• Photonics Research
  • Vol. 10, Issue 5, 1210 (2022)
Zheng Sun1、†, Minghui Duan1、†, Yabing Zheng, Yi Jin*, Xin Fan, and Jinjin Zheng
Author Affiliations
  • Department of Precision Machinery and Precision Instruments, University of Science and Technology of China, Hefei 230022, China
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    DOI: 10.1364/PRJ.451818 Cite this Article Set citation alerts
    Zheng Sun, Minghui Duan, Yabing Zheng, Yi Jin, Xin Fan, Jinjin Zheng. Intensity diffusion: a concealed cause of fringe distortion in fringe projection profilometry[J]. Photonics Research, 2022, 10(5): 1210 Copy Citation Text show less

    Abstract

    Fringe projection profilometry (FPP) is widely used in optical three-dimensional (3D) measurements because of its high stability. In FPP, fringe distortion is an inevitable and highly complex systematic error that significantly reduces the 3D measurement accuracy. At this point, the existing causes of fringe distortion represented by gamma distortion, high-order harmonics, and image saturation have been effectively analyzed and compensated to restore high-quality fringe images. In this paper, we innovatively reveal a concealed cause of fringe distortion, i.e., intensity diffusion across pixels, which is induced by photocarrier diffusion between photodiodes. To the best of our knowledge, intensity diffusion has not been studied in the field of fringe restoration. Based on the motion of photocarrier diffusion, we theoretically analyze the mechanism of how the intensity diffusion affects FPP. Subsequently, an intensity diffusion model is established for quantifying the diffused intensity in each pixel, and an intensity diffusion correction algorithm is presented to remove the diffused intensity from the fringe images and correct the fringe distortion. Experiments demonstrate the impact of intensity diffusion on FPP, and the 3D measurement results prove the effectiveness of the proposed methods on improving the 3D measurement accuracy by correcting the fringe distortion.
    Id=c·Is,

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    Ip=A+Bcosϕp,

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    Ir=Gr(ηIp+Ia),

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    Ihp=Ilp+2Bcosϕhp.

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    Ild=crIhp=cr[G(ηIlp+Ia)+2Bcosϕhp].

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    Ic=Ir+Id+In,

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    SNRl=rIlprIa+Ild+In=1cosϕhpc(1+cosϕhp)+(1+c)rIa+InrI.

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    SNRl(I)=2csin2ϕhp[(1+c)Ia+Inr][c(1+cosϕhp)I+(1+c)Ia+Inr]3.

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    SNRl0=rIlprIa+In=(1cosϕhp)IIa+Inr.

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    f(I)=IldIlc=c[Ia+(1+cosϕhp)I](1+c)Ia+[(1+c)(1c)cosϕhp]I+Inr.

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    f(I)=2Iacosϕhp+(1+cosϕhp)Inr{(1+c)Ia+[(1+c)(1c)cosϕhp]I+Inr}2.

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    SNRl(c)=[sin2ϕhpI2+(1cosϕhp)Ia][c(1+cosϕhp)I+(1+c)Ia+Inr]2,

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    SNRl(c)=SNRl(c)·2(1+c)+(1+cosϕhp)I+Ia[c(1+cosϕhp)I+(1+c)Ia+Inr]2,

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    Ip=I[1+cos(ϕp+ϕ0)],

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    ϕc=ϕϕ0+ΔϕFTP,

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    ΔϕFTP=arctan[sin(ϕp+2ϕ0ϕ)cos(ϕp+2ϕ0ϕ)+A1r·SNRIp],

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    Inp=I[1+cos(ϕpδn)],n=1,2,,N,

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    ϕc=arctann=1NIncsinδnn=1NInccosδn=ϕp+ΔϕPSA,

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    ΔϕPSA=2n=1Nsin(δnϕp)·r[1+cos(ϕpδn)]N·SNRn,

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    Φ=ϕwp+2πk,

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    kPCU=Round[f(ϕsp+π)2π+fΔϕs2π],

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    kMFU=Round(fflϕlpϕwpp2π+fflΔϕlΔϕwp2π),

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    {ETPCU=fΔϕs2πETMFU=fflΔϕlΔϕwp2π.

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    ΔET=ETPCUETMFU=fΔϕsfflΔϕl+Δϕwp2π.

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    c(x,y)=c0μ[D(x,y)D0],

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    D(x,y)=D0(xx0)2+(yy0)2,

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    {xp=T×ϕV(xc,yc)/2πyp=T×ϕH(xc,yc)/2π,

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    Id(x,y)=m=1M{c0μ[D((xm,ym)D0)]}Ims(xm,ym),

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    Id(x,y)=m=1Mc(xm,ym)Ir(xm,ym).

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    Zheng Sun, Minghui Duan, Yabing Zheng, Yi Jin, Xin Fan, Jinjin Zheng. Intensity diffusion: a concealed cause of fringe distortion in fringe projection profilometry[J]. Photonics Research, 2022, 10(5): 1210
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