Two-step phase shifting in fringe projection: modeling and analysis

This work proposes a two-step phase-shifting algorithm as an improvement of fringe projection profilometry. Considering the working process of fringe projection, the captured fringe image is formulated with two variables, i.e. surface reflectivity and phase value. And a phase shift of 3π/2 is introduced to get the two-step phase-shifting. After appropriate variable substitution, expressions of two fringe images can be transformed into two equations corresponding to a line and a circle respectively. With this circle-line model, the characteristic of solution and the phase error due to non-zero ambient light are analyzed. Then the approach of error compensation is proposed based on estimation of the real fringe contrast and non-linear least square optimization. The validity of the proposed approach is demonstrated with both simulations and experiments.

[1]  Xiaoyuan He,et al.  Two-step phase-shifting fringe projection profilometry: intensity derivative approach. , 2007, Applied optics.

[2]  Luc Van Gool,et al.  Fast 3D Scanning with Automatic Motion Compensation , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[3]  Sai Siva Gorthi,et al.  Fringe projection techniques: Whither we are? , 2010 .

[4]  Franck Marzani,et al.  Integration of 3D and multispectral data for cultural heritage applications: Survey and perspectives , 2013, Image Vis. Comput..

[5]  Meng Wang,et al.  Improved performance of multi-view fringe projection 3D microscopy. , 2017, Optics express.

[6]  Peter Kühmstedt,et al.  Array projection of aperiodic sinusoidal fringes for high-speed three-dimensional shape measurement , 2014 .

[7]  Dongliang Zheng,et al.  Phase-shifting profilometry combined with Gray-code patterns projection: unwrapping error removal by an adaptive median filter. , 2017, Optics express.

[8]  X. Su,et al.  High-speed optical measurement for the drumhead vibration. , 2005, Optics express.

[9]  L Z Cai,et al.  Wavefront reconstruction and three-dimensional shape measurement by two-step dc-term-suppressed phase-shifted intensities. , 2009, Optics letters.

[10]  Zonghua Zhang,et al.  Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques , 2012 .

[11]  Ricardo Legarda-Saenz,et al.  Color-fringe pattern profilometry using a generalized phase-shifting algorithm. , 2015, Applied optics.

[12]  Jae-Sang Hyun,et al.  High-speed and high-accuracy 3D surface measurement using a mechanical projector. , 2018, Optics express.

[13]  Qican Zhang,et al.  Dynamic 3-D shape measurement method: A review , 2010 .

[14]  Huai Min Shang,et al.  Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting. , 2003, Applied optics.

[15]  Feipeng Da,et al.  Novel 3D measurement system based on speckle and fringe pattern projection. , 2016, Optics express.

[16]  Hui Li,et al.  Real-time microscopic 3D shape measurement based on optimized pulse-width-modulation binary fringe projection , 2017 .

[17]  Tak-Wai Hui,et al.  3-D Measurement of Solder Paste Using Two-Step Phase Shift Profilometry , 2008, IEEE Transactions on Electronics Packaging Manufacturing.

[18]  Meng Wang,et al.  Fringe projection 3D microscopy with the general imaging model. , 2015, Optics express.

[19]  Jingang Zhong,et al.  Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry. , 2004, Applied optics.

[20]  Xiang Peng,et al.  Dynamic 3D imaging based on acousto-optic heterodyne fringe interferometry. , 2014, Optics letters.

[21]  Song Zhang.  Recent progresses on real-time 3D shape measurement using digital fringe projection techniques , 2010 .

[22]  Rainer Tutsch,et al.  Optical three-dimensional metrology with structured illumination , 2011 .