Phase error compensation based on Tree-Net using deep learning

Abstract The nonlinear effect in phase shifting profilometry (PSP) is an essential source of phase error in 3D measurement. In this paper, we propose a universal phase error compensation method with a three-to-three deep learning framework (Tree-Net). Perfectly meeting the phase error compensation requirements, Tree-Net can construct six-step phase-shifting patterns from three-step. As a result, this compact network of fringe-to-fringe transformation has excellent performance when coping with different PSP systems after only one training. Experimental results demonstrate that the phase error can be reduced by about 90% in three-step PSP, which verified the effectiveness, universality, and robustness of the proposed method.

[1]  C. R. Coggrave,et al.  High-speed surface profilometer based on a spatial light modulator and pipeline image processor , 1999 .

[2]  K. Iwata,et al.  Profile measurement taken with liquid-crystal gratings. , 1999, Applied optics.

[3]  Gunther Notni,et al.  Digital fringe projection in 3D shape measurement: an error analysis , 2003, SPIE Optical Metrology.

[4]  Michael Elad,et al.  Unified Single-Image and Video Super-Resolution via Denoising Algorithms , 2018, IEEE Transactions on Image Processing.

[5]  Thomas Brox,et al.  U-Net: Convolutional Networks for Biomedical Image Segmentation , 2015, MICCAI.

[6]  Song Zhang,et al.  Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector. , 2007, Applied optics.

[7]  Song Zhang,et al.  Phase error compensation for three-dimensional shape measurement with projector defocusing. , 2011, Applied optics.

[8]  C. Rathjen,et al.  Statistical properties of phase-shift algorithms , 1995 .

[9]  Anand Asundi,et al.  Temporal phase unwrapping using deep learning , 2019, Scientific Reports.

[10]  Song Zhang,et al.  High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method. , 2006, Optics express.

[11]  Xiaodong Xu,et al.  A fully stabilized low-phase-noise Kerr-lens mode-locked Yb:CYA laser frequency comb with an average power of 1.5 W , 2020, Applied Physics B.

[12]  Anand Asundi,et al.  Fringe pattern denoising based on deep learning , 2019, Optics Communications.

[13]  Qinghua Guo,et al.  Label enhanced and patch based deep learning for phase retrieval from single frame fringe pattern in fringe projection 3D measurement. , 2019, Optics express.

[14]  Trevor Darrell,et al.  Fully Convolutional Networks for Semantic Segmentation , 2017, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  Zhongwei Li,et al.  Gamma-distorted fringe image modeling and accurate gamma correction for fast phase measuring profilometry. , 2011, Optics letters.

[16]  Rihong Zhu,et al.  A fast and accurate gamma correction based on Fourier spectrum analysis for digital fringe projection profilometry , 2012 .

[17]  Alexei A. Efros,et al.  Image-to-Image Translation with Conditional Adversarial Networks , 2016, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[18]  Wei Xiong,et al.  Foreground-Aware Image Inpainting , 2019, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[19]  Liang Zhang,et al.  Fringe pattern analysis using deep learning , 2018, Advanced Photonics.

[20]  Zhenkun Lei,et al.  Multi-frequency inverse-phase fringe projection profilometry for nonlinear phase error compensation , 2015 .

[21]  Yi Zhang,et al.  Dynamic 3-D measurement based on fringe-to-fringe transformation using deep learning. , 2020, Optics express.

[22]  Mohammad Saadatseresht,et al.  Exponential fringe pattern projection approach to gamma-independent phase computation without calibration for gamma nonlinearity in 3D optical metrology. , 2017, Optics express.

[23]  Yajun Wang,et al.  Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques , 2014 .

[24]  Zhijian Liu,et al.  A multi-frequency inverse-phase error compensation method for projector nonlinear in 3D shape measurement , 2018 .

[25]  Dawei Tu,et al.  Generic nonsinusoidal fringe model and gamma calibration in phase measuring profilometry. , 2012, Journal of the Optical Society of America. A, Optics, image science, and vision.

[26]  Mumin Song,et al.  Overview of three-dimensional shape measurement using optical methods , 2000 .

[27]  Joe F. Chicharo,et al.  Elimination of ? Non-linear Luminance Effects for Digital Video Projection Phase Measuring Profilometers , 2008, 4th IEEE International Symposium on Electronic Design, Test and Applications (delta 2008).

[28]  Dacheng Tao,et al.  Perceptual Adversarial Networks for Image-to-Image Transformation , 2017, IEEE Transactions on Image Processing.

[29]  Song Zhang,et al.  Flexible 3-D shape measurement using projector defocusing. , 2009, Optics letters.

[30]  Zaixing He,et al.  Beyond phase error compensation: pixel mapping-based error correction for high-accuracy 3D surface measurement , 2020 .

[31]  Hongwei Guo,et al.  Correction of projector nonlinearity in multi-frequency phase-shifting fringe projection profilometry. , 2018, Optics express.

[32]  Xiang Peng,et al.  Phase-3D mapping method developed from back-projection stereovision model for fringe projection profilometry. , 2017, Optics express.

[33]  Xin Wang,et al.  Full-field phase error detection and compensation method for digital phase-shifting fringe projection profilometry , 2015 .

[34]  Xianyu Su,et al.  Automated phase-measuring profilometry using defocused projection of a Ronchi grating , 1992 .

[35]  Y Surrel,et al.  Design of algorithms for phase measurements by the use of phase stepping. , 1996, Applied optics.

[36]  Jian Sun,et al.  Identity Mappings in Deep Residual Networks , 2016, ECCV.

[37]  Xianyu Su,et al.  Flexible gamma calculation algorithm based on probability distribution function in digital fringe projection system. , 2019, Optics express.

[38]  Zhang Liang,et al.  High-speed high dynamic range 3D shape measurement based on deep learning , 2020 .

[39]  D. Lau,et al.  Gamma model and its analysis for phase measuring profilometry. , 2010, Journal of the Optical Society of America. A, Optics, image science, and vision.

[40]  Anand K. Asundi,et al.  Micro Fourier Transform Profilometry (μFTP): 3D shape measurement at 10, 000 frames per second , 2017, ArXiv.

[41]  Rama Krishna Sai Subrahmanyam Gorthi,et al.  PhaseNet: A Deep Convolutional Neural Network for Two-Dimensional Phase Unwrapping , 2019, IEEE Signal Processing Letters.

[42]  X. Su,et al.  3D shape from phase errors by using binary fringe with multi-step phase-shift technique , 2015 .

[43]  Xiang Peng,et al.  Flexible phase error compensation based on Hilbert transform in phase shifting profilometry. , 2015, Optics express.

[44]  Guohua Gu,et al.  Micro deep learning profilometry for high-speed 3D surface imaging , 2019, Optics and Lasers in Engineering.

[45]  Yajun Wang,et al.  Some recent advance on high-speed, high-resolution 3-D shape measurement using projector defocusing , 2010, 2010 International Symposium on Optomechatronic Technologies.

[46]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[47]  Song Zhang,et al.  Optimal pulse width modulation for sinusoidal fringe generation with projector defocusing. , 2010, Optics letters.

[48]  Qican Zhang,et al.  A flexible phase error compensation method based on probability distribution functions in phase measuring profilometry , 2020 .

[49]  Dung A. Nguyen,et al.  Some practical considerations in fringe projection profilometry , 2010 .

[50]  Dongliang Zheng,et al.  Absolute phase retrieval for defocused fringe projection three-dimensional measurement , 2014 .

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

[52]  Chao Zuo,et al.  Deep learning-based fringe modulation-enhancing method for accurate fringe projection profilometry. , 2020, Optics express.

[53]  Peisen S. Huang,et al.  Phase error compensation for a 3-D shape measurement system based on the phase-shifting method , 2005, SPIE Optics East.

[54]  Peisen S. Huang,et al.  Phase error compensation for a 3-D shape measurement system based on the phase-shifting method , 2007 .

[55]  Anand Asundi,et al.  Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry. , 2009, Optics letters.

[56]  William M. Wells,et al.  Medical Image Computing and Computer-Assisted Intervention — MICCAI’98 , 1998, Lecture Notes in Computer Science.

[57]  Zhaoyang Wang,et al.  Generic gamma correction for accuracy enhancement in fringe-projection profilometry. , 2010, Optics letters.

[58]  Fu-Pen Chiang,et al.  High-speed 3-D shape measurement based on digital fringe projection , 2003 .

[59]  Zhimin Zhao,et al.  Digital fringe image gamma modeling and new algorithm for phase error compensation , 2014 .

[60]  Jianlin Zhao,et al.  One-step robust deep learning phase unwrapping. , 2019, Optics express.