【正文】 。因?yàn)楦缮鏃l紋的光強(qiáng)是關(guān)于待測(cè)物體相位的余弦函數(shù)，與物體表面形貌相關(guān)，通過對(duì)相移干涉圖進(jìn)行分析和解調(diào)制，即可求解出待測(cè)物體的包裹相位信息，再通過相位解包裹算法得到連續(xù)的相位信息，從而重構(gòu)待測(cè)物體的表面輪廓或三維形貌。相移干涉測(cè)量技術(shù)(PhaseShifting Interferometry，簡(jiǎn)稱PSI)是光學(xué)干涉測(cè)量中的重要技術(shù)[4]，其測(cè)量的基本原理是：在光學(xué)系統(tǒng)的參考光路中加入相移器件（如壓電陶瓷微位移器(PZT)、半波片、1/4波片、偏振片或衍射光柵等），使其有序地改變參考光波和物光波之間的光程差，即產(chǎn)生了相移。AbstractPhaseshift interferometry technology, which is an optical interferometry method with high precision, has been widely used in the field of optical measurement and detection. In this paper, we introduce the basic principle and the development of phaseshift interferometry and kinds of phaseshift algorithms for phase shift extraction and phase retrieval. In the research of phase shift extraction, the arccosine algorithm, the algorithm based on Euclidean matrix norm and the algorithm based on the 1norm of the matrix for phase shift extraction are introduced. And a new algorithm for phase shift extraction based on the ratio of inner product is proposed, this algorithm can determine the phase shifts by using only twoframe phaseshifting interferograms, as well as the phase shifts among a sequence of interferograms. In the research of phase retrieval, we introduce the traditional phase shifting algorithms, and analyze their advantages and disadvantages. Then the advanced iterative algorithm and the algorithm based on the principle ponent analysis are introduced. Aiming at the twostep phaseshift algorithm, which can retrieve the phase by only twoframe interferograms, the algorithm based on the Gram–Schmidt orthonormalization method, the algorithm based on the correlation coefficient and the algorithm based on the extreme value of the interference are introduced. And we propose an improved algorithm based on Gram–Schmidt orthonormalization and a new algorithm for phase retrieval based on the ratio of the inner product of the twoframe interferograms. To verify the performance and the characteristics of the proposed algorithms paring with other algorithms, we have employed these algorithms to the simulation fringe patterns and experimental interferograms to extract the phase shifts and retrieve the measured phase, both of the results show that the proposed algorithms are suitable for phase shifts extraction and phase retrieval. This paper provides a new thought and method for phase shift and phase extraction in the phaseshift interferometry.The main contents of this paper are listed as follows:1. The advantages and disadvantages of several algorithms for phase shift extraction in the phaseshift interferometry are summarized and the scopes of their application are analyzed. A new phase shift extraction algorithm is proposed, which can determine the phase shifts with high precision in the case of only twoframe phaseshifting interferograms exist, as well as the case of multiframe interferograms.2. The advantages and disadvantages for phase retrieval and the application scope of the multistep phaseshifting algorithm are analyzed, as well as the twostep phaseshifting algorithm.3. Several methods and their principles for filtering the background of the interferograms are introduced, and bined with the twostep phaseshifting algorithm, the filtering effect of each method are analyzed.4. The precision and global sign of phase retrieved by the twostep phaseshifting and the relationship with the range of phase shift values are analyzed.5. Several phase unwrapping algorithms and their principles are introduced, and their advantages and disadvantages are analyzed.The innovation points of this paper are listed as follows:1. An improved algorithm based on Gram–Schmidt orthonormalization is proposed. Compared with the original algorithm, while maintaining the precision of original algorithm, the improved algorithm simplifies the process, reduce the amount of calculation and accelerate the speed.2. A twostep phase retrieval algorithm based on the ratio of inner products of phaseshifting interferograms is proposed，which can retrieve the measured phase with high precision rapidly. Compared with several twostep phaseshift algorithm, the result shows that the proposed algorithm has advantages in speed, and the accuracy is almost the same with the other twostep phaseshifting algorithm.KEY WORDS: phaseshifting interferometry, phase shift extraction, phase retrieval, ratio of the inner products，unwrappingVII目 錄摘要 IAbstract III第一章 引言 1 相移干涉測(cè)量技術(shù)概述 1 相移干涉測(cè)量技術(shù)的發(fā)展及研究現(xiàn)狀 2 本文的研究目的、內(nèi)容及創(chuàng)新點(diǎn) 4第二章 相移干涉測(cè)量中的相移量提取算法研究 6 相移量提取算法概述 6 現(xiàn)有的相移量提取算法 6 反余弦算法 6 歐幾里德矩陣范數(shù)法 8 矩陣1范數(shù)法 9 本文提出的相移量提取算法 11 相移量提取算法的比較 12 計(jì)算機(jī)模擬 12 實(shí)驗(yàn)結(jié)果 16第三章 相移干涉測(cè)量中的多步相移算法研究 19 多步相移算法概述 19 定步長(zhǎng)相移算法 19 三步相移算法 19 四步相移算法 20 五步相移算法 20 21 改進(jìn)迭代算法 21 主成分分析算法 24 不同多步相移算法的比較與分析 27第四章 相移干涉測(cè)量中的兩步相移算法研究 28 兩步相移算法概述 28 現(xiàn)有的兩步相移算法 28 施密特正交化算法 28 相關(guān)系數(shù)算法 30 干涉極值法 31 本文提出的兩步相移算法 33 33 34 不同兩步相移算法的比較與分析 35 計(jì)算機(jī)模擬 35 實(shí)驗(yàn)結(jié)果與討論 37第五章 影響兩步相移算法精度的因素分析 41 現(xiàn)有的濾除干涉圖背景項(xiàng)的方法 41. 高斯高通濾波法 41. 時(shí)域平均法 41. 逐點(diǎn)遍歷法 42. 差分法 42 各濾波方法的對(duì)比 43 相移量的取值范圍 44第六章 相位解包裹算法的研究 46 相位解包裹算法簡(jiǎn)介 46 現(xiàn)有的相位解包裹算法 46 行列逐點(diǎn)算法 46 枝切法 47 最小二乘算法 47 不同解包裹算法的比較與分析 48 計(jì)算機(jī)模擬 48 實(shí)驗(yàn)結(jié)果與討論 51第七章 總結(jié)與展望 54 全文總結(jié) 54 展望 55參考文獻(xiàn) 57致 謝 62附 錄 63相移干涉測(cè)量中的相移相位提取算法及解包裹算法研究第一章 引言 相移干涉測(cè)量技術(shù)概述光學(xué)干涉測(cè)量技術(shù)是利用光的波動(dòng)性和干涉原理，將待測(cè)物體的三維形貌信息以干涉條紋和光學(xué)強(qiáng)度的形式記錄下來，通過對(duì)干涉條紋和光強(qiáng)的分析得到待測(cè)物體的相位，進(jìn)而重構(gòu)物體的三維形貌[1]。將其與現(xiàn)有的兩步相移算法進(jìn)行比較，內(nèi)積之比算法在速度上有一定的優(yōu)勢(shì)，在精度上與其他兩步相移算法相當(dāng)。本文的創(chuàng)新點(diǎn)如下：1. 提出了一種改進(jìn)的施密特正交化兩步相移算法，與原施密特正交化算法相比，在保持原算法高精度的同時(shí)，改進(jìn)的算法簡(jiǎn)化了計(jì)算過程，減少了計(jì)算量，加快了運(yùn)算速度。4. 研究了兩步相移算法所恢復(fù)的相位精度和全局符號(hào)與相移量的取值范圍之間的關(guān)系。2. 研究了相移干涉測(cè)量中的多步相移算法與兩步相移算法，并對(duì)比了各相位恢復(fù)算法的的優(yōu)缺點(diǎn)及適用范圍。通過計(jì)算機(jī)模擬和實(shí)驗(yàn)驗(yàn)證的方法，分析比較了所提出的新算法和各種現(xiàn)有算法的特點(diǎn)及其適用范圍，為相移干涉測(cè)量中的相移相位提取提供了新的方法和思路。在提取相移量的研究中，介紹了反余弦算法、歐幾里德矩陣范數(shù)算法和矩陣1范數(shù)算法，并提出了一種既可以在多幅干涉圖的情況下提取相移量，又可以在僅有兩幅干涉圖的情況下提取相移量的內(nèi)積之比算法。分類號(hào) 密級(jí) 公開 UDC 學(xué)號(hào) 2012021579 碩士學(xué)位論文相移干涉測(cè)量中的相移相位提取算法及解包裹算法研究學(xué)位申請(qǐng)人： 牛 文 虎 專業(yè)名稱： 光學(xué)工程