• Chinese Optics Letters
  • Vol. 16, Issue 3, 031201 (2018)
Xiangjun Dai1、2、*, Tianyu Yuan1, Hanyang Jiang2, Xinxing Shao2, Meiling Dai2, Hai Yun1, Fujun Yang2, and Xiaoyuan He2
Author Affiliations
  • 1School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255049, China
  • 2Department of Engineering Mechanics, Southeast University, Nanjing 210096, China
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    DOI: 10.3788/COL201816.031201 Cite this Article Set citation alerts
    Xiangjun Dai, Tianyu Yuan, Hanyang Jiang, Xinxing Shao, Meiling Dai, Hai Yun, Fujun Yang, Xiaoyuan He. Multi-frequency lateral shear interferometer system for simultaneous measurement of thickness and three-dimensional shape[J]. Chinese Optics Letters, 2018, 16(3): 031201 Copy Citation Text show less

    Abstract

    This Letter demonstrates a novel lateral shear interferometer system for simultaneous measurement of three-dimensional (3D) shape and thickness of transparent objects. Multi-frequency fringe patterns can be created by tilting mirrors at different inclination angles. With a single camera, the multi-frequency fringes are recorded in one image. The phase-shift of the fringes can be generated synchronously only by moving a plane-parallel plate along an in-plane parallel direction. According to the feature of transparent materials, the thickness and 3D shape can be reconstructed simultaneously based on the relationship between the in-plane displacement and their characteristics. The experiment was conducted on a thin transparent film subjected to a shearing force, which verifies the feasibility of the proposed system.
    f=mS,(1)

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    S=t·sin2in2sin2i,(2)

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    ϕku(x,y)=ϕkw(x,y)+2π·INT[(fk/fk1)·ϕk1u(x,y)ϕkw(x,y)2π],k=2,3,(3)

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    ϕw=arctan[(I1I4)+(I2I3)][3(I2I3)(I1I4)]|(I2+I3)(I1+I4)|,(4)

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    δx1=B1·cos[α1+(π2α1+Δθi1)/n1]·cosΔθi1cos[(π2α1+Δθi1)/n1]·sinα1,(5)

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    δx2=B1·cos[α2+(π2α2+Δθi1)/n1]·cosΔθi1cos[(π2α2+Δθi1)/n1]·sinα2,(6)

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    Δθi1=arctan[4.26×(0.9X120.810.92×(X12)20.96×X12+0.44)],(7)

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    B1=δx2·cos[(π2α2+Δθi1)/n1]·sinα2cos[α2+(π2α2+Δθi1)/n1]·cosΔθi1.(8)

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    Hr=12+B1B+12·(tanπ4+Δθi11.517·sin2Δθi1cos2Δθi1).(9)

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    Xiangjun Dai, Tianyu Yuan, Hanyang Jiang, Xinxing Shao, Meiling Dai, Hai Yun, Fujun Yang, Xiaoyuan He. Multi-frequency lateral shear interferometer system for simultaneous measurement of thickness and three-dimensional shape[J]. Chinese Optics Letters, 2018, 16(3): 031201
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