利用奇異值分解設計擴展景深光學系統濾波器

Design of Filter for Extended Depth of Field Optical System By Singular Value Decomposition Method

黃中平

指導教授 ： 楊士禮

國立清華大學/電機資訊學院/光電工程研究所/碩士(2010年)

摘要

在手機要求輕薄短小的前提下，要能夠達到長景深對光學設計是很大的一個挑戰。利用影像處理技術和光學設計結合達到此目的是一個比較嶄新的領域，主要的方式是在光學系統的後端，加上一個濾波器。當光學系統不是點對點成像時，影像經過光學系統之後會變成模糊的影像，此時濾波器能夠將模糊影像修復。以目前而言，大部分的技術都是用在單一個濾波器修復單一個模糊影像，當不同景深的物經過光學系統，由於失焦的關係，每一張影像的模糊程度有所差異，要用單一濾波器而能修復整個光學系統對於不同景深的物所造成的各種模糊影像是一個難題。在本論文中，提出以模擬的方式，其中運用優化的概念，配合奇異值分解的理論，設計出一個濾波器，能夠同時修復因為不同景深的物經過光學系統而產生不同的模糊影像，我們最後得到的結果，將直接對因為不同景深的物經過光學系統而產生不同的模糊影像進行修復，而此濾波器與以往平均型的濾波器比較，我們直接將修復後影像與原先的物取均方根誤差，可知在修復影像的品質方面是有優勢的。在我的論文裡，將會提出如何將奇異值分解運用在優化的方式，在優化的過程中，奇異值分解方法可以讓我們在優化時，減少相當程度的變數量，而使原先無法經由優化得到解的問題，能夠因此而得到一個結果。

關鍵字

濾波器 ； 影像處理 ； 擴展景深光學系統

並列摘要

Required light, thin, short and small prerequisites in mobile phone, it was a very big challenge to achieve the long depth of field to the optical system design. It was a quite brand-new domain to combine digital image processing technology and the optical system design. The main way was to add a filter in optical system's rear end. When the optical system was not the point-to-point image, the image after optical system would turn the blur image, this time the filter could restore the blur image. To the present, the majority of technologies were use single filter to restore single blur image. When the different depth of field objects passed through the optical system, as a result of the defocusing, there was different degree of blur to each image. It was a difficult problem to use the single filter to restore the entire optical system that each kind of blur image which created regarding the different depth of field objects. In this paper, we proposed simulation method, utilized the concept with optimizes, coordinated the theory of singular value decomposition designed a filter that could restore the different blur images that achieved by different depth of field objects passed through the optical system. Finally, we obtained the result, would direct to restore the different blur images. Comparing this filter and the average filter, we would take the root mean square error between the restored image and the object and knew the quality of the restored image has the superiority. In my paper, we would propose that how the singular value decomposition applied in optimization. In the optimized process, the singular value decomposition method might let us reduce the suitable degree the number of variables and such that problem which cannot solve by optimization before, can be solve after.

參考文獻

Rafael C. Gonzales and Richard E. Woods,“Digital image processing”2/e

B.E.A. Saleh and M.C. Teich, ”Fundamentals of Photonics.”

Robert E. Fischer, Biljana Tadic-Galeb and Paul R. Yoder, “Optical System Design” 2/e (2008)

Edward R. Dowski Jr. and W. Thomas Cathey, “Extended depth of field through wave-front coding.” Appl. Opt. 1861 -1864 (1995)

Chung-Ping Huang, Hsin-Yueh Sung, and Sidney S. Yang, “ The analysis of PSF similarity and image restorability, ”