Investigation of accurate fringe analysis techniques for fringe projection profilometry

Optical 3D measurement techniques have been studied and developed for a long time in literature now due to its non-contact, high speed, high accuracy, and sensitivity, for 3D measurements. Fringe pattern analysis (FPA) is an important aspect of all optical measurement techniques. Fringe patterns are usually generated by a well-known phenomenon of optical interference. The surface of an object is then, reconstructed by analyzing the phase distribution of these fringe patterns- a process called phase extraction. To analyze the phase distributions in both spatial and spectral domains, pixel-wise phase shifting and global Fourier transform have been established as the two pillar techniques for fringe analysis. To use both the properties simultaneously, Windowed Fourier Transform (WFT) has emerged as an in-between technique to analyze the fringe patterns block by block. In the past decade, FPA has made great progress for 3D measurements. Several methods have been developed for 3D surface measurement based on varied principles. These include time of flight, laser triangulation, stereo vision, shape from focus and defocus, structured light projections and digital fringe projection (DFP). Among these, structured light fringe projections and digital fringe projections (DFP) are commonly used in fringe projection profi lometry (FPP) systems due to their simple setup and the ability to achieve high-speed and high-accuracy. However, two key issues still prevail which need further improvement. First, with the rapid demand for 3D reconstruction of object surfaces which can be readily applied and used in various applications such as virtual reality, animations, a precision inspection of optical components and many more, obtaining a high-speed and highly accurate surface measurement has become a necessity. Second, with several fringe analysis methods being developed over the past decades, it has become increasingly difficult to understand, analyze and introspect some of the best-suited applications and conditions where different fringe analysis methods can prove useful and thus, requires a link to be set up between different algorithms for further investigation. Both these issues revolve around a central idea: robustness and high-accuracy 3D measurement. Since the spectral information of a patch of fringe pattern is much simpler to analyze and thus, more effective, instead of resolving some of the major error sources in existing FPP systems in spatial and spectral domain separately, in this thesis, author proposes to use the local in-between Windowed Fourier Transform (WFT) technique for the same with an agenda to be able to investigate the link between some of the best suited techniques for various applications under certain measurement conditions. First, some state-of-the-art fringe analysis techniques are reviewed. Also, some major issues in fringe analysis for FPP systems are inspected such as nonlinear gamma, uneven background, edge discontinuity, and high dynamic range, and the existing state-of-the-art techniques for resolving these issues including both the phase-shifting and transform-based methods in the past decades are reviewed. It is found that the accuracy of measurement can be improved by either using a large number of fringe patterns or by iterating the algorithm many times thus, leaving scope for further improvement. Second, to resolve these error issues in fringe analysis one by one, we fi rst try to tackle nonlinear gamma errors caused by the nonlinear nature of the devices projector and camera. A theoretical analysis for resolving the nonlinear gamma errors using Windowed Fourier Ridges (WFR) for carrier phase demodulation is then proposed. It fi rst, analyzes the local frequency error and phase extraction error for the carrier fringe pattern in order to depict the amount of gamma nonlinearity and then, resolves the error with the help of a performance prediction and error control using WFR. It was observed that despite being challenging it is possible to reduce the peak phase error to be as low as 0.05 rad in the presence of the error source. Third, after tackling the issue of nonlinear gamma in single carrier fringe pattern, we then fi rst try to analyze nonlinear gamma in phase-shifting technique and thus, resolve the error by using WFR for phase-shifted fringe patterns which are squeezed to a single carrier fringe pattern. After that, uneven and discontinuous background is chosen as the second error source which needs to be resolved. To tackle this issue in a single carrier fringe pattern, a Windowed Fourier fi ltering (WFF) based background removal technique is proposed. It uses a mirroring approach to tackle the error around the corner pixels. An ideal window of (50, 50) is used for both the algorithms for effectively resolving the error sources. Fourth, after discussing the two major issues in fringe analysis, a comparative study is then performed between two state-of-the-art fringe analysis techniques - WFR and Sampling Moire (SM), to analyze the effectiveness of the two algorithms for a single carrier fringe pattern for the very first time. While SM converts a single carrier fringe pattern into multiple phase-shifted Moire patterns to demodulate phase, WFR obtains the phase information in the window-based Fourier domain. Despite appearing two completely different approaches for fringe analysis and despite having separate applications, both simulations and experimental results con rm that both the algorithms appear as two sides of the same coin and thus, can be used interchangeably in various applications. In the presence of noise, both algorithms give outstanding performance. Finally, a link between WFR and spatial carrier phase-shifting (SCPS) algorithm is proposed for the very first time. Since phase-shifting and Fourier transform are the two pillar techniques for fringe analysis, and as Windowed Fourier transform has already been established as the extension of the Fourier transform, it is crucial to understand the link between the two, in order to select a proper technique for effective fringe analysis. It is observed that whenever SCPS is used to analyze a fringe pattern, WFR can always be attempted for better results.Doctor of Philosoph