Abstract

To have the advantages of both spatial and temporal heterodyne techniques and to make efficient use of the limited spatiotemporal frequency bandwidth of image detection systems, we propose a technique of spatiotemporal heterodyne interferometry using both spatial and temporal carrier frequencies. By means of spatiotemporal frequency multiplexing, the technique permits the simultaneous recording of multiple-phase objects on a single space–time interferogram.

© 1992 Optical Society of America

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References

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  1. See, for example, J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1990), Vol. 28, pp. 273–359; K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. 26, pp. 349–393; P. Hariharan, “Interferometry with lasers,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1987), Vol. 24, pp. 103–164; R. Dändliker, “Heterodyne holographic interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1980), Vol. 17, pp. 1–84.
    [CrossRef]
  2. See, for example, N. A. Massie, R. D. Nelson, S. Holly, “High-performance real-time heterodyne interferometry,” Appl. Opt. 18, 1797–1803 (1979).
    [CrossRef] [PubMed]
  3. See, for example, J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [CrossRef] [PubMed]
  4. See, for example, M. Takeda, “Spatial-carrier fringe-pattern analysis and its applications to precision interferometry and profilometry: an overview,” Indust. Metrol. 1, 79–99 (1990).
    [CrossRef]
  5. N. A. Massie, J. Hartlove, D. Jungwirth, J. Morris, “High accuracy interferometric measurements of electron-beam pumped transverse-flow laser media with 10-μsec time resolution,” Appl. Opt. 20, 2372–2378 (1981); see also N. A. Massie, “Real-time digital heterodyne interferometry: a system,” Appl. Opt. 19, 154–160 (1980).
    [CrossRef] [PubMed]
  6. N. A. Massie, M. Dunn, D. Swain, S. Muenter, J. Morris, “Measuring laser flow fields with a 64-channel heterodyne interferometer,” Appl. Opt. 22, 2141–2151 (1983).
    [CrossRef] [PubMed]
  7. See, for example, K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985); S. Nakadate, H. Saito, “Fringe scanning speckle-pattern interferometry,” Appl. Opt. 24, 2172–2180 (1985).
    [CrossRef] [PubMed]
  8. D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Spectral line interferometry with temporal and spatial resolution,” Opt. Commun. 57, 39–44 (1986).
    [CrossRef]
  9. 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]
  10. C. Roddier, F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 26, 1668–1673 (1987).
    [CrossRef] [PubMed]
  11. D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
    [CrossRef] [PubMed]
  12. B. A. Horwitz, “Multiplex techniques for real-time shearing interferometry,” Opt. Eng. 29, 1223–1232 (1990).
    [CrossRef]
  13. J. M. Huntley, J. E. Field, “High resolution moiré photography: application to dynamic stress analysis,” Opt. Eng. 28, 926–933 (1989).
    [CrossRef]
  14. See, for example, Y. Ishii, “Recent developments in laser-diode interferometry,” Opt. Lasers Eng. 14, 293–309 (1991).
    [CrossRef]
  15. M. Kujawińska, J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991).
    [CrossRef]
  16. See, for example, K. Itoh, “Analysis of the phase unwrapping algorithm,” Appl. Opt. 21, 2470 (1982); R. M. Goldstein, H. A. Zebker, C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 712–720 (1988); J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989).
    [CrossRef] [PubMed]
  17. M. Suematsu, M. Takeda, “Wavelength-shift interferometry for distance measurements using the Fourier-transform technique for fringe analysis,” Appl. Opt. 30, 4046–4055 (1991).
    [CrossRef] [PubMed]

1991 (3)

See, for example, Y. Ishii, “Recent developments in laser-diode interferometry,” Opt. Lasers Eng. 14, 293–309 (1991).
[CrossRef]

M. Kujawińska, J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991).
[CrossRef]

M. Suematsu, M. Takeda, “Wavelength-shift interferometry for distance measurements using the Fourier-transform technique for fringe analysis,” Appl. Opt. 30, 4046–4055 (1991).
[CrossRef] [PubMed]

1990 (2)

See, for example, M. Takeda, “Spatial-carrier fringe-pattern analysis and its applications to precision interferometry and profilometry: an overview,” Indust. Metrol. 1, 79–99 (1990).
[CrossRef]

B. A. Horwitz, “Multiplex techniques for real-time shearing interferometry,” Opt. Eng. 29, 1223–1232 (1990).
[CrossRef]

1989 (1)

J. M. Huntley, J. E. Field, “High resolution moiré photography: application to dynamic stress analysis,” Opt. Eng. 28, 926–933 (1989).
[CrossRef]

1987 (1)

1986 (2)

D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
[CrossRef] [PubMed]

D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Spectral line interferometry with temporal and spatial resolution,” Opt. Commun. 57, 39–44 (1986).
[CrossRef]

1985 (1)

1983 (1)

1982 (2)

1981 (1)

1979 (1)

1974 (1)

Bachor, H.-A.

D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Spectral line interferometry with temporal and spatial resolution,” Opt. Commun. 57, 39–44 (1986).
[CrossRef]

D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
[CrossRef] [PubMed]

Bone, D. J.

D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Spectral line interferometry with temporal and spatial resolution,” Opt. Commun. 57, 39–44 (1986).
[CrossRef]

D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
[CrossRef] [PubMed]

Brangaccio, D. J.

Bruning, J. H.

Creath, K.

Dunn, M.

Field, J. E.

J. M. Huntley, J. E. Field, “High resolution moiré photography: application to dynamic stress analysis,” Opt. Eng. 28, 926–933 (1989).
[CrossRef]

Gallagher, J. E.

Hartlove, J.

Herriott, D. R.

Holly, S.

Horwitz, B. A.

B. A. Horwitz, “Multiplex techniques for real-time shearing interferometry,” Opt. Eng. 29, 1223–1232 (1990).
[CrossRef]

Huntley, J. M.

J. M. Huntley, J. E. Field, “High resolution moiré photography: application to dynamic stress analysis,” Opt. Eng. 28, 926–933 (1989).
[CrossRef]

Ina, H.

Ishii, Y.

See, for example, Y. Ishii, “Recent developments in laser-diode interferometry,” Opt. Lasers Eng. 14, 293–309 (1991).
[CrossRef]

Itoh, K.

Jungwirth, D.

Kobayashi, S.

Kujawinska, M.

M. Kujawińska, J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991).
[CrossRef]

Massie, N. A.

Morris, J.

Muenter, S.

Nelson, R. D.

Roddier, C.

Roddier, F.

Rosenfeld, D. P.

Sandeman, R. J.

D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
[CrossRef] [PubMed]

D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Spectral line interferometry with temporal and spatial resolution,” Opt. Commun. 57, 39–44 (1986).
[CrossRef]

Schwider, J.

See, for example, J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1990), Vol. 28, pp. 273–359; K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. 26, pp. 349–393; P. Hariharan, “Interferometry with lasers,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1987), Vol. 24, pp. 103–164; R. Dändliker, “Heterodyne holographic interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1980), Vol. 17, pp. 1–84.
[CrossRef]

Suematsu, M.

Swain, D.

Takeda, M.

White, A. D.

Wójciak, J.

M. Kujawińska, J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991).
[CrossRef]

Appl. Opt. (9)

N. A. Massie, J. Hartlove, D. Jungwirth, J. Morris, “High accuracy interferometric measurements of electron-beam pumped transverse-flow laser media with 10-μsec time resolution,” Appl. Opt. 20, 2372–2378 (1981); see also N. A. Massie, “Real-time digital heterodyne interferometry: a system,” Appl. Opt. 19, 154–160 (1980).
[CrossRef] [PubMed]

N. A. Massie, M. Dunn, D. Swain, S. Muenter, J. Morris, “Measuring laser flow fields with a 64-channel heterodyne interferometer,” Appl. Opt. 22, 2141–2151 (1983).
[CrossRef] [PubMed]

See, for example, K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985); S. Nakadate, H. Saito, “Fringe scanning speckle-pattern interferometry,” Appl. Opt. 24, 2172–2180 (1985).
[CrossRef] [PubMed]

See, for example, N. A. Massie, R. D. Nelson, S. Holly, “High-performance real-time heterodyne interferometry,” Appl. Opt. 18, 1797–1803 (1979).
[CrossRef] [PubMed]

See, for example, J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
[CrossRef] [PubMed]

C. Roddier, F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 26, 1668–1673 (1987).
[CrossRef] [PubMed]

D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
[CrossRef] [PubMed]

See, for example, K. Itoh, “Analysis of the phase unwrapping algorithm,” Appl. Opt. 21, 2470 (1982); R. M. Goldstein, H. A. Zebker, C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 712–720 (1988); J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989).
[CrossRef] [PubMed]

M. Suematsu, M. Takeda, “Wavelength-shift interferometry for distance measurements using the Fourier-transform technique for fringe analysis,” Appl. Opt. 30, 4046–4055 (1991).
[CrossRef] [PubMed]

Indust. Metrol. (1)

See, for example, M. Takeda, “Spatial-carrier fringe-pattern analysis and its applications to precision interferometry and profilometry: an overview,” Indust. Metrol. 1, 79–99 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Spectral line interferometry with temporal and spatial resolution,” Opt. Commun. 57, 39–44 (1986).
[CrossRef]

Opt. Eng. (2)

B. A. Horwitz, “Multiplex techniques for real-time shearing interferometry,” Opt. Eng. 29, 1223–1232 (1990).
[CrossRef]

J. M. Huntley, J. E. Field, “High resolution moiré photography: application to dynamic stress analysis,” Opt. Eng. 28, 926–933 (1989).
[CrossRef]

Opt. Lasers Eng. (2)

See, for example, Y. Ishii, “Recent developments in laser-diode interferometry,” Opt. Lasers Eng. 14, 293–309 (1991).
[CrossRef]

M. Kujawińska, J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325–339 (1991).
[CrossRef]

Other (1)

See, for example, J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1990), Vol. 28, pp. 273–359; K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. 26, pp. 349–393; P. Hariharan, “Interferometry with lasers,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1987), Vol. 24, pp. 103–164; R. Dändliker, “Heterodyne holographic interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1980), Vol. 17, pp. 1–84.
[CrossRef]

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Figures (16)

Fig. 1
Fig. 1

Typical spatiotemporal frequency spectra: (a) temporal carrier technique, (b) spatial carrier technique.

Fig. 2
Fig. 2

Separability of spectra: (a) temporal carrier technique, (b) spatial carrier technique, (c) spatiotemporal carrier technique.

Fig. 3
Fig. 3

Spatiotemporal frequency multiplexing: (a) temporal carrier technique, (b) spatial carrier technique, (c) spatiotemporal carrier technique.

Fig. 4
Fig. 4

Spatiotemporal frequency multiplex interferometers: (a) Michelson-type interferometer, (b) tree-type interferometer, (c) Mach–Zehnder-type interferometer. BS’s, beam splitters; LD’s, laser diodes; M’s, mirrors.

Fig. 5
Fig. 5

3-D spatiotemporal frequency bandpass filtering to retrieve the desired phase distribution.

Fig. 6
Fig. 6

Michelson-type two-channel interferometer. BS’s, beam splitters; LD, laser diode; M’s, mirrors.

Fig. 7
Fig. 7

Interferogram of two gas flows superposed.

Fig. 8
Fig. 8

Space–time interferogram.

Fig. 9
Fig. 9

(a) Spatiotemporal frequency spectra, (b) spectrum selected by filtering.

Fig. 10
Fig. 10

Spatiotemporal phase distribution without correction.

Fig. 11
Fig. 11

Spatiotemporal phase distributions of two different gas flows.

Fig. 12
Fig. 12

Reduction of a 3-D to a 2-D space–time interferogram with space–time degeneracy.

Fig. 13
Fig. 13

Mach–Zehnder-type interferometer; abbreviations as in Fig. 4.

Fig. 14
Fig. 14

Space–time interferogram based on space–time degeneracy.

Fig. 15
Fig. 15

Spatiotemporal frequency spectra.

Fig. 16
Fig. 16

Spatiotemporal phase distributions of two phase patterns.

Equations (10)

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g ( x , y ; t ) = a ( x , y ; t ) + b ( x , y ; t ) cos [ 2 π f 0 T t + ϕ ( x , y ; t ) ] ,
g ( x , y ; t ) = a ( x , y ; t ) + b ( x , y ; t ) × cos [ 2 π ( f 0 X x + f 0 Y y ) + ϕ ( x , y ; t ) ] ,
g ( x , y ; t ) = a ( x , y ; t ) + b ( x , y ; t ) × cos [ 2 π ( f 0 X x + f 0 Y y + f 0 T t ) + ϕ ( x , y ; t ) ] .
g ( x , y ; t ) = a ( x , y ; t ) + m < n b m n ( x , y ; t ) × cos [ 2 π ( f m n X x + f m n Y y + f m n T t ) + ϕ m n ( x , y ; t ) ] ,
g ( x , y ; t ) a ( x , y ; t ) + n = 1 N b 0 n ( x , y ; t ) × cos [ 2 π ( f 0 n X x + f 0 n Y y + f 0 n T t ) + ϕ 0 n ( x , y ; t ) ] .
g ( x , y ; t ) = a ( x , y ; t ) + m < n c m n ( x , y ; t ) × exp [ 2 π i ( f m n X x + f m n Y y + f m n T t ) ] + m < n c m n * ( x , y ; t ) exp [ - 2 π i ( f m n X x + f m n Y y + f m n T t ) ] ,
c m n ( x , y ; t ) = ½ b m n ( x , y ; t ) exp [ i ϕ m n ( x , y ; t ) ] .
G ( f X , f Y ; f T ) = A ( f X , f Y ; f T ) + m < n C m n ( f X - f m n X , f Y - f m n Y ; f T - f m n T ) + m < n C m n * [ - ( f X + f m n X ) , - ( f Y + f m n Y ) ; - ( f T + f m n T ) ] ,
log [ c m n ( x , y ; t ) ] = log [ ½ b m n ( x , y ; t ) ] + i [ ϕ m n ( x , y ; t ) ] ,
ϕ ( x , y ; t ) = ϕ ( x , y - v t ; 0 ) ,

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