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To determine the shape of a complex object with vertical measurement mode and higher accuracy, a novel modulation measuring profilometry realizing auto-synchronous phase shifting and vertical scanning is proposed. Coaxial optical system for projection and observation instead of triangulation system is adopted to avoid shadow and occlusion. In the projecting system, sinusoidal grating is perpendicular to optical axis. For moving the grating along a direction at a certain angle to optical axis, 1D precision translation platform is applied to achieve purposes of both phase-shifting and vertical scanning. A series of fringe patterns with different modulation variations are captured by a CCD camera while scanning. The profile of the tested object can be reconstructed by the relationship between the height values and the modulation distributions. Unlike the previous method based on Fourier transform for 2D fringe pattern, the modulation maps are calculated from the intensity curve formed by the points with definite pixel coordinates in the captured fringe patterns. The paper gives the principle of the proposed method, the set-up of measurement system and the method for system calibration. Computer simulation and experiment results proved its feasibility.

A two-dimensional continuous wavelet transform employing a real mother wavelet is applied to phase analysis of spatial carrier fringe patterns. In this method, a Hilbert transform is first performed on a carrier fringe pattern to get an analytic signal. Then a two-dimensional wavelet transform is calculated for the signal that is yielded by the first transform. Finally, the height-demodulated phase information can be gotten from the wavelet transform coefficients at the wavelet ridge position. The performance of the proposed method has been evaluated by using computer-generated and real fringe patterns. The result performed better than that of one-dimensional real wavelet transform algorithms in the area with phase discontinuous points and high phase variation, especially when there is much noise in the fringe patterns. Computer simulations and experiments verified the validity of the proposed method.

Abstract: In this paper, we proposed a new algorithm, the Sparse AUC maximizing support vector machine, to get more sparse features and higher AUC than standard SVM. By applying p-norm where 0 < p < 1 to the weight w of the separating hyperplane (w·x) + b = 0, the new algorithm can delete less important features corresponding to smaller |w|. Besides, by applying the AUC maximizing objective function, the algorithm can get higher AUC which make the decision function have higher prediction ability. Experiments demonstrate the new algorithm''s effectiveness. Some contributions as follows: (1) the algorithm optimizes AUC instead of accuracy; (2) incorporating feature selection into the classification process; (3) conduct experiments to demonstrate the performance. [Copyright &y& Elsevier]

Crossed-grating phase-shifting profilometry (CGPSP) has great utility in three-dimensional shape measurement due to its ability to acquire horizontal and vertical phase maps in a single measurement. However, CGPSP is extremely sensitive to the non-linearity effect of a digital fringe projection system, which is not studied in depth yet. In this paper, a mathematical model is established to analyze the phase error caused by the non-linearity effect. Subsequently, two methods used to eliminate the non-linearity error are discussed in detail. To be specific, a double five-step algorithm based on the mathematical model is proposed to passively suppress the second non-linearity. Furthermore, a precoding gamma correction method based on probability distribution function is introduced to actively attenuate the non-linearity of the captured crossed fringe. The comparison results show that the active gamma correction method requires less fringe patterns and can more effectively reduce the non-linearity error compared with the passive method. Finally, employing CGPSP with gamma correction, a faster and reliable inverse pattern projection is realized with less fringe patterns. [ABSTRACT FROM AUTHOR]

Phase unwrapping algorithm plays very important role in noncontract optical profilometry, beacuse the phase map acquired derectly is limited from π to −π, which is called wrapped phase. It must be unwrapped to retrieve the nature phase employing suitable phase unwrapping algorithm. In this paper, we review a phase unwrapping algorithm based on the reliability-guided parameter map. In this algorithm we select a parameter or group of parameters to identify the reliability of the phase data or the direction of phase unwrapping. The path of phase unwrapping is guided according to the parameter map. It means that the pixel with higher parameter value in the parameter map will be phase unwrapped earlier. The intensity modulation and the spatial frequency of the fringe pattern are usually used as important parameters characterizing the reliability. Other parameters, such as the phase difference between neighboring pixels, the signal-to-noise ratio, or some band elimination filter center around defect region assigned by user, could be selected as the optimized parameter for phase unwrapping. Sometimes we can combine two or three parameters to produce a more optimized parameter map for phase unwrapping. The advantage of this approach is that the path of phase unwrapping is always along the direction from the pixel with higher reliability value to the pixel with low reliability value. Therefore, in the worse case the error is limited, if there is any, to local minimum areas. [Copyright &y& Elsevier]

• A universal two-coefficient phase error model is established for the inaccuracy of phase shift, which is suitable for any multi-step phase-shifting algorithm. • The nonlinear error compensation can be realized by an iterative process after finding 2 error coefficients without calculating the phase shift error, so it has high universality. • After obtained the PDF curve of the measured fringes, a correlation process is used to find the most similar one from the pre-simulated PDF curves, then the corresponding error coefficients of the simulated curve are that of the real curve. • A two-coefficient model will highly reduce the computation complexity. • Phase-error compensation without complicated phase unwrapping process. In non-digital projection systems, the inaccuracy of phase shifts is one of the most important nonlinear errors. In this paper, an efficient and universal compensation algorithm is proposed, which does not need to find the exact phase shift amounts, but to compensate the periodical errors by a universal two-coefficient error model. With this model, only two error coefficients should to be searched for any multi-step phase shift algorithm. To find the error coefficients, a correlation process and a tool known as the probability density function (PDF) are used. First, a set of pre-simulated PDF curves are generated with the different error coefficients. Second, a practical PDF curve from captured fringes is calculated. Finally, the correlation process is carried out to locate the most similar simulated PDF curve, whose error coefficients are the practical ones. In this paper, we demonstrate the compensation for three, four and five-step phase-shifting algorithms separately. Experimental results show that this method has high universality, and can meet the requirements of rapid and high accuracy measurement. [ABSTRACT FROM AUTHOR]

Abstract: A coordinate measuring method is presented, which is specially devised to perform the measurement of coordinates with projected fringe techniques of projectors in three dimensions. The system is composed of two parts: one is a target which can move freely in three dimensions, and the other is a stationary two-dimensional array of photodetectors. The mini-projector is tied to the target, and the projected fringe is monitored by the photodetectors. The phase of the photodetectors can be precisely measured with the phase-shifting algorithm, so that, the xyz location of the target can be determined with the geometric model of multilateration using the method of optimization. In this paper, the measuring principle, iterative method, computer simulation and preliminary results are given. The phase-shifting technique has the advantages of high accuracy and noise endurance. The method will provide the basis for follow-up iterative optimization calculation. The experimental results prove that the proposed coordinate measuring method is of high precision. [Copyright &y& Elsevier]