Three-dimensional shape measurement with modal phase measuring deflectometry

Phase Measuring Deflectometry (PMD) is a powerful tool to measure the three-dimensional shape for freeform specular surfaces. In this work, a model based method is applied to PMD, called as Modal Phase Measuring Deflectometry (MPMD). The surface height and slopes are represented in mathematical models and updated by optimizing the model coefficients, in order to minimize the discrepancy between the reprojection in ray tracing and the actual measurement. The pose of the screen relative to the camera is pre-calibrated and then optimized together with the surface shape coefficients. Moreover, the correspondence residuals because of the discrepancies between the modal estimation and practical acquisition are analyzed. Slope residuals are calculated from these discrepancies. Zonal integration methods which are good at dealing with local variations are used to reconstruct the height residual for compensation. Simulations and experiments are conducted to demonstrate the feasibility of the proposed approach.

[1]  Peng Su,et al.  Instrument transfer function of slope measuring deflectometry systems. , 2015, Applied optics.

[2]  Markus C. Knauer,et al.  Phase measuring deflectometry: a new approach to measure specular free-form surfaces , 2004, SPIE Photonics Europe.

[3]  Huimin Yue,et al.  A carrier removal method in phase measuring deflectometry based on the analytical carrier phase description. , 2013, Optics express.

[4]  Christian Faber,et al.  Deflectometry challenges interferometry: the competition gets tougher! , 2012, Other Conferences.

[5]  Lei Huang,et al.  Model mismatch analysis and compensation for modal phase measuring deflectometry. , 2017, Optics express.

[6]  Peter J. de Groot,et al.  Principles of interference microscopy for the measurement of surface topography , 2015 .

[7]  Xiang Peng,et al.  A generalized temporal phase unwrapping algorithm for three-dimensional profilometry , 2008 .

[8]  Werner P. O. Juptner,et al.  High-resolution 3D shape measurement on specular surfaces by fringe reflection , 2004, SPIE Photonics Europe.

[9]  Feng Gao,et al.  Iterative optimization calibration method for stereo deflectometry. , 2015, Optics express.

[10]  W. Southwell.  Wave-front estimation from wave-front slope measurements , 1980 .

[11]  Yuankun Liu,et al.  Fast and accurate deflectometry with crossed fringes , 2014, 1404.5727.

[12]  A. Asundi,et al.  Dynamic three-dimensional sensing for specular surface with monoscopic fringe reflectometry. , 2011, Optics express.

[13]  Rainer Tutsch,et al.  Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces , 2005, SPIE Optics + Photonics.

[14]  Anand Asundi,et al.  Comparison of two-dimensional integration methods for shape reconstruction from gradient data , 2015 .

[15]  Mathieu Salzmann,et al.  Mirror Surface Reconstruction from a Single Image , 2015, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[16]  Yanqiu Li,et al.  Improving wavefront reconstruction accuracy by using integration equations with higher-order truncation errors in the Southwell geometry. , 2013, Journal of the Optical Society of America. A, Optics, image science, and vision.

[17]  X. Su,et al.  3D shape measurement of the aspheric mirror by advanced phase measuring deflectometry. , 2008, Optics express.

[18]  Christoph von Kopylow,et al.  Measuring deformations with deflectometry , 2014, Optics & Photonics - Optical Engineering + Applications.

[19]  A. Asundi,et al.  Phase invalidity identification framework with the temporal phase unwrapping method , 2011 .

[20]  Kenneth A. Goldberg,et al.  Modal wavefront reconstruction from its gradient , 2015 .

[21]  Guang-ming Dai,et al.  Modal wave-front reconstruction with Zernike polynomials and Karhunen–Loève functions , 1996 .

[22]  Philip C L Stephenson,et al.  Recurrence relations for the Cartesian derivatives of the Zernike polynomials. , 2014, Journal of the Optical Society of America. A, Optics, image science, and vision.

[23]  Jan Burke,et al.  Absolute optical surface measurement with deflectometry , 2012, Other Conferences.

[24]  Bo Gao,et al.  Modal phase measuring deflectometry. , 2016, Optics express.

[25]  Lirong Wang,et al.  Software configurable optical test system: a computerized reverse Hartmann test. , 2010, Applied optics.

[26]  Anand Asundi,et al.  Fast full-field out-of-plane deformation measurement using fringe reflectometry , 2012 .

[27]  Mourad Idir,et al.  Non-null full field X-ray mirror metrology using SCOTS: a reflection deflectometry approach. , 2012, Optics express.

[28]  James H. Burge,et al.  High-accuracy aspheric x-ray mirror metrology using Software Configurable Optical Test System/deflectometry , 2015 .

[29]  Svenja Ettl,et al.  Shape reconstruction from gradient data. , 2007, Applied optics.

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

[31]  Chao Zuo,et al.  Spline based least squares integration for two-dimensional shape or wavefront reconstruction , 2017 .

[32]  Xianyu Su,et al.  Flexible geometrical calibration for fringe-reflection 3D measurement. , 2012, Optics letters.

[33]  Christian Faber,et al.  Deflectometric Self-Calibration for arbitrary specular surfaces , 2011 .

[34]  Lei Huang,et al.  Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review , 2016 .

[35]  Osami Sasaki,et al.  Modal wavefront reconstruction based on Zernike polynomials for lateral shearing interferometry: comparisons of existing algorithms. , 2012, Applied optics.