• Infrared and Laser Engineering
  • Vol. 51, Issue 4, 20210403 (2022)
Yanjun Fu1、2, Xiaoqi Cai1, Kejun Zhong1, Baiheng Ma2, and Zhanjun Yan2
Author Affiliations
  • 1Key Laboratory of Nondestructive Testing, Education Ministry of China, Nanchang Hangkong University, Nanchang 330063, China
  • 2Science and Technology on Electro-optic Control Laboratory, Luoyang 471023, China
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    DOI: 10.3788/IRLA20210403 Cite this Article
    Yanjun Fu, Xiaoqi Cai, Kejun Zhong, Baiheng Ma, Zhanjun Yan. Method for phase-height mapping calibration based on fringe projection profilometry[J]. Infrared and Laser Engineering, 2022, 51(4): 20210403 Copy Citation Text show less

    Abstract

    For a $ {\text{36}}{{\text{0}}^ \circ } $ 3D shape measurement based on fringe projection profilometry with turntable assistance, calibrating the system’s geometric parameters with a moving stage has the problems of complicated operation and inconvenient carrying. A novel flexible technique was presented to calibrate the monocular system of the panoramic 3D shape measurement based on a turntable consisting of a camera, projector, computer and turntable. The proposed algorithm mainly uses the turntable and marker point to complete the system geometric parameter calibration. For the complete calibration procedure, this method only requires the camera to capture the deformed fringe image of the reference plane, deformed fringe image on the calibration plane after rotation, and marker point image after rotation. In contrast with the traditional method, the proposed method is more convenient and time-saving. The new phase height mapping calibration method was used to reconstruct the calibration plane with a height of 10.000 mm, the result was 10.047 mm. Experiments have been performed to validate the performance of the proposed technique.
    $ h(u,v) = \frac{{L(u,v)\Delta \varphi (u,v)}}{{2\pi fd(u,v) + \Delta \varphi (u,v)}} $(1)

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    $ I(u,v) = a(u,v) + b(u,v)\cos (\varphi (u,v) + \delta ) $(2)

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    $ \begin{split} {I_n}(x,y) =& a(x,y) + b(x,y)\cos \Bigg[\varphi (x,y) +\\ & \dfrac{{2\pi (n - 1)}}{N}\Bigg](n = 1,2,3 \cdots N) \end{split} $(3)

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    $ \left\{ {\begin{array}{*{20}{c}} {{I_1} = a(x,y) + b(x,y)\cos [\varphi (x,y) + {\text{0}}]} \\ {{I_2} = a(x,y) + b(x,y)\cos \left[\varphi (x,y) + \dfrac{\pi }{2}\right]} \\ {{I_3} = a(x,y) + b(x,y)\cos [\varphi (x,y) + \pi ]} \\ {{I_4} = a(x,y) + b(x,y)\cos \left[\varphi (x,y) + \dfrac{{3\pi }}{2}\right]} \end{array}} \right. $(4)

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    $ \phi (x,y) = \arctan \left[ {\frac{{{I_4}(x,y) - {I_2}(x,y)}}{{{I_1}(x,y) - {I_3}(x,y)}}} \right] $(5)

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    $ \varphi (x,y) = \phi (x,y) + k(x,y) \cdot 2\pi $(6)

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    $ \frac{1}{{h(u,v)}} = \frac{1}{{L(u,v)}} + \frac{{2\pi fd(u,v)}}{{L(u,v)}} \cdot \frac{1}{{\varDelta \varphi (u,v)}} $(7)

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    $ \frac{1}{{h(u,v)}} = {C_1}(u,v) + {C_2}(u,v) \cdot \frac{1}{{\Delta \varphi (u,v)}} $(8)

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    $ \Delta {\varphi _i}(u,v) = {\varphi _i}(u,v) - {\varphi _0}(u,v)\begin{array}{*{20}{c}} {}&{i = 1,...,n} \end{array} $(9)

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    $ {h_i} = a\sin \theta + (i - 1)l\sin \theta (i = 1,2, \cdots ,n) $(10)

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    $ \frac{1}{{{h_i}(u,v)}} = {C_1}(u,v) + {C_2}(u,v) \cdot \frac{1}{{\Delta {\varphi _i}(u,v)}} $(11)

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    $ S = \sum\limits_{i = 1}^n {\left[ {\frac{1}{{L(u,v)}} + \frac{{2\pi fd(u,v)}}{{L(u,v)}} \cdot \frac{1}{{\Delta \varphi (u,v)}} - \frac{1}{{{h_i}(u,v)}}} \right]} $(12)

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    $ \sigma = \sqrt {\sum {{{\left[ {h(u,v) - A} \right]}^2}/m} } $(15)

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    Yanjun Fu, Xiaoqi Cai, Kejun Zhong, Baiheng Ma, Zhanjun Yan. Method for phase-height mapping calibration based on fringe projection profilometry[J]. Infrared and Laser Engineering, 2022, 51(4): 20210403
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