Analysis and reduction of the phase error caused by the non-impulse system psf in fringe projection profilometry

The fringe projection profilometry (FPP) has obtained increasing popularity in the field of industrial automation, inverse engineering and graphics. Recent literature reveals that the non-ideal system point spread function (PSF) in FPP will cause phase error in the area around the discontinuous edge. Existing error reduction methods need to detect the location of all the edges accurately first, which are hard to accomplish when the camera is defocused. Meanwhile, the corrected data in the error area relies heavily on the data in its nearest unaffected area, which makes the corrected data unreliable. We prove that the non-ideal system PSF will also induce phase error in the area of surface details, and this is a problem seldom discussed in FPP. In this work, the relationships between the PSF-induced phase error and system parameters are deduced mathematically and numerically. Additionally, a deconvolution-based method is proposed to reduce the PSF-induced phase error in this paper. The proposed method can overcome the shortcomings of the existing approaches. Both simulation and experiment results show that our proposed method can reduce the Root Mean Square phase/height error by up to 4 times, and can also improve the measured 3D details significantly.