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Circular fringe projection profilometry (CFPP), as a branch of carrier fringe projection profilometry, has attracted research interest in recent years. 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. 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. In this paper, an improved CFFTP method based on a non-telecentric model is presented. 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 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 mathematical model and theoretical analysis are presented. Simulations and experiments have demonstrated the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

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]

The high-speed three-dimensional (3-D) shape measurement technique has become more and more popular recently, because of the strong demand for dynamic scene measurement. The single-shot nature of Fourier Transform Profilometry (FTP) makes it highly suitable for the 3-D shape measurement of dynamic scenes. However, due to the band-pass filter, FTP method has limitations for measuring objects with sharp edges, abrupt change or non-uniform reflectivity. In this paper, an improved Temporal Fourier Transform Profilometry (TFTP) algorithm combined with the 3-D phase unwrapping algorithm based on a reference plane is presented, and the measurement of one deformed fringe pattern producing a new 3-D shape of an isolated abrupt objects has been achieved. Improved TFTP method avoids band-pass filter in spatial domain and unwraps 3-D phase distribution along the temporal axis based on the reference plane. The high-frequency information of the measured object can be well preserved, and each pixel is processed separately. Experiments verify that our method can be well applied to a dynamic 3-D shape measurement with isolated, sharp edges or abrupt change. A high-speed and low-cost structured light pattern sequence projection has also been presented, it is capable of projection frequencies in the kHz level. Using the proposed 3-D shape measurement algorithm with the self-made mechanical projector, we demonstrated dynamic 3-D reconstruction with a rate of 297 Hz, which is mainly limited by the speed of the camera. [ABSTRACT FROM AUTHOR]