層之串擾雜訊。

In the thesis, I present a method to generating layered three-dimensional (3D) images using the angular spectrum (AS) method and the experimental results of the four-layered 3D images implemented in spatial volumes. The AS method has the advantages in non-approximate solutions and simple calculations of diffraction wave propagation.
The AS method was adopted in an iterative algorithm, called the iterative angular spectrum algorithm (IASA), to design individual diffractive optical elements (DOEs) for 3D layered images. In the previous research, the crosstalk noise between layers were not taken into account. In order to reduce the aliasing of four-layer mixing crosstalk, I proposed random interleaved sub-DOE method and circular iterative angular spectrum algorithm (CIASA) method to improve image quality.
 
First, the 3D DOE was composed of four sub-DOEs (at distances of 125, 135, 145, and 155 mm) made the interleaved DOE. Sub-DOEs were generated by IASA and randomly interleaved using sub-DOE method for projecting two-dimensional (2D) images. Sub-DOEs were interleaved to constract a large DOE to display on a phase-modulation spatial light modulator and to produce four 2D diffraction images without using any optical imaging components. Final, I used CIASA to reduce the four-layer mixing crosstalk in interleaved DOE.
The experiment results showed the four 2D images successfully constructed a layered 3D. Random interleaved sub-DOE method and CIASA method can make the image noise very low.

摘要 i
ABSTRACT ii
誌謝 iv
目錄 v
表目錄 vii
圖目錄 viii
第一章 緒論 1
1.1 前言 1
1.2 動機 2
1.3 論文架構 4
第二章 文獻回顧 5
2.1 角頻譜數值模擬相關文獻 5
2.2 遞迴角頻譜演算法(IASA) 7
2.3 利用IASA實現三維影像相關文獻之差異性 7
第三章 角頻譜 9
3.1 角頻譜繞射的物理意義 10
3.2 角頻譜的傳遞 13
3.3 循環摺積問題 15
3.4 空間頻域極值 17
3.4.1 以訊號證明空間頻域極值 17
3.4.2 以光學證明空間頻域極值 20
第四章 以層狀結構設計三維影像 23
4.1 層狀結構 23
4.1.1 遮罩式組合法 23
4.1.2 隨機排列之遮罩式組合法 26
4.2 遞迴角頻譜演算法 28
4.2.1 遞迴角頻譜演算法設計流程 28
4.2.1 循環遞迴角頻譜演算法設計流程 30
第五章 實驗結果與討論 33
5.1 實驗方法 33
5.1.1 空間光調變器 33
5.1.2 實驗架構 34
5.2 三維層狀影像之DOE與實際結果 35
5.2.1 柱狀影像模擬與實際拍攝結果 35
5.2.2 錐狀影像模擬與實際拍攝結果 40
5.2.3 模擬評價函數 43
第六章 結論 47
6.1 總結 47
6.2 未來展望 48
6.2.1 三維影像之強度均勻度 48
參考文獻 49
附錄 54

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