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The lateral shift of the fringe pattern caused by the measured object will be along the X-axis direction when a circular pattern is projected onto the object and captured by the camera. ![]() Several planes R i( i = 1, 2,…, N) are drawn to exhibit out-of-plane height. The plane in which two optical axes lie is parallel to the X– Z plane. The optical axis of the projector and the camera intersects the point O r on the reference plane. On the top-left of this figure, an orthogonal co-ordinate system is determined for exhibiting spatial directions, where d and l are structural parameters of the measurement system. The schematic diagram of the geometric model of CFFTP is the same as that of traditional FPP based on the triangulation principle, as shown in Figure 1. However, a series of fringe patterns with different frequencies are needed. Certainly, temporal phase unwrapping methods such as multi-frequency and multi-wavelength approaches can be used to obtain the absolute phase by determining 2π discontinuous locations. The marker provides a reference for unwrapping the phase. For eliminating this ambiguity, a common method is embedding a marker point into fringe patterns or adding a marker on the surface of the object. However, one disadvantage of linear fringe projection is that the unwrapped phase map obtained by spatial unwrapping algorithms has 2π ambiguity because the value of the continuous phase depends on the unwrapping starting point. In traditional Fourier transform profilometry (FTP), the popularly projected fringe pattern is a sinusoidal straight or oblique fringe for the ease of extraction of the fundamental spectrum lobe carrying surface information of the measured object. įourier fringe analysis is one of the most popular methods aimed at calculating the phase value from a single spatial carrier pattern or at most two spatial carrier patterns through Fourier transform, filtering operation and inverse Fourier transform. The comparative analysis of different carrier fringe pattern techniques has been given in references. To reconstruct phase information from these patterns, algorithms based on phase shifting, Fourier transform, wavelet transform, or windowed Fourier transform have been developed. have been used in fringe projection profilometry as well. ![]() Saw-tooth fringe, triangular fringe, hexagonal fringe, circular fringe, etc. The straight fringe and oblique fringe are popular. The height of the measured object will change the phase distribution of the fringe, which can be obtained by different demodulation algorithms based on the number of fringes. In a fringe projection system based on a triangular configuration frame, the structured fringe patterns are projected onto the object by a projector, then the distorted images will be captured by a camera from another view angle. Simulations and experiments have demonstrated the effectiveness of the proposed method.įringe projection profilometry (FPP), as a common active optical three-dimensional (3D) measurement technology, has advantages of high-precision, non-contact, and full-field measurement. The mathematical model and theoretical analysis are presented. In addition, Gerchberg iteration is employed to eliminate phase error of the region close to the circular center, and the plane calibration technique is used to eliminate system error by establishing a displacement-to-height look-up table. ![]() The calculation of displacement amount is performed by solving a linear equation instead of a quadratic equation after introducing an extra projection of circular fringe with circular center translation. In this paper, an improved CFFTP method based on a non-telecentric model is presented. However, the existing CFFTP method needs to solve a quadratic equation to calculate the pixel displacement amount related to the height of the object, in which the root-seeking process may get into trouble due to the phase error and the non-uniform period of reference fringe. Circular fringe Fourier transform profilometry (CFFTP) has been used to measure out-of-plane objects quickly because the absolute phase can be obtained by employing fewer fringes. ![]() Circular fringe projection profilometry (CFPP), as a branch of carrier fringe projection profilometry, has attracted research interest in recent years.
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