• Infrared and Laser Engineering
  • Vol. 49, Issue 6, 20200049 (2020)
Yuwei Wang1, Xiangcheng Chen2, and Yajun Wang3、*
Author Affiliations
  • 1安徽农业大学 工学院,安徽 合肥 230036
  • 2武汉理工大学 自动化学院,湖北 武汉 430070
  • 3武汉大学 测绘遥感信息工程国家重点实验室,湖北 武汉 430079
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    DOI: 10.3788/IRLA20200049 Cite this Article
    Yuwei Wang, Xiangcheng Chen, Yajun Wang. Modified dual-frequency geometric constraint fringe projection for 3D shape measurement[J]. Infrared and Laser Engineering, 2020, 49(6): 20200049 Copy Citation Text show less

    Abstract

    Dual-frequency fringe projection methods have been widely used in three-dimensional (3D) shape measurement, but the phase unwrapping is very sensitive to random noises. A modified dual-frequency geometric constraint fringe was presented. The robustness of phase unwrapping can be effectively enhanced by improving the frequency of low-frequency phase. During the 3D shape measurement, firstly, the five-step phase-shifting algorithm was used to extract two wrapped phases. Secondly, the low-frequency phase was unwrapped based on the geometric constraint method. Finally, the dual-frequency algorithm was used to unwrap the high-frequency phase, and then the 3D shape could be reconstructed. Both simulations and experiments demonstrate that the modified dual-frequency fringe is more robust and applicable than the traditional one.
    $\begin{split} & {I_n}(x,y) = A(x,y) + \\ &{B_{\rm{h}}}(x,y)\cos [{\phi _{\rm{h}}}(x,y) + 2{\text{π}} n/N] + \\ & {B_{\rm{l}}}(x,y)\cos [{\phi _{\rm{l}}}(x,y) + 4{\text{π}} n/N] \end{split} $(1)

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    ${\phi _{\rm{h}}}(x,y) = {\rm{arctan}}\left[ {\frac{{\sum\nolimits_{n = 1}^N {{I_n}\sin (2{\text{π}} n/N)} }}{{\sum\nolimits_{n = 1}^N {{I_n}\cos (2{\text{π}} n/N)} }}} \right]$(2)

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    ${\phi _{\rm{l}}}(x,y) = {\rm{arctan}}\left[ {\frac{{\sum\nolimits_{n = 1}^N {{I_n}\sin (4{\text{π}} n/N)} }}{{\sum\nolimits_{n = 1}^N {{I_n}\cos (4{\text{π}} n/N)} }}} \right]$(3)

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    ${K_{\rm{h}}}(x,y) = {\rm{round}}\left[ {\frac{{({f_{\rm{h}}}/{f_{\rm{l}}}) \times {\varPhi _{\rm{l}}} - {\phi _{\rm{h}}}}}{{2\pi }}} \right]$(4)

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    ${\varPhi _{\rm{h}}}(x,y) = {\phi _{\rm{h}}}(x,y) + 2{\text{π}} {K_{\rm{h}}}(x,y)$(5)

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    $K = {\rm{ceil}}\left( {\frac{{{\varPhi _{{\rm{min}}}} - \phi }}{{2\pi }}} \right)$(6)

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    Yuwei Wang, Xiangcheng Chen, Yajun Wang. Modified dual-frequency geometric constraint fringe projection for 3D shape measurement[J]. Infrared and Laser Engineering, 2020, 49(6): 20200049
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