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分类号密级公开UDC学号2012021579硕士学位论文相移干涉测量中的相移相位提取算法及解包裹算法研究学位申请人：牛文虎专业名称：光学工程研究方向：微纳成像检测与应用所在院系：信息光电子科技学院导师姓名及职称：吕晓旭教授论文提交日期：2015年5月20日I相移干涉测量中的相移相位提取算法及解包裹算法研究专业名称：光学工程申请者姓名：牛文虎导师姓名：吕晓旭摘要相移干涉测量技术作为一种高精度的光学干涉测量手段，在光学测量与检测领域具有广泛应用。本文介绍了相移干涉测量技术的基本原理、发展现状及各类相移量提取算法和相位恢复算法。在提取相移量的研究中，介绍了反余弦算法、欧几里德矩阵范数算法和矩阵1-范数算法，并提出了一种既可以在多幅干涉图的情况下提取相移量，又可以在仅有两幅干涉图的情况下提取相移量的内积之比算法。在恢复相位的研究中，分析了传统多步相移算法的优缺点，引入了改进迭代算法和主成分分算法，并深入研究了仅从两幅干涉图就可以恢复相位的两步相移算法，介绍了施密特正交化算法、相关系数算法和干涉极值法的原理，并提出了新的两步相移算法：改进的施密特正交化算法与内积之比算法。通过计算机模拟和实验验证的方法，分析比较了所提出的新算法和各种现有算法的特点及其适用范围，为相移干涉测量中的相移相位提取提供了新的方法和思路。本文的主要内容如下：1.分析了相移干涉测量中的相移量提取算法，并对比了各算法的优缺点及适用范围。2.研究了相移干涉测量中的多步相移算法与两步相移算法，并对比了各相位恢复算法的的优缺点及适用范围。3.介绍了几种常见的滤除干涉图背景项的方法和原理，并结合两步相移算法分析了各方法的滤波效果。4.研究了两步相移算法所恢复的相位精度和全局符号与相移量的取值范围之间的关系。II5.介绍了常见的解包裹算法及其原理，对比分析了各算法的优缺点。本文的创新点如下：1.提出了一种改进的施密特正交化两步相移算法，与原施密特正交化算法相比，在保持原算法高精度的同时，改进的算法简化了计算过程，减少了计算量，加快了运算速度。2.提出了基于内积之比的两步相移算法，可以快速并准确地恢复待测相位。将其与现有的两步相移算法进行比较，内积之比算法在速度上有一定的优势，在精度上与其他两步相移算法相当。关键词：相移干涉术，相移量提取，相位恢复，内积之比，解包裹IIIRESEARCHONTHEALGORITHMSFORPHASESHIFTANDPHASEEXTRACTIONANDPHASEUNWRAPPINGINTHEPHASE-SHIFTINGINTERFEROMETRYMajor：OpticalEngineeringName：WenhuNiuSupervisor：XiaoxuLüAbstractPhase-shiftinterferometrytechnology,whichisanopticalinterferometrymethodwithhighprecision,hasbeenwidelyusedinthefieldofopticalmeasurementanddetection.Inthispaper,weintroducethebasicprincipleandthedevelopmentofphase-shiftinterferometryandkindsofphase-shiftalgorithmsforphaseshiftextractionandphaseretrieval.Intheresearchofphaseshiftextraction,thearccosinealgorithm,thealgorithmbasedonEuclideanmatrixnormandthealgorithmbasedonthe1-normofthematrixforphaseshiftextractionareintroduced.Andanewalgorithmforphaseshiftextractionbasedontheratioofinnerproductisproposed,thisalgorithmcandeterminethephaseshiftsbyusingonlytwo-framephase-shiftinginterferograms,aswellasthephaseshiftsamongasequenceofinterferograms.Intheresearchofphaseretrieval,weintroducethetraditionalphase-shiftingalgorithms,andanalyzetheiradvantagesanddisadvantages.Thentheadvancediterativealgorithmandthealgorithmbasedontheprinciplecomponentanalysisareintroduced.Aimingatthetwo-stepphase-shiftalgorithm,whichcanretrievethephasebyonlytwo-frameinterferograms,thealgorithmbasedontheGram–Schmidtorthonormalizationmethod,thealgorithmbasedonthecorrelationcoefficientandthealgorithmbasedontheextremevalueoftheinterferenceareintroduced.AndweproposeanimprovedalgorithmbasedonGram–Schmidtorthonormalizationandanewalgorithmforphaseretrievalbasedontheratiooftheinnerproductofthetwo-frameinterferograms.Toverifytheperformanceandthecharacteristicsoftheproposedalgorithmscomparingwithotheralgorithms,wehaveemployedthesealgorithmstothesimulationfringepatternsandexperimentalinterferogramstoextractIVthephaseshiftsandretrievethemeasuredphase,bothoftheresultsshowthattheproposedalgorithmsaresuitableforphaseshiftsextractionandphaseretrieval.Thispaperprovidesanewthoughtandmethodforphaseshiftandphaseextractioninthephase-shiftinterferometry.Themaincontentsofthispaperarelistedasfollows:1.Theadvantagesanddisadvantagesofseveralalgorithmsforphaseshiftextractioninthephase-shiftinterferometryaresummarizedandthescopesoftheirapplicationareanalyzed.Anewphaseshiftextractionalgorithmisproposed,whichcandeterminethephaseshiftswithhighprecisioninthecaseofonlytwo-framephase-shiftinginterferogramsexist,aswellasthecaseofmulti-frameinterferograms.2.Theadvantagesanddisadvantagesforphaseretrievalandtheapplicationscopeofthemulti-stepphase-shiftingalgorithmareanalyzed,aswellasthetwo-stepphase-shiftingalgorithm.3.Severalmethodsandtheirprinciplesforfilteringthebackgroundoftheinterferogramsareintroduced,andcombinedwiththetwo-stepphase-shiftingalgorithm,thefilteringeffectofeachmethodareanalyzed.4.Theprecisionandglobalsignofphaseretrievedbythetwo-stepphase-shiftingandtherelationshipwiththerangeofphaseshiftvaluesareanalyzed.5.Severalphaseunwrappingalgorithmsandtheirprinciplesareintroduced,andtheiradvantagesanddisadvantagesareanalyzed.Theinnovationpointsofthispaperarelistedasfollows:1.AnimprovedalgorithmbasedonGram–Schmidtorthonormalizationisproposed.Comparedwiththeoriginalalgorithm,whilemaintainingtheprecisionoforiginalalgorithm,theimprovedalgorithmsimplifiestheprocess,reducetheamountofcalculationandacceleratethespeed.2.Atwo-stepphaseretrievalalgorithmbasedontheratioofinnerproductsofphase-shiftinginterferogramsisproposed，whichcanretrievethemeasuredphasewithhighprecisionrapidly.Comparedwithseveraltwo-stepphase-shiftalgorithm,theresultshowsthattheproposedalgorithmhasadvantagesinspeed,andtheaccuracyisalmostthesamewiththeothertwo-stepphase-shiftingalgorithm.KEYWORDS:phase-shiftinginterferometry,phaseshiftextraction,phaseretrieval,ratiooftheinnerproducts，unwrappingV目录摘要.....................................................................................................................................................IAbstract.........................................................................................................................................III第一章引言..........................................