In this work, we introduce the windowed generalized phase-shifting algorithms (WG-PSAs) using static and dynamic weighting functions/widows. These algorithms are derived from a weighted least square fitted to the monochromatic temporal fringe, thereby, the selection of the window plays an important role due to the fact that it shall reduce the influence of those intensities jeopardizing the phase estimation. In order to make the best selection, we propose to employ an adaptive/dynamic window which has the ability to detect the fringe patterns that jeopardize the phase retrieval. This window is computed iteratively by analyzing the error between the measured and fitted intensities. Furthermore, we provide the analysis of our scheme using the frequency transfer function (FTF) formalism for phaseshifting algorithms. Finally, we executed numerical experiments with synthetic data in which we compare the performance of the dynamic window versus several static ones from the state-of-the-art; although our scheme is more computationally expensive due to the iterative procedure, it works better than the traditional generalized PSAs with a window included or not.
In this work, we proposed a procedure for the calibration of 3D surface shape measurement system, which is based on fringe projection and phase shifting algorithms. Our approach consists in the use of temporal phase unwrapping methods to determine the phase-to-height mapping relationship. In particular, we propose the use of the two-step temporal phase-unwrapping algorithm. For that, two sequences of fringe patterns (low and high sensitivity) are projected onto the reference plane, which is shifted perpendicularly to the camera-projector plane. Then, the phase maps at each shifting step are retrieved from acquired sequences of sinusoidal intensity patterns using the two-step temporal unwrapping formula. Finally, using the phase maps at well-known in a least-squares scheme, the system parameters, nonlinear model of calibration, are estimated, i.e. the phase-to-height mapping relationship. Validation experiments are presented.
KEYWORDS: Calibration, Mathematical modeling, 3D modeling, Fringe analysis, 3D metrology, Data modeling, Phase shifts, Digital Light Processing, CCD cameras
In three-dimensional shape measurement by fringe projection, the calibration of the measurement system is an essential procedure to determine the relationship between the retrieval phase and the object height. In this work, we present an analysis of three calibration methods that had been proposed in the literature. These are based on three mathematical models: linear, quadratic and nonlinear. The linear and nonlinear mathematical models were deduced from the geometry of the measurement system, and parameters of the model were estimated by employing the ordinary least-squares method. The implementation of this calibration method was performed by translating a reference plane at different positions with known depths. The measurement accuracy for these three models was compared by numerical simulations, and the nonlinear model was employed to measure data.
The optical profilometry techniques have become more and more used in dynamic 3-D shape measurement. In particular, there are two problems to overcome. One is to recover the phase from a single fringe. The second problem is the phase recovering from a pattern avoiding that the harmonics introduced by the projector. In this work, we analyzed two kinds of techniques: off-axis and slightly off-axis interferometry algorithms for phase retrieval. The Hilbert transform is implemented in both cases. Validation experiments are presented.
We propose a fringe-projection profilometry technique for shape defects measurement, which can be employed for three-dimensional (3-D) quality inspection. The proposal consists of using a template surface to design phase-shifting algorithms with special-purpose phase response via the frequency transfer function. These algorithms can jointly and directly estimate the spatial phase deviations in a 3-D inspection. Phase deviations correspond to shape differences between the template shape and a testing one. The phase-unwrapping procedure is unnecessary when phase differences are small, as is usual in quality inspections. Experimental results show that our technique is so sensitive that the ripples in a fingerprint can be retrieved.
In fringe projection profilometry, temporal phase unwrapping is an essential procedure to recover an unambiguous absolute phase even in the presence of large discontinuities or spatially isolated surfaces. In this work, a dual-sensitivity profilometry technique is presented, which is based on defocused projection of binary and sinusoidal fringe patterns with a high and low-frequency spatial carrier, respectively. The binary defocusing techniques (based on PWM or square-wave profile patterns, whose pitch is relatively narrow) have demonstrated successful for high-quality three-dimensional shape measurement when the projector presents a nonlinear response. But they suffer if pitch fringe is wide. On the other hand, using dual sensitivity profilometry, the quality of the unwrapped phase is determined by the high-frequency carrier. Thus, working with only one binary pattern, one can use a single defocusing level (low) in order to reduce the data acquisition time and maintain the quality of the unwrapped phase. Experimental results are presented to verify the success of the proposed method.
We present a polarization sensitive measurement focused on retrieve elliptical phase retardation properties. The system is based on rotating two linear polarizers. And a demodulation algorithm is proposed to retrieve a partial matrix of Muller from the intensity output signal. The polarimetry setup also employs a monochrome camera as detection system and a HeNe laser as light source. Simulation and experimental results in transparent samples are presented showing the feasibility of the measurement and the potential usage in a multiwavelength arrangement.
KEYWORDS: Linear filtering, Reconstruction algorithms, Reflectivity, 3D image reconstruction, Cameras, Light sources, 3D image processing, 3D modeling, Machine vision, 3D vision
There are several algorithms to solve the shape from shading problem. Most of these algorithms rely on basic assumptions about the surface reflective properties, camera projection and location, and the light source distribution. In this paper, we implemented an algorithm based on a Wiener filter to obtain surface estimation from a single image. We tested the algorithm with images generated synthetically and also employing images from a real object. We were able to obtain the shape of objects with different geometries.
In this work, we propose a novel technique to retrieve the 3D shape of dynamic objects by the simultaneous projection of a fringe pattern and a homogeneous white light pattern that are both coded in an RGB image. The first one is used to retrieve the phase-map by an iterative least-squares method. The last one is used to match pixels from the object in consecutive images, which are acquired at various positions. The proposal successfully full fills the requirement of projecting different frequency fringes. One extracts the object’s information and the other retrieves the phase-map. Experimental results show the feasibility of the proposed scheme.
Three-dimensional shape profiling by sinusoidal phase-shifting methods is affected by the non-linearity of the projector. To overcome this problem, the defocused projection of binary patterns has become an important alternative to generate sinusoidal fringe patterns. In this paper, we present an efficient technique to generate binary fringe patterns where we use the symmetry and periodicity properties of binary-coded sinusoidal intensity. This reduces the search-space for the optimization problem. The patterns are projected out-of-focus to generate quasi-sinusoidal patterns, which can be used together with a phase-shifting algorithm to retrieve 3-D shape measurements. Simulations and experimental results show the feasibility of the proposed scheme.
Phase-shifting is an important technique for phase retrieval in interferometry and three dimensional profiling by fringe projection, which requires a series of intensity measurement with known phase-steps. Usual algorithms are based on the assumption that the phase-steps are evenly spaced. In practice, the phase steps are not evenly spaced or exactly determined or measurement, which leads to errors in the recovered phase. Based in this fact, some iterative algorithms have been proposed, e.g. Advanced Iterative Algorithm, which is a self-calibration algorithm for phase retrieval, however, it converges slowly. In this work, we propose an efficient-computational strategy for implementation of the AIA algorithm. The proposal consists of two steps: a method to reduce the number of iterations, and the use of high performance computing techniques to reduce the computation time at each iteration. The strategy is validated using synthetic and real data. Results show a drastic reduction in the number of iterations and increased performance.
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