Phase error elimination considering gamma nonlinearity, system vibration, and noise for fringe projection profilometry

Abstract

Abstract. Fringe projection profilometry (FPP) using a digital video projector is widely used for three-dimensional shape measurement. However, the gamma nonlinearity, system vibration, and noise cause the captured fringe patterns to be nonsinusoidal waveforms and have a grayscale deflection from their true value. This leads to an additional phase measurement error for a general phase-shifting algorithm. Based on the theoretical analysis, we propose a method to eliminate the phase error considering two factors. In this method, four-step phaseshifting is done four times with an initial phase offset of 22.5 deg and the average of these four phase maps precisely results in the real phase. As a result, phase error caused by gamma nonlinearity can be effectively suppressed. In addition, every image in phase shifting is replaced by the average of 20 fringe images continuously captured at the same state to avoid the phase error caused by system vibration and noise. Experimental results show that this method is effective in eliminating the phase error in practical phase-shifting FPP. In general, more than 90% of the phase error can be reduced.

Machine learning to empower electrohydrodynamic processing

“…The 'gold standard' in ML algorithms for images is CNN, which is a network-based ML, but compared with neural networks with similar sized layers, CNNs have fewer connections and parameters, and thus are easier to train [154]. Moreover, CNNs are able to capture the nonlinearity in datasets; non-linearity is commonly found in images, such as photographs and electron micrographs, because of a number of elements [155][156][157][158][159][160]. Two studies have demonstrated the feasibility of utilising CNN for EHD process monitoring.…”

Design of a projection moiré system based on a nonuniform grating projection

“…Phase extraction based on such fringe patterns has a nonlinear error, which requires a phase error elimination algorithm. [6][7][8][9][10][11] At present, the measurement resolution of fringe projection profilometry can generally reach 1/10,000 of the measurement field of view. 12,13 In the projection moiré method, a two-stage imaging and receiving system was proposed.…”

Vibration Detection and Motion Compensation for Multi-Frequency Phase-Shifting-Based 3D Sensors

“…Vibration is inevitable and sporadic in factories, especially forging factories, and may cause fatal errors to the optical systems. For an inspection system using phase-shifting profilometry (PSP), vibration may cause mistakes or losses in the reconstructed 3D data [2], which will affect the inspection results and confuse the following procedures. This kind of vibration is hard to prevent or predict, and the only economical and feasible solution is to detect if a vibration occurs and then try to compensate the motion error caused by the vibration.…”