Abstract

A new computer-based technique for automatic 3-D shape measurement is proposed and verified by experiments. In contrast to the moire contouring technique, a grating pattern projected onto the object surface is Fourier-transformed and processed in its spatial frequency domain as well as in its space-signal domain. This technique has a much higher sensitivity than the conventional moire technique and is capable of fully automatic distinction between a depression and an elevation on the object surface. There is no requirement for assigning fringe orders and interpolating data in the regions between contour fringes. The technique is free from errors caused by spurious moire fringes generated by the higher harmonic components of the grating pattern.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. See, for example, D. M. Meadows, W. O. Johnson, J. B. Allen, Appl. Opt. 9, 942 (1970);H. Takasaki, Appl. Opt. 9, 1467 (1970).
    [CrossRef] [PubMed]
  2. M. Idesawa, T. Yatagai, T. Soma, Appl. Opt. 16, 2152 (1977).
    [CrossRef] [PubMed]
  3. T. Yatagai, M. Idesawa, Opt. Laser Eng. 3, 73 (1982).
    [CrossRef]
  4. D. T. Moore, B. E. Truax, Appl. Opt. 18, 91 (1979).
    [CrossRef] [PubMed]
  5. M. Takeda, H. Ina, S. Kobayashi, J. Opt. Soc. Am. 72, 156 (1982).
    [CrossRef]
  6. Y. YoshinoKogaku (Jpn. J. Opt.) 1, 128 (1972).
  7. M. Suzuki, K. Suzuki, Bull. Jpn. Soc. Precis. Eng. 8, 23 (1974).
  8. M. Idesawa, T. Yatagai, Sci. Pap. Inst. Phys. Chem. Res. Jpn. 71, 57(1977).
  9. J. L. Doty, J. Opt. Soc. Am. 73, 366 (1983).
    [CrossRef]
  10. M. Takeda, Opt. Laser Eng. 3, 45 (1982).
    [CrossRef]
  11. M. Takeda, M. Kawabuchi, T. OseKogaku (Jpn. J. Opt.) 3, 373 (1974).
  12. See, for example, J. J. Downing, Modulation Systems and Noise (Prentice-Hall, Englewood Cliffs, N.J., 1964), pp. 86–112.

1983 (1)

1982 (3)

M. Takeda, H. Ina, S. Kobayashi, J. Opt. Soc. Am. 72, 156 (1982).
[CrossRef]

T. Yatagai, M. Idesawa, Opt. Laser Eng. 3, 73 (1982).
[CrossRef]

M. Takeda, Opt. Laser Eng. 3, 45 (1982).
[CrossRef]

1979 (1)

1977 (2)

M. Idesawa, T. Yatagai, T. Soma, Appl. Opt. 16, 2152 (1977).
[CrossRef] [PubMed]

M. Idesawa, T. Yatagai, Sci. Pap. Inst. Phys. Chem. Res. Jpn. 71, 57(1977).

1974 (2)

M. Suzuki, K. Suzuki, Bull. Jpn. Soc. Precis. Eng. 8, 23 (1974).

M. Takeda, M. Kawabuchi, T. OseKogaku (Jpn. J. Opt.) 3, 373 (1974).

1972 (1)

Y. YoshinoKogaku (Jpn. J. Opt.) 1, 128 (1972).

1970 (1)

Allen, J. B.

Doty, J. L.

Downing, J. J.

See, for example, J. J. Downing, Modulation Systems and Noise (Prentice-Hall, Englewood Cliffs, N.J., 1964), pp. 86–112.

Idesawa, M.

T. Yatagai, M. Idesawa, Opt. Laser Eng. 3, 73 (1982).
[CrossRef]

M. Idesawa, T. Yatagai, Sci. Pap. Inst. Phys. Chem. Res. Jpn. 71, 57(1977).

M. Idesawa, T. Yatagai, T. Soma, Appl. Opt. 16, 2152 (1977).
[CrossRef] [PubMed]

Ina, H.

Johnson, W. O.

Kawabuchi, M.

M. Takeda, M. Kawabuchi, T. OseKogaku (Jpn. J. Opt.) 3, 373 (1974).

Kobayashi, S.

Meadows, D. M.

Moore, D. T.

Ose, T.

M. Takeda, M. Kawabuchi, T. OseKogaku (Jpn. J. Opt.) 3, 373 (1974).

Soma, T.

Suzuki, K.

M. Suzuki, K. Suzuki, Bull. Jpn. Soc. Precis. Eng. 8, 23 (1974).

Suzuki, M.

M. Suzuki, K. Suzuki, Bull. Jpn. Soc. Precis. Eng. 8, 23 (1974).

Takeda, M.

M. Takeda, Opt. Laser Eng. 3, 45 (1982).
[CrossRef]

M. Takeda, H. Ina, S. Kobayashi, J. Opt. Soc. Am. 72, 156 (1982).
[CrossRef]

M. Takeda, M. Kawabuchi, T. OseKogaku (Jpn. J. Opt.) 3, 373 (1974).

Truax, B. E.

Yatagai, T.

T. Yatagai, M. Idesawa, Opt. Laser Eng. 3, 73 (1982).
[CrossRef]

M. Idesawa, T. Yatagai, Sci. Pap. Inst. Phys. Chem. Res. Jpn. 71, 57(1977).

M. Idesawa, T. Yatagai, T. Soma, Appl. Opt. 16, 2152 (1977).
[CrossRef] [PubMed]

Yoshino, Y.

Y. YoshinoKogaku (Jpn. J. Opt.) 1, 128 (1972).

Appl. Opt. (3)

Bull. Jpn. Soc. Precis. Eng. (1)

M. Suzuki, K. Suzuki, Bull. Jpn. Soc. Precis. Eng. 8, 23 (1974).

J. Opt. Soc. Am. (2)

Jpn. J. Opt. (2)

Y. YoshinoKogaku (Jpn. J. Opt.) 1, 128 (1972).

M. Takeda, M. Kawabuchi, T. OseKogaku (Jpn. J. Opt.) 3, 373 (1974).

Opt. Laser Eng. (2)

T. Yatagai, M. Idesawa, Opt. Laser Eng. 3, 73 (1982).
[CrossRef]

M. Takeda, Opt. Laser Eng. 3, 45 (1982).
[CrossRef]

Sci. Pap. Inst. Phys. Chem. Res. Jpn. (1)

M. Idesawa, T. Yatagai, Sci. Pap. Inst. Phys. Chem. Res. Jpn. 71, 57(1977).

Other (1)

See, for example, J. J. Downing, Modulation Systems and Noise (Prentice-Hall, Englewood Cliffs, N.J., 1964), pp. 86–112.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Crossed-optical-axes geometry.

Fig. 2
Fig. 2

Parallel-optical-axes geometry.

Fig. 3
Fig. 3

Spatial frequency spectra of deformed grating image for a fixed y value. Only a spectrum Q1 (dotted) is selected by the filtering operation.

Fig. 4
Fig. 4

Condition for separating fundamental frequency spectrum Q1 (dotted) from other spectra.

Fig. 5
Fig. 5

Schematic diagram of experimental setup.

Fig. 6
Fig. 6

Deformed grating pattern with straight lines in the background for reference signals.

Fig. 7
Fig. 7

Irradiance profile of deformed grating pattern for a fixed y value.

Fig. 8
Fig. 8

Spatial frequency spectra of deformed grating pattern.

Fig. 9
Fig. 9

Wrapped phase distribution. The line along discontinuities with 2π-phase jumps corresponds to a fringe contour in moire topography.

Fig. 10
Fig. 10

Unwrapped phase distribution.

Fig. 11
Fig. 11

Comparison with contact measurement. Solid lines denote measurements by FTP, and circles denote measurements by the contact method.

Equations (34)

Equations on this page are rendered with MathJax. Learn more.

g T ( x , y ) = n = A n exp ( 2 π in f 0 x ) ,
f 0 = 1 / p 0 = cos θ / p
g 0 ( x , y ) = n = A n exp { 2 π in f 0 [ x + s 0 ( x ) ] } ,
g 0 ( x , y ) = n = A n exp { i [ 2 π n f 0 x + n ϕ 0 ( x ) ] } ,
ϕ 0 ( x ) = 2 π f 0 s 0 ( x ) = 2 π f 0 B C ¯ .
g ( x , y ) = r ( x , y ) n = A n exp { 2 π in f 0 [ x + s ( x , y ) ] } ,
g ( x , y ) = r ( x , y ) n = A n exp { i [ 2 π n f 0 x + n ϕ ( x , y ) ] } ,
ϕ ( x , y ) = 2 π f 0 s ( x , y ) = 2 π f 0 B D ¯ ,
ϕ 0 ( x ) = 2 π f 0 s 0 ( x ) = 2 π f 0 B C ¯ = 0 ,
ϕ ( x , y ) = 2 π f 0 s ( x , y ) = 2 π f 0 C D ¯ .
g ( x , y ) = n = q n ( x , y ) exp ( 2 π i n f 0 x ) ,
q n ( x , y ) = A n r ( x , y ) exp [ i n ϕ ( x , y ) ] .
G ( f , y ) = g ( x , y ) exp ( 2 π ifx ) d x = n = Q n ( f n f 0 , y ) ,
g ̂ ( x , y ) = q 1 ( x , y ) exp ( 2 π i f 0 x ) = A 1 r ( x , y ) exp { i [ 2 π f 0 x + ϕ ( x , y ) ] } .
g ̂ 0 ( x , y ) = A 1 exp { i [ 2 π f 0 x + ϕ 0 ( x ) ] } ,
g ̂ ( x , y ) g ̂ 0 * ( x , y ) = | A 1 | 2 r ( x , y ) exp { i [ Δ ϕ ( x , y ) ] } ,
Δ ϕ ( x , y ) = ϕ ( x , y ) ϕ 0 ( x ) = 2 π f 0 ( B D ¯ B C ¯ ) = 2 π f 0 C D ¯ .
ϕ 0 ( y ) = 2 π f 0 y tan ( δ α ) ,
log [ g ̂ ( x , y ) g ̂ 0 * ( x , y ) ] = log [ | A 1 | 2 r ( x , y ) ] + i Δ ϕ ( x , y ) .
C D ¯ = d h ( x , y ) / [ l 0 h ( x , y ) ] ,
h ( x , y ) = l 0 Δ ϕ ( x , y ) / [ Δ ϕ ( x , y ) 2 π f 0 d ] .
h ( x , y ) = l 0 p 0 [ Δ ϕ ( x , y ) / 2 π ] / { p 0 [ Δ ϕ ( x , y ) / 2 π ] d } .
f n = 1 2 π x [ 2 π n f 0 x + n ϕ ( x , y ) ] = n f 0 + n 2 π ϕ ( x , y ) x .
( f 1 ) max < ( f n ) min , ( n = 2 , 3 , )
f b < ( f 1 ) min ,
f 0 + 1 2 π ( ϕ x ) max < n f 0 + n 2 π ( ϕ x ) min , ( n = 2 , 3 , ) ,
f b < f 0 + 1 2 π ( ϕ x ) min .
f 0 + 1 2 π | ϕ x | max < n f 0 n 2 π | ϕ x | max , ( n = 2 , 3 , ) ,
f b < f 0 1 2 π | ϕ x | max ,
| ϕ x | max < ( n 1 n + 1 ) 2 π f 0 , ( n = 2 , 3 , ) ,
| ϕ x | max < 2 π ( f 0 f b ) .
| ϕ x | max < 2 π f 0 3 .
ϕ ( x , y ) Δ ϕ ( x , y ) ( 2 π f 0 d / l 0 ) h ( x , y ) ,
| h ( x , y ) x | max < 1 3 ( l 0 d ) .

Metrics