Abstract

A method of linearly coded profilometry is proposed. It uses linear-structure light with isosceles triangle teeth to code the object being measured and a phase-shifting technique to decode the profile. For reducing the effect of noise more than three equally spaced samples are used, and, according to the least-squares method, the general formulas of the decoded phase are given. The experimental results of a model of a head are shown.

© 1999 Optical Society of America

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References

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  1. G.-C. Jin, S. Tang, “Automated moiré contouring of diffuse surfaces,” Opt. Eng. 28, 1211–1215 (1989).
    [CrossRef]
  2. M. Takeda, K. Mutch, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1989).
    [CrossRef]
  3. V. Srinivasan, H. C. Liu, M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23, 3105–3108 (1984).
    [CrossRef] [PubMed]
  4. Q. Fang, S. Zheng, “Linearly coded profilometry,” Appl. Opt. 36, 2401–2407 (1997).
    [CrossRef] [PubMed]
  5. Q. Fang, “Linearly coded profilometry with a coding light that has isosceles triangle teeth: even-number-sample decoding method,” Appl. Opt. 36, 1615–1620 (1997).
    [CrossRef] [PubMed]

1997 (2)

1989 (2)

G.-C. Jin, S. Tang, “Automated moiré contouring of diffuse surfaces,” Opt. Eng. 28, 1211–1215 (1989).
[CrossRef]

M. Takeda, K. Mutch, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1989).
[CrossRef]

1984 (1)

Fang, Q.

Halioua, M.

Jin, G.-C.

G.-C. Jin, S. Tang, “Automated moiré contouring of diffuse surfaces,” Opt. Eng. 28, 1211–1215 (1989).
[CrossRef]

Liu, H. C.

Mutch, K.

Srinivasan, V.

Takeda, M.

Tang, S.

G.-C. Jin, S. Tang, “Automated moiré contouring of diffuse surfaces,” Opt. Eng. 28, 1211–1215 (1989).
[CrossRef]

Zheng, S.

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Figures (5)

Fig. 1
Fig. 1

Linear-structure light: (a) light with isosceles triangle teeth and (b) light with a sawtooth edge.

Fig. 2
Fig. 2

Distribution of I n : (a) case 1 for [ϕ(x, y)] m < T/2 and (b) case 2 for [ϕ(x, y)] m > T/2.

Fig. 3
Fig. 3

Schematic sequential diagram of the measuring system.

Fig. 4
Fig. 4

(a) Intensity distribution on the reference plane. (b) The deformed pattern on the object.

Fig. 5
Fig. 5

Three-dimensional plot of the results of the measurement of the model of a head.

Equations (13)

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Ix, y=A+Bxm0xm<T/2A+BT-xmT/2xm<T,
Ix, y=Rx, yAx, y+Bx, yϕx, ym0ϕx, ym<T/2Rx, y{Ax, y+Bx, yT-ϕx, ym}T/2ϕx, ym<T,
Ix, y=Mx, yx0x, y+ϕx, y+δm0ϕx, y+δm<T/2Mx, yx0x, y+T-ϕx, y+δmT/2ϕx, y+δm<T,
In=Mx0+ϕ+nN T0ni-1Mx0+T-ϕ-nN Tinj-1Mx0+ϕ+nN T-TjnN-1,
E=n=0i-1In-Mx0+ϕ+nN T2+n=ij-1In-Mx0+T-ϕ-nN T2+n=jN-1In-Mx0+ϕ+nN T-T2.
EM=Eϕ=Ex0=0,
n=0i-1In-Mx0+ϕ+nN Tx0+ϕ+nN T+n=ij-1In-Mx0+T-ϕ-nN Tx0+T-ϕ-nN T+n=jN-1In-Mx0+ϕ+nN T-T×x0+ϕ+nN T-T=0,
n=0i-1In-Mx0+ϕ+nN T-n=ij-1In-Mx0+T-ϕ-nN T+n=jN-1In-Mx0+ϕ+nN T-T=0,
n=0i-1In-Mx0+ϕ+nN T-T+n=ij-1In-Mx0+T-ϕ-nN T+n=jN-1In-Mx0+ϕ+nN T-T=0.
ϕ=λA2C3-A3C2-A2C1-A1C2A2A1+B1-2λA2A3 T,
λ=A2D1-A1D2/A2D3-A3D2, A1=j-ij+i-1+N-2j+1N/2, A2=j-i,  A3=N-j+i, B1=NN-2j+1/2, C1=j-12N-j-i2+i/2-N-12N-1/6, C2=j-i2N-i-j+1/2N, C3=j+i2-i-N2-j2-N+j/2N, D1=-n=0i-1 nIn+n=ij-1 nIn-n=jN-1 nIn+N=jN-1 NIn, D2=n=ij-1 In,  D3=n=0i-1 In+n=jN-1 In.
In=Mx0-ϕ-nN T+T0ni-1Mx0+ϕ+nN T-Tinj-1Mx0-ϕ-nN T+2TjnN-1.
λ=A2D1-A1D2/A2D3-A3D2, A1=i-jj+i-1-N-2j+1N/2, A2=N-j+i,  A3=j-i, B1=NN-2j+1/2, C1=N-jj-N-1+N2-1/6, C2=2N-j+i-i2-i+N2-j2-N+j/2N, C3=i-j2N-i-j+1/2N, D1=n=0i-1 nIn-n=ij-1 nIn+n=jN-1 nIn-N=jN-1 NIn, D2=n=0i-1 In+n=jN-1 In,  D3=n=ij-1 In.

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