Abstract
The number-theoretical phase unwrapping method has recently been widely applied in fringe projection profilometry. But fringe order errors may occur due to noise or distortion, leading to errors in the unwrapped phase map, and eventually affecting the accuracy of the reconstructed object surface. In this paper, we propose a novel fringe order correction method based on the maximum likelihood principle. The direct cause of fringe order error is the deviation of an intermediate variable which in theory should be an integer, and the ground truth of the integer stays unchanged within a valid neighborhood. By modeling the calculated intermediate variable as an observed sample from the normal distribution of the unknown ground truth integer, we can determine a valid neighborhood relative to the observed pixel. Then the ground truth integer can be calculated by maximizing the likelihood function and then the fringe order error is corrected. The simulation results and experimental comparisons have verified the feasibility, robustness, and superiority of the proposed method in contrast with other fringe order correction methods.
Highlights
Fringe projection profilometry (FPP) is an important technique for three-dimensional measurement due to its accuracy and high efficiency [1]
The principle of the FPP technique is to project fringe patterns onto the object surface, calculate phase information of the images captured by the camera in another direction, and the height of the object surface is obtained by phase-height calibration [2]–[4]
Unlike the above fringe order correction methods, this paper proposes a method that focused on the intermediate variable ψ that determines the fringe orders
Summary
Fringe projection profilometry (FPP) is an important technique for three-dimensional measurement due to its accuracy and high efficiency [1]. The principle of the FPP technique is to project fringe patterns onto the object surface, calculate phase information of the images captured by the camera in another direction, and the height of the object surface is obtained by phase-height calibration [2]–[4]. Where xP, yP is the coordinate of the projected pixels, aP is the direct current component of the intensity, bP is the amplitude, λP0 is the spatial wavelength of the sinusoidal signal, n is the phase-shift index, and N is the total number of phase-shift steps After projecting these patterns onto the object surface, the phase signals are modulated, and the images captured by the camera can be expressed as: In (x, y) = A (x, y) + B (x, y) cos (x, y) − 2π n N (2). Since the phase is calculated pixel-by-pixel, the pixel coordinate index (x, y) is removed from equations in this paper
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