Abstract

A new triangulation-based optical profilometry—linearly coded profilometry (LCP)—is presented. In this method, a linear coding technique is introduced. It uses a periodic sawtoothlike structure light to code the surface being measured and the phase-shifting technique to decode the profile. A coding light that has isosceles triangle teeth is proposed. To realize the decoding, at least three samples are needed. When more than three samples are used, higher accuracy can be obtained. A decoding method of LCP with an even number of samples is provided. This method has been realized in my laboratory and the experimental results verify the reliability of LCP. Because the coding method used in LCP is simpler than that used in phase-measuring profilometry, LCP has a faster measuring speed.

© 1997 Optical Society of America

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References

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  1. D. M. Meadows, W. O. Johnson, J. B. Allen, “Generation of surface contour by moiré patterns,” Appl. Opt. 9, 942–947 (1970).
    [Crossref] [PubMed]
  2. M. Takeda, K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D objects shapes,” Appl. Opt. 22, 3977–3982 (1983).
    [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. M. Takeda, H. Ina, S. Kobayashi, “Fourier transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [Crossref]

1984 (1)

1983 (1)

1982 (1)

1970 (1)

Allen, J. B.

Halioua, M.

Ina, H.

Johnson, W. O.

Kobayashi, S.

Liu, H. C.

Meadows, D. M.

Mutoh, K.

Srinivasan, V.

Takeda, M.

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Figures (7)

Fig. 1
Fig. 1

Section drawing of the coding intensity.

Fig. 2
Fig. 2

Distribution of the samples when 0 < φ m ≤ (N/2 - J + 1) T/N.

Fig. 3
Fig. 3

Distribution of the samples when 0 < φ m ≤ (N/2 - J) T/N.

Fig. 4
Fig. 4

Distribution of the samples when T/2 < φ m ≤ (N - J + 1) T/N.

Fig. 5
Fig. 5

Distribution of the samples when T/2 < φ m ≤ (N - J) T/N.

Fig. 6
Fig. 6

Schedule diagram of the hardware measuring system.

Fig. 7
Fig. 7

Experimental results: (a) original sphere, (b) coded sphere, (c) 3D display of the measuring result.

Equations (48)

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Ix, y=a+bxTm0 xTm<T2a+b T-xTmT2xTm<T=bx0+xTm0xTm<T2bx0+T-xTmT2xTm<T
Ix, y=Rx, ybx0+φx, yTm0φx, yTm<T/2Rx, ybx0+T-φx, yTmT/2φx, yTm<T,
Ix, y=Mx, yx0+φx, y+δTm0φx, y+δTm<T/2Mx, yx0+T-φx, y+δTmT/2φx, y+δTmT,
δi=iN T, i=0,1,,N-1,
IJIJ-1  IJIJ+1  IJ-1IJ+1
I0=Mx0+φm  IJ-1=Mx0+φm+J-1TN, IJ=Mx0+T-φm-J TN  IJ-1+N/2=Mx0+T-φm-J-1+N/2TN,IJ+N/2=Mx0+φm+J+N/2TN-T  IN-1=Mx0+φm+N-1TN-T,
E=n=0J-1In-Mx0+φm+nTN2+n=JJ-1+N/2×In-M x0+T-φm-nTN2+n=J+N/2N-1×In-Mx0+φm+nTN-T2.
n=0J-1In-Mx0+φm+nTN+n=JJ-1+N/2In-Mx0+T-φm-nTN+n=J+N/2N-1In-Mx0+φm+nTN-T=0,
n=0J-1In-Mx0+φm+nTN-n=JJ-1+N/2In-Mx0+T-φm-nTN+n=J+N/2N-1In-Mx0+φm+nTN-T=0,
n=0J-1In-Mx0+φm+nTNx0+φm+nTN+n=JJ-1+N/2In-Mx0+T-φm-nTN×x0+T-φm-nTN+n=J+N/2N-1×In-Mx0+φm+nTN-T×x0+φm+nTN-T=0.
n=0J-1In-Mx0+φm+nTN+n=J+N/2N-1×In-M x0+φm+nTN-T=0,
n=JJ-1+N/2In-Mx0+T-φm-nTN=0.
TNn=0J-1In-Mx0+φm+nTNn-TNn=JJ-1+N/2×In-Mx0+T-φm-nTNn+n=J+N/2N-1×In-Mx0+φm+nTN-Tn TN-T=0.
C1=N2 Mx0+N2 Mφm-N8-J2+14MT,
C2=N2 Mx0-N2 Mφm+3N8-J2+14MT,
C3=-N4 Mx0+J-12Mφm+16N-N24-J2+14-JN+J2NMT,
C1=n=0J-1In+n=j+N/2N-1In,
C2=n=JJ-1+N/2In,
C3=1Nn=0J-1Inn+n=J+N/2N-1Inn-n=JJ-1+N/2Inn-n=J+N/2N-1In.
C1-C2=NMφm-Z1MT,
C1+2C3=N2+2J-1Mφm+Z2MT.
Z1=N2-J+12,
Z2=14-12 J-524 N+13N-2JN+2J2N.
φm=TC1-C2Z2+C1+2C3Z1C1+2C3N-C1-C2N/2+2J-1.
IJIJ-1IJIJ+1IJ-1<IJ+1,
I0=Mx0+φm  IJ=Mx0+φm+JTN,IJ+1=Mx0+T-φm-J+1TN  IJ+1N/2=Mx0+T-φm-J+N/2TN, IJ+1+N/2=Mx0+φm+J+1+N/2TN-T  IN-1=Mx0+φm+N-1TN-T.
φm=TC2-C1Z2+C1+2C3Z1C1+2C3N+C2-C1N/2+2J+1,
C1=n=0JIn+n=J+1+N/2N-1In,
C2=n=J+1J+N/2 In,
C3=1Nn=0JInn+n=J+1+N/2N-1Inn-n=J+1J+N/2Inn-n=J+1+N/2N-1In,
Z1=N2-J-12,
Z2=14+12 J+524 N-13N-2JN-2J2N,
IJIJ-1IJIJ+1IJ-1IJ+1,
I0=Mx0+T-φm  IJ-1=Mx0+T-φm-J-1TN, IJ=Mx0-T+φm+JTN  IJ-1+N/2=Mx0-T+φm+J-1+N/2TN, IJ+N/2=Mx0-φm-J+N/2TN+2T  IN-1=Mx0-φm-N-1TN+2T.
φm=TC2-C1Z2-C2+2C3Z1C2-C1N/2-2J+1-C2+2C3N,
C1=n=0J-1 In+n=J+N/2N-1In,
C2=n=JJ-1+N/2In,
C3=1Nn=0J-1Inn+n=J+N/2N-1Inn-n=JJ-1+N/2Inn-n=J+N/2N-1In,
Z1=N-J+½,
Z2=54-52 J+1324 N+13N-2JN+2J2N.
IJIJ-1IJIJ+1IJ-1>IJ+1,
I0=Mx0+T-φm  IJ=Mx0+T-φm-JTN,IJ+1=Mx0-T+φm+J+1TN  IJ+N/2=Mx0-T+φm+J+N/2TN,IJ+1+N/2=Mx0-φm-J+1+N/2TN+2T  IN-1=Mx0-φm-N-1TN+2T.
φm=TC2-C1Z2-C2+2C3Z1C2-C1N/2-2J-1-C2+2C3N,
C1=n=0JIn+n=J+1+N/2N-1In
C2=n=J+1J+N/2In,
C3=1Nn=0JInn+n=J+1+N/2N-1Inn-n=J+1J+N/2Inn-n=J+1+N/2N-1In,
Z1=N-J-½,
Z2=-54-52 J+1324 N+13N+2JN+2J2N.

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