Study On Three Dimensional Deformation Measurement Based On Local Frequency Without Phase Unwrapping Process

Optical interferometric techniques have been widely used in many research fields.The researchers who work in scientific and engineering fields require a simple and high accuracy measurement technique to assist their work.A novel three-dimensional(3D)deformation measurement technique which can obtain whole-field 3D displacement map from two consecutive interferograms is proposed in this paper.The following steps are given to obtain the out-of-plane displacement field: Firstly,local frequency of the original interferogram is required to be extracted by Windowed Fourier Ridges(WFR)and the in-plane displacement fields between two images is estimated by Optical Flow(OF)method in advance.Subsequently,the relation among local frequency of the original interferogram,in-plane displacement field between two images and out-of-plane deformation-phase can be determined based on the optical flow constrained equation.Finally,according to this relation,the out-of-plane displacement map can be easily obtained.However,due to the restriction of the optical flow method,errors will be occurred at the the points near the boundary of the in-plane displacement.To fix this issue,Digital Imaging Correlation(DIC)method was introduced to estimate the in-plane displacement maps with higher accuracy.In this paper,principle of Electronic Speckle Pattern Interferometry(ESPI),WFR,OF method and DIC method are presented and the proposed algorithm is applied to simulated and experimental interferograms,which is generated by the deformation of a centrally loaded and edge-clamped plate.The results of simulation and experiment show that the algorithm can combine the out-of-plane component of deformation-phase with the visible in-plane displacement field and extract three-dimensional displacement field simultaneously.The proposed method has simple setup and works perfectly in areas with dense fringes.Moreover,neither space-frequency domain conversion nor unwrapping process were necessary.The new algorithm provides a new approach for whole-field 3D displacement measurement and dynamic deformation measurement.In addition,two novel deformation measurement techniques which can suppress noise effectively are introduced at the end of this paper.In order to verify the effectiveness,these two methods are applied to the optical interference fringe patterns.Meanwhile,the prospects for 3D deformation measurement on these methods are discussed.The main points of every chapters are listed as below:1.Recent research advances in 3D deformation measurement and the definitions of phaseunwrapping process and wrapped phase are introduced in Chapter 1.The significance ofdeveloping phase-unwrapping technique was emphasized.2.The principle of ESPI and two general methods for phase unwrapping are introduced inChapter 2.Since Phase Shifting Interferometry(PSI)required more images to obtain accurateresults,it is not appropriate for dynamic deformation measurement.On the other hand,although the Fourier transform method is appropriate for dynamic deformationmeasurements,it can not be applied to closed fringe.The works in the following chapters areinspired by the content of this chapter.3.The principle of local frequency extraction based on WFR is presented in Chapter 3.Theoriginal WFR algorithm is improved and the new algorithm is applied to simulated fringepattern.Result of simulation shows that the improved algorithm has higher precision andbroader range of applications than the original WFR algorithm.Data of the local frequencyextraction in this chapter have important applications in following chapters.4.The main contribution of Chapter 4 is that a new 3D deformation measurement methodbased on OF is presented.Definitions of OF and recent research advances in OF field areintroduced at the beginning of this chapter.Subsequently,the relation among local frequencyof the original interferogram,in-plane displacement field between two images andout-of-plane deformation-phase is determined based on the optical flow constrained equation.According to this relation,the out-of-plane displacement map can be easily extracted fromvisible in-plane displacement field.The results of simulation and experiment show that 3Ddisplacement measurement can be realized by this method.5.Due to the inevitable boundary effect of the OF method,estimation errors will be occurredat the edge of optical flow field.To overcome this issue,in Chapter 5,OF algorithm in 3Ddeformation measurement method of Chapter 4 is substituted by DIC algorithm.Theprinciple of gradient-based DIC method is introduced and the simulation and experiment inChapter 4 are redone by the improved 3D deformation measurement method.The results ofsimulation and experiment show that the improved method in Chapter 5 works perfectly atthe boundary of the image.6.The principle of Carrier Squeezing Interferometry(CSI)and Speckle Phase Singularities(SPS)Method are introduced in Chapter 6.CSI is a technique which can suppress phase errorsfrom the inaccurate phase shift.Result of experiment shows that CSI can be applied to ESPIto obtain the displacement data with lower errors.2D Continuous WaveletTransform(CWT)-based SPS method is a technique which can measure in-planedisplacement between two images.In order to verify the effectiveness,sub-pixel in-planedisplacements between two images are measured by the combination of CWT-based SPSalgorithm and OF algorithm.Further,the prospect for out-of-plane measurement on thecombined method is discussed at the end of this chapter.7.In Chapter 7,the main contributions of this paper is summarized and the following worksare briefly introduced.