Development of digital image correlation method for displacement and shape measurement

DEVELOPMENT OF DIGITAL IMAGE CORRELATION METHOD FOR DISPLACEMENT AND SHAPE MEASUREMENT HUANG YUANHAO B Sc., Peking University (2002) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE JUNE 2004 Dedicated to my beloved father and mother my brother-in-law and sister and my happy family ACKNOWLEDGEMENT ACKNOWLEDGEMENT The author would like to express his sincere appreciation to his supervisors Dr Quan Chenggen and Associate Professor Tay Cho Jui for their guidance and advice throughout his research Their constant encouragement and support have greatly contributed to the completion of this work Special thanks are due to Dr Wang Shihua, Mr Fu Yu, Mr Deng Mu, Mr Chen Lujie, and Mr Wu Tao for their priceless suggestion and discussion which have ensured the completion of this work Special thanks are due to all technologists and colleagues in the Experimental Mechanics Laboratory for their assistance in experimental set-ups and valuable discussions The author found it enjoyable to study and work in such a friendly environment Last but not least, the author wishes to thank the National University of Singapore for awarding the research scholarship and providing facilities to carry out the present work i TABLE OF CONTENTS TABLE OF CONTENTS ACKNOWLEDGEMENTS ⅰ TABLE OF CONTENTS ⅱ SUMMARY ⅴ LIST OF FIGURES ⅶ LIST OF SYMBOLS x CHAPTER INTRODUCTION 1.1 Various Optical Methods 1.2 The Method of Digital Image Correlation (DIC) 1.3 Objective and Scope CHAPTER LITERATURE REVIEW 2.1 Development of DIC Algorithms 2.2 Application of DIC for Two-Dimensional Measurement 2.3 Application of DIC for Three-Dimensional Measurement CHAPTER 3.1 THEORY 11 The Method of Digital Image Correlation 11 3.1.1 Basic Concepts 11 3.1.2 Numerical Implementation 12 3.1.3 Some Important Points in Digital Image Correlation 15 ii TABLE OF CONTENTS 3.2 Principle for Out-of-Plane Displacement Measurement 17 3.3 Principle for Shape Measurement 19 3.4 Principle for Three-Dimensional Deformation Measurement 22 3.4.1 The Method of Fringe Projection 22 3.4.2 Fourier Transform for Phase Evaluation and Fringe Filtering 23 3.4.3 Out-of-Plane Displacement Measurement by Fringe Projection 24 3.4.4 3-D Displacement Measurement by Fringe Projection and DIC 25 CHAPTER EXPERIMENTAL WORK 35 4.1 Experiment for Out-of-Plane Measurement 35 4.2 Experiment for Shape Measurement 36 4.3 Experiment for 3-D Deformation Measurement 38 CHAPTER RESULTS AND DISCUSSION 43 Out-of-Plane Displacement Measurement 43 5.1.1 Rigid-Body Displacement Measurement 43 5.1.2 Deflection of a Cantilever Beam 44 5.1.3 Measurement of Non-Planar Object 45 5.1.4 Discussion 46 Shape Measurement 47 5.2.1 Measurement of a Step Change 48 5.2.2 Measurement of a Bulb Sample 49 5.2.3 Discussion 50 3-D Displacement Measurement 51 5.3.1 3-D Rigid-Body Displacement Measurement 51 5.3.2 3-D Deformation Measurement 54 5.3.3 Discussion 55 5.1 5.2 5.3 iii TABLE OF CONTENTS CHAPTER CONCLUSIONS AND FUTURE WORK 92 6.1 Conclusions 92 6.2 Future Work 94 BIBLIOGRAPHY APPENDDIX A LIST OF PUBLICATIONS 96 105 iv SUMMARY SUMMARY In this thesis, the method of digital image correlation (DIC), which is mainly employed for in-plane deformation measurement, is developed for full three-dimensional displacement and shape measurement The major findings of this project have been submitted for publication (see Appendix A) By use of DIC method to detect an apparent in-plane displacement introduced by an out-of-plane displacement of a test object, the unknown whole field out-of-plane displacement can be retrieved from a simple mathematical model Similarly, shape information of a test object is modulated in the apparent in-plane displacement field obtained by applying DIC to images before and after an in-plane translation Thus the object shape can be subsequently retrieved from the apparent in-plane displacement DIC is also combined with fringe projection technique to obtain three-dimensional displacement The combination method is carried out in two ways The first captures one image with projected fringes at each displaced state and uses a restored image for DIC to obtain in-plane displacement This procedure is suitable for dynamic measurement since only one image at each state is needed The second way captures two images, one with and the other without fringes, for deformation measurement in three directions v SUMMARY This thesis is divided into six chapters: Chapter introduces various optical methods for displacement and shape measurement Emphasis is given to the DIC which has some advantages over most of the other methods Objectives and scope of this thesis are also included Chapter reviews the development of various DIC algorithms and the applications of DIC systems for two-dimensional and three-dimensional measurements Chapter develops the theoretical background for the present work Basic concepts and numerical implementation for DIC are described in detail Mathematical model of the imaging system is presented and principles for out-of-plane displacement and shape measurement are given The combination of DIC and fringe projection is also described in detail Chapter describes the experimental arrangements and procedures Chapter presents the measurement results of out-of-plane displacement, shape and three-dimensional displacement Comparisons between experimental and theoretical results are given Various parameters which affect the measurement results are discussed Chapter gives a conclusion of the present research work It summarizes the accomplishments of the present study and recommends some improvements on algorithm development and applications of DIC method vi LIST OF FIGURES LIST OF FIGURES Fig 3.1 Typical set-up for digital image correlation 28 Fig 3.2 Typical images (a) before and (b) after a deformation 28 Fig 3.3 Schematic diagram of planar deformation process 29 Fig 3.4 Effect of various interpolation methods for gray value reconstruction 30 Fig 3.5 Relation between out-of-plane and apparent in-plane displacements 31 Fig 3.6 Illustration of influence of object distance on magnification 32 Fig 3.7 Schematic diagram of pinhole camera model 33 Fig 3.8 Schematic diagram for fringe projection 33 Fig 3.9 Three-dimensional displacement measurement system 34 Fig 4.1 Experimental set-up for out-of-plane displacement measurement 40 Fig 4.2 Experimental set-up for shape measurement 41 Fig 4.3 Experimental set-up for 3-D displacement measurement 42 Fig 5.1 Speckle image of a flat plate 57 Fig 5.2 Typical apparent in-plane displacement (a) u and (b) v 58 Fig 5.3 Calibration for initial object distance b 59 Fig 5.4 Experimental results for prescribed out-of-plane displacement of (a) 800 µm and (b) 60 µm 60 Fig 5.5 Apparent in-plane displacement (a) u and (b) v of a cantilever beam 61 Fig 5.6 Out-of-plane displacement of the cantilever beam (a) Experimental result (b) theoretical results and (c) Comparison for a mid-section 63 Fig 5.7 Out-of-plane displacement of the cantilever beam after correction (a) Experimental result (b) theoretical results and (c) Comparison for a mid-section 65 vii LIST OF FIGURES Fig 5.8 The surface of a plate with a step change 66 Fig 5.9 Apparent in-plane displacement (a) u and (b) v for a surface with a step 67 Fig 5.10 Experimental results for prescribed out-of-plane displacement of mm 68 Fig 5.11 Relation between out-of-plane displacement and magnification change 69 Fig 5.12 X-axis calibration chart for the step at (a) z = b and (b) z = b-1.5 mm 70 Fig 5.13 (a) In-plane displacement field obtained from DIC, (b) object distance obtained, and (c) the middle cross-section of the object distance map 72 Fig 5.14 Speckle image of a bulb sample 73 Fig 5.15 X-axis calibration chart for the bulb at (a) z = b and (b) z = b-12 mm 74 Fig 5.16 In-plane displacement obtained by digital image correlation 75 Fig 5.17 Experiment-obtained object distance b 75 Fig 5.18 Experiment-obtained shape of the bulb 76 Fig 5.19 The middle cross-section of the bulb sample 76 Fig 5.20 Comparison between the result from the proposed method and that from a commercial instrument 77 Fig 5.21 (a) Image of a speckle and (b) gray value distribution at section A-A 78 Fig 5.22 (a) Image of a coin and (b) gray value distribution at section B-B 79 Fig 5.23 Calibration in y-direction using image of (a) a speckle and (b) a coin 80 Fig 5.24 Image of a coin with projected fringes 81 Fig 5.25 Image spectrum (a) before and (b) after filtering 82 Fig 5.26 Image of a coin (a) after fringe removal and (b) with no projection fringes 83 Fig 5.27 Comparison of calibration in y-direction 84 Fig 5.28 Calibration in x-direction after fringe removal 84 Fig 5.29 3-D plot of coin surface 85 viii Table 5.1 Comparison of prescribed and measured 3-D rigid-body displacements CHAPTER RESULTS AND DISCUSSION - 91 - CHAPTER CONCLUSIONS AND FUTURE WORK CHAPTER SIX CONCLUSIONS AND FUTURE WORK 6.1 Conclusions In this thesis, the method of digital image correlation (DIC), which is conventionally used for in-plane displacement measurement, is further developed for out-of-plane displacement and shape measurement Furthermore, DIC is also combined with fringe projection technique to measure full-field three-dimensional deformation using a single camera Measurements are performed by a simple optical set-up which consists of a CCD camera, a 3-axis translation stage, a fringe projector and a personal computer for data processing Conventionally, DIC system with a single camera is only used for in-plane displacement measurement In this study, a method is developed for whole-field out-of-plane displacement measurement The proposed method employs DIC for an apparent in-plane displacement calculation and subsequently retrieves the out-of-plane displacement In the experiments conducted, the proposed method indicates a resolution of micron for rigid-body displacement measurement and the error is less than 5% The resolution could be further improved by increasing the magnification However this would lead to a reduction in the measuring area The proposed method is also able to measure non-planar object like a step change Since - 92 - CHAPTER CONCLUSIONS AND FUTURE WORK this method utilizes only a single camera, the measuring system is much simpler than most existing systems for out-of-plane displacement measurement Other advantages of the proposed method include insensitivity to rigid-body in-plane displacement and large measurement range The system for out-of-plane displacement measurement is also modified and further developed for shape measurement, which is normally performed by a camera-projector [47, 73] or a multiple-camera system The magnification variation introduced by the surface profile is determined by the use of DIC algorithm and the shape of the object is subsequently retrieved from a pinhole camera model Experiments are conducted to measure a step change and a bulb The results indicate a resolution of 0.05 mm and the error is less than 4% Both experimental and theoretical analysis shows that this method is especially suitable for step change or large object measurement which presents a larger magnification variation The proposed method also employs direct viewing of the object, and has no shadow problems as in fringe projection or shadow moiré method Digital image correlation is also combined with fringe projection in one measuring system to obtain three-dimensional deformation In the combination method, Fast Fourier transform (FFT) is employed to obtain phase information of the surface profile and out-of-plane displacement, and DIC method is used to measure in-plane displacement Experiments conducted on a rigid-body translated coin indicate - 93 - CHAPTER CONCLUSIONS AND FUTURE WORK submicron resolution in both in-plane and out-of-plane directions for small displacement measurement Experimental data obtained on an end-loaded cantilever beam also indicate an error of less than 5% for larger deformation measurement There are two alternatives for in-plane displacement measurement The first one uses images restored from fringe-presented images for DIC Since only one image is captured at each state in this method, it has the advantage of being suitable for dynamic measurement The second alternative uses fringe-free images for DIC and thus provides more accurate in-plane displacement measurement The compact measuring system proposed has many advantages Unlike existing multiple-camera systems used for three-dimensional displacement or shape measurement, the system proposed herein uses a single direct-viewing camera which avoids tedious calibration process and problems of shadows This measuring system is also able to accommodate varying magnifications for various applications and provide high accuracy measurement Since the measuring system can be easily pre-calibrated, it can also be used for in-situ and real-time measurement 6.2 Future Work Future work should include development of more accurate and computation time saving algorithms One possible improvement of current DIC algorithm is full-image correlation In the current DIC method, the choice of subset size is - 94 - CHAPTER CONCLUSIONS AND FUTURE WORK somewhat arbitrary Normally the subset should be big enough to contain unique speckle feature However a bigger subset also has a greater smoothing effect and the need for more computation time Different subset size can also yield slightly different results To solve this problem, a full-image correlation method should be attempted Since the displacement field is continuous and smooth, especially in the case of small displacement, some continuous function, such as B-Spline function can be used to represent whole field displacement, and the whole image can be correlated without defining a subset This would be an improvement over the subset-based correlation method The combination of DIC method with other 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Tay, C Quan, Y Fu and Y H Huang, “Instantaneous Velocity Displacement and Contour Measurement by Use of Shadow Moire and Temporal Wavelet Analysis”, Accepted for publication in Appl Opt C J Tay, C Quan, Y H Huang and Y Fu, “Digital Image Correlation for Whole Field Out-of-Plane Displacement Measurement Using a Single Camera”, Submitted for publication Y H Huang, C Quan, C J Tay and L J Chen, “Shape Measurement by the Use of Digital Image Correlation”, Submitted for publication - 105 - ... algorithm development and applications of DIC method vi LIST OF FIGURES LIST OF FIGURES Fig 3.1 Typical set-up for digital image correlation 28 Fig 3.2 Typical images (a) before and (b) after a deformation... in Digital Image Correlation 15 ii TABLE OF CONTENTS 3.2 Principle for Out -of- Plane Displacement Measurement 17 3.3 Principle for Shape Measurement 19 3.4 Principle for Three-Dimensional Deformation... of the object, images of the object before and after deformation are captured The surface profiles of the undeformed and deformed object are determined by using FFT for phase evaluation Out -of- plane