Abstract
For temporal phase unwrapping in phase measuring profilometry, it has recently been reported that two phases with co-prime frequencies can be absolutely unwrapped using a look-up table; however, frequency selection and table construction has been performed manually without optimization. In this paper, a universal phase unwrapping method is proposed to unwrap phase flexibly and automatically by using geometric analysis, and thus we can programmatically build a one-dimensional or two-dimensional look-up table for arbitrary two co-prime frequencies to correctly unwrap phases in real time. Moreover, a phase error model related to the defocus effect is derived to figure out an optimal reference frequency co-prime to the principal frequency. Experimental results verify the correctness and computational efficiency of the proposed method.
Highlights
Phase measuring profilometry (PMP) is high speed and high accuracy three-dimensional (3D) scanning technique where high, spatial-frequency, sinusoidal patterns are employed to suppress errors caused by sensor noise as well as projector/camera nonlinearities, but in order to avoid ambiguities in phase reconstruction, high-frequency phases must be correctly unwrapped
In this paper first motivated by Ding et al [21, 22] for two co-prime frequencies, we propose to unwrap phases in real time through a one-dimensional (1-D) look-up tables (LUT) that is derived from a geometric model bridging the orders of wrapped phases
The resolution of projector and camera are set as 800 × 600 and 640 × 480, respectively, and the camera works in grayscale mode
Summary
Phase measuring profilometry (PMP) is high speed and high accuracy three-dimensional (3D) scanning technique where high, spatial-frequency, sinusoidal patterns are employed to suppress errors caused by sensor noise as well as projector/camera nonlinearities, but in order to avoid ambiguities in phase reconstruction, high-frequency phases must be correctly unwrapped. Compared with spatial phase unwrapping [1,2,3,4], temporal phase unwrapping [5,6,7,8] enjoys robust performance without suffering from phase discontinuities, phase jumps, and other distortions [9], but traditional temporal phase unwrapping methods [5, 7, 10, 11] typically need multi-frequency patterns, starting from unit-frequency This procedure is very robust, the added patterns increase the total scan time as well as require more computation. We suppose the size of the PSF is 5 × 5 for facilitating our analysis
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