相位編碼元件精度對景深擴張範圍的影響

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張銓仲(Chuan-Chung Chang) 查詢紙本館藏

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光電科學與工程學系

論文名稱

相位編碼元件精度對景深擴張範圍的影響
(A Definition of Tolerance Effectiveness for Pupil Engineering)

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摘要(中)

對於光學取像系統來說，如何將取像系統的公差分析結果與系統所擷取之影像的影像品質相互連結一直是尚待解決的問題，尤其是具備相位編碼元件的數位取像系統，因最終的影像除了鏡頭的成像之外，也須考慮影像還原對最終影像的影響，因此僅僅利用傳統鏡頭的公差分析手法，並無法有效的對相位編碼取像系統進行分析。對於具備景深擴展能力的相位編碼取像系統而言，雖然已有相關研究指出因相位編碼元件具有抵抗取像系統中偏心誤差的能力，所以仍能維持良好的景深擴展能力。但對於相位編碼元件本身因加工製程所殘留的表面誤差，對景深擴展能力的影響程度仍需進一步的釐清，同時過去的研究多著重於相位編碼元件的光學傳遞函數特性，卻忽略了在此類數位取像系統，當影像經還原處理後，影像還原的傳遞函數對整體取像系統景深擴展能力的影響。為了能夠分析因相位編碼元件表面誤差，對相位編碼取像系統景深擴展能力的影響程度，我們首次提出了利用相位編碼元件的點擴散函數相似性、成像模擬、影像還原以及影像品質評估的分析方法，並以具有輪幅狀表面誤差的三次式相位編碼元件為例，進行系統的景深擴展能力分析。
在論文的第一章中，我們簡單介紹了相位編碼系統的基本原理以及目前在此領域的研究現況；在第二章中對於目前相位編碼取像系統中所使用的三次式相位編碼元件進行理論的推導，並加入了系統所需的影像還原原理與處理方法說明；在第三章中，分別對在論文中模擬計算時所採用的點擴散函數計算、表面誤差模型、成像模擬、影像還原以及影像品質評估的方法做完整的說明；在第四章中對具備輪幅狀表面誤差的三次式相位編碼元件進行模擬計算，以理想無表面誤差的相位編碼元件作為景深擴展性能的基準，探討在景深擴展分析時點擴散函數相似性與影像品質參數-峰值信噪比(peak signal to noise ratio, PSNR)的差異，最後並以一個經實際加工所得之相位編碼元件，其點擴散函數的實際量測與模擬結果比較來確認論文所分析結果的可靠度。
在比較點擴散函數與影像品質參數後，我們發現當相位編碼元件存在表面誤差時，點擴散函數相似性無法有效反應系統實際的景深擴展能力；但藉由引入影像品質參數後，可有效對系統的景深擴展能力進行分析。同時亦發現藉由第三章所提出的分析方法，當相位編碼元件的表面誤差的峰谷值小於0.1個波長時，系統的景深擴展能力不受表面誤差中輪幅數量的影響；當表面誤差的峰谷值需從0.1個波長放寬至0.25甚至0.50個波長時，表面誤差的輪幅數量須介於10至100之間。因此對於景深擴展能力的相位編碼取像系統，藉由論文所提出之方法，我們最終可明確知道相位編碼元件所需的製作精度以及系統的景深擴展能力受到表面誤差下的影響程度。
最後我們亦針對論文中所提出的分析方法，指出了數項須待進一步改善的方案，並藉由所觀察到的現象，對相位編碼元件的研究方向提供一些建議以作為未來的參考。

摘要(英)

How to connect the result of tolerance analysis to image quality is a challenging problem for an imaging system. Because of the image quality is affected by imaging lens and image restoration in a phase coding image system, so this is much more difficult for such kind of imaging system. Although some studies have shown the performance of depth of field for a phase coding imaging system will not be affected by centering error, but variation of depth of field which causing form surface error on phase coding element is not considered yet. And most of studies focus on the properties of transfer function of phase coding element, and ignore the transfer function of image restoration itself. In order to understand the effect of surface error on phase coding element, we present a method which combining similarity of point spread function, imaging simulation, image restoration and image metric for first time to analysis the variation of depth of field. And the tolerance analysis of cubic phase mask is discussed which a spoke type surface error is included
In Chap. 1, we introduce the basic working principle of phase coding imaging system and summarize results of current related researches for it. In Chap. 2, the theories of cubic phase coding and image restoration are both described. In Chap. 3, the detail calculation produces of similarity of point spread function, imaging simulation, image restoration and image metric are described. In Chap.4, the present method which considering the effects of spoke type surface error in phase coding element is considered. And effectiveness of similarity of point spread function and an image metric (peak signal to noise ratio, PSNR) are discussed. Finally, simulation and experiment results for a cubic phase coding element are both presented also.
We find that, for a phase coding element which existing surface error, similarity of point spread function can not represent the performance of depth of field; but image metric PSNR can. And also we find if the peak to valley for a phase coding element can be better than 0.1λ, the performance of depth of field will not affected by numbers of spoke ring. If some 10 to 100 numbers of spoke ring are existed, the peak to valley of surface error can be released form 0.1λ to 0.25λ or even 0.50λ. So by using our method, the required accuracy of phase coding element and the performance of depth of filed in phase coding imaging system can be determined.
Finally, we also point out the potation applications and prospect of future research items.

關鍵字(中)

★ 影像品質參數
★ 表面誤差
★ 相位編碼
★ 景深
★ 焦深

關鍵字(英)

★ image metric
★ depth of focus
★ surface error
★ depth of field
★ phase coding

論文目次

中文摘要 i
英文摘要 iv
目錄 vi
圖目錄 viii
表目錄 xv
符號說明 xvi
一、研究背景 1
1-1 緒論 1
1-2 三次式相位編碼簡介 2
1-3 相關研究整理 6
1-4 論文結構 11
二、相位編碼理論 12
2-1 光學成像 12
2-2 三次式相位編碼 14
2-3 系統工作原理 18
三、研究方法 21
3-1 點擴散函數計算 21
3-2 表面誤差模型 24
3-3 點擴散函數相似性 28
3-4 成像模擬 32
3-5 影像還原 34
3-6 影像品質評估 36
四、公差分析流程與模擬結果 38
4-1 公差分析流程 38
4-2 數值模擬與實驗結果 41
五、結論 88
參考文獻 92

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指導教授

李正中(Cheng-Chung Lee)

審核日期

2010-6-14

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