• Chinese Optics Letters
  • Vol. 16, Issue 11, 111202 (2018)
Pengfei Li, Ping Cai*, Jun Long, Chiyue Liu, and Hao Yan
Author Affiliations
  • Department of Instrument, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
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    DOI: 10.3788/COL201816.111202 Cite this Article Set citation alerts
    Pengfei Li, Ping Cai, Jun Long, Chiyue Liu, Hao Yan. Measurement of out-of-plane deformation of curved objects with digital speckle pattern interferometry[J]. Chinese Optics Letters, 2018, 16(11): 111202 Copy Citation Text show less

    Abstract

    Digital speckle pattern interferometry (DSPI) is a high-precision deformation measurement technique for planar objects. However, for curved objects, the three-dimensional (3D) shape information is needed in order to obtain correct deformation measurement in DSPI. Thus, combined shape and deformation measurement techniques of DSPI have been proposed. However, the current techniques are either complex in setup or complicated in operation. Furthermore, the operations of some techniques are too slow for real-time measurement. In this work, we propose a DSPI technique for both 3D shape and out-of-plane deformation measurement. Compared with current techniques, the proposed technique is simple in both setup and operation and is capable of fast deformation measurement. Theoretical analysis and experiments are performed. For a cylinder surface with an arch height of 9 mm, the error of out-of-plane deformation measurement is less than 0.15 μm. The effectiveness of the proposed scheme is verified.
    ΔL=MP+MH=d(1+cosθ),(1)

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    ΔØ=2πΔ/λ.(2)

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    d=λ2πΔØ1+cosθ,(3)

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    dn=λ2πΔØcosε(1+cosθ),(4)

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    i(x,y)=a(x,y)+b(x,y)cos[δ(x,y)+2πfxx+2πfyy],(5)

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    i(x,y)=a(x,y)+c(x,y)[exp(2πfxxi)+exp(2πfyyi)]+c*(x,y)[exp(2πfxi)+exp(2πfyyi)],(6)

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    c(x,y)=12b(x,y)exp[δ(x,y)i],(7)

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    I(ffx,ffy)=A(ffx,ffy)+C*(ffxfx,ffyfy)+C*(ffx+fx,ffy+fy),(8)

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    Ø(x,y)=Im[c(x,y)]Re[c(x,y)].(9)

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    ΔØ(x,y)=Im[c1(x,y)×c2*(x,y)]Re[c1(x,y)×c2*(x,y)],(10)

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    ΔØ=2πΔLλ=2π(MIMI)λ.(11)

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    ΔL=(xx1)2+(yy1)2+(zz1)2x2+y2+z2xx1+yy1+zz1x2+y2+z2.(12)

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    x1=xΔθ,z1=zΔθ.(13)

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    ΔL=(zsinθ+xcosθ)Δθ,(14)

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    sinθ=xx2+y2+z2,cosθ=zx2+y2+z2.(15)

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    z=ΔØλ2πsinθΔθxtanθΔθ.(16)

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    F(x,y,z)=ΔØλ2πsinθΔθxtanθΔθz=0.(17)

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    ε=arccosn0,nop.(18)

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    sinθ(xm,yn)=x0+mu(x0+mu)2+(y0+nu)2+z02,cosθ(xm,yn)=z0(x0+mu)2+(y0+nu)2+z02,(19)

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    e=ΔØλ2π[sinθ0sinθ(xm,yn)]Δθx[tanθ0sinθ(xm,yn)]Δθ.(20)

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    Pengfei Li, Ping Cai, Jun Long, Chiyue Liu, Hao Yan. Measurement of out-of-plane deformation of curved objects with digital speckle pattern interferometry[J]. Chinese Optics Letters, 2018, 16(11): 111202
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