Research On New Methods Of Fringe Analysis In ESPI And FPP Based On Variational Image Decomposition

Electronic Speckle Pattern Interferometry(ESPI) and Fringe Projection Profilometry(FPP) are two kinds of important whole field nondestructive testing methods in optical measurement techniques. ESPI can be used for displacement, strain and surface tomography measurement. FPP is a very popular method for rapid and high resolution three dimensional shape measurement. ESPI and FPP as important tools of scientific research have penetrated into all kinds of research fields. In ESPI and FPP measurement, the physical quantities to be measured are related with phase which is encoded in fringe pattern. It requires computer aided fringe analysis to get phase information. The study on advanced methods of fringe analysis plays an important role in the development and application of ESPI and FPP with both theoretical value and practical engineering significance.Variation based image decomposition is a relatively new research filed with broad prospects. In recent years the variational image decomposition at its related areas has gradually become a hotspot in the area of image processing. In this dissertation, mainly based on variational image decomposition, the study on the difficult problems and key problems of fringe analysis in ESPI and FPP is deeply conducted, with proposition of new fringe analysis methods. The work in this dissertation is listed as follows:1. We proposed a fast numerical algorithm for solving oriented partial differential equation(PDE) methods, which is applied to the filtering of high density ESPI fringe patterns. The goal in the related research field is to filter the ESPI fringe patterns and meanwhile preserve the completeness of fringe patterns. Oriented partial differential equation methods are considered as effective ways to implement the filtering of high density ESPI fringe patterns for that they make filtering along the fringe orientation. However, the oriented partial differential equations require many iterations and a long computational time in its implementation. To address these problems, a fast numerical algorithm for oriented partial differential equation methods is proposed at the basis of Gauss-Seidel algorithm, which significantly improves the computational efficiency, and is put forward into high density fringe patterns.2. Based on variational image decomposition, we proposed a new filtering method for ESPI fringe patterns with large density variety. It is a more challenging task to filter the ESPI fringe patterns with the said feature, when compared with the filtering of ESPI fringe patterns with uniform density, or purely high density. The new method employs the Beppo-Levi space to describe the sparse fringes, and employs the adaptive Hilbert space to describe the dense fringes, making it capable of separating sparse fringes, dense fringes and noise effectively, and finally realizes the sufficient smoothing of the sparse fringes and the preservation of the dense fringes. The new method is successfully applied in the dynamic thermal measurements of the Printed Circuit Borad with out-plane displacement and in the study for debonding part of rotor blade.3. Based on variational image decomposition, we proposed a new method for FPP background removal. The new method employs the Bounded Variation(BV) space, the adaptive Hilbert space and the L2 space to respectively describe the background part, fringe part and noise part of FPP fringe pattern, which effectively separates the three parts. Compared with the existing advanced empirical mode decomposition method, the new method is more robust to noise. In addition, the existing methods for FPP background removal are based on frequency or time-frequency analysis, while the new method is based on spatial domain analysis, with the basis of variation and partial differential equation methods, which makes full use of variation and partial differential equation methods.4. Based on variational image decomposition, we proposed a new FPP phase retrieval method. The phase retrieval is implemented on condition that the background removal is performed by variatonal image decomposition. Based on the variety of spaces used to describe the fringe part and noise part, many new models are proposed as well as the corresponding numerical algorithms for solving them. In the new models, the spaces for describing the fringe part include the G space and the adaptive Hilbert space, and meanwhile the spaces for describing the noise part include the L2 space, the E space, the homogenous Contourlet space, the homogenous Curvelet space and the homogenous Shearlet space. Additionally, the Block Matching and 3D filtering(BM3D) method is introduced to describe the noise part. The performances of representative models are compared and analyzed via the simulated and experimental data, and after that the performances and adaptability of representative models are provided. Further, the proposed method is used in dynamic three dimensional shape measurement of hand gesture and face expression, which gives ideal results.5. Based on variational image decomposition, we proposed a new phase retrieval method for orthogonally composed FPP fringe pattern. In the proposed new method, the background part, fringe part and noise part is separated and the fringe part is obtained by using variational image decomposition to deal with orthogonally composed FPP fringe pattern, then the horizontal and vertical fringe patterns are obtained by using variational mode decomposition, and then the gradient of phase is obtained from the horizontal and vertical fringe patterns, and finally the phase is obtained by integrating the gradient of phase. Compared with the classical Fourier method used in the phase retrieval for orthogonally composed FPP fringe pattern, the new method recovers the phase with more details and improves the resolution of phase.This dissertation, on one hand, promotes the development of variational image decomposition; on the other hand, it provides new methods and techniques for ESPI and FPP fringe analysis, to attain the goal of addressing the difficult and key problems in ESPI and FPP, making ESPI and FPP techniques more effective in measurement with higher complexity.