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In this paper, a vision-based method is proposed for three-degree-of-freedom (3-DOF) planar position () measurement. This method uses a single camera to capture the image of a 2D periodic pattern and then uses the 2D discrete Fourier transform (2D DFT) method to estimate the phase of its fundamental frequency component for position measurement. To improve position measurement accuracy, the phase estimation error of 2D DFT is analyzed and a phase estimation method is proposed. Different simulations are done to verify the feasibility of this method and study the factors that influence the accuracy and precision of phase estimation. To demonstrate the performance of the proposed method for position measurement, a prototype encoder consisting of a black-and-white industrial camera with VGA resolution (480  ×  640 pixels) and an iPhone 4s has been developed. Experimental results show the peak-to-peak resolutions to be 3.5 nm in X axis, 8 nm in Y axis and 4 in axis. The corresponding RMS resolutions are 0.52 nm, 1.06 nm, and 0.60 respectively. [ABSTRACT FROM AUTHOR]

The phase-to-coordinate conversion is an important step for accurate 3-D shape measurement by use of structured light methods. We propose to use an absolute phase map in the Fourier transform method to achieve better accuracy in the phase-to-coordinate conversion. A cross-shaped marker is embedded in the fringe pattern that is projected onto the object. The position of the marker in the captured fringe image is detected and utilized to calculate the absolute phase map. For phase analysis of the fringe image, the marker is removed and the sinusoidal intensity distribution of the fringe pattern is restored before the forward and inverse Fourier transforms are applied. Experimental results of absolute phase retrieval and 3-D reconstruction are presented to show the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

This paper describes a novel phase error compensation method for reducing the measurement error caused by nonsinusoidal waveforms in phase-shifting methods. For 3-D shape measurement systems using commercial video projectors, the nonsinusoidal waveform of the projected fringe patterns as a result of the nonlinear gamma of projectors causes significant phase measurement error and therefore shape measurement error. The proposed phase error compensation method is based on our finding that the phase error due to the nonsinusoidal waveform depends only on the nonlinearity of the projector’s gamma. Therefore, if the projector’s gamma is calibrated and the phase error due to the nonlinearity of the gamma is calculated, a lookup table that stores the phase error can be constructed for error compensation. Our experimental results demonstrate that by using the proposed method, the measurement error can be reduced by 10 times. In addition to phase error compensation, a similar method is also proposed to correct the nonsinusoidality of the fringe patterns for the purpose of generating a more accurate flat image of the object for texture mapping. While not relevant to applications in metrology, texture mapping is important for applications in computer vision and computer graphics. [ABSTRACT FROM AUTHOR]