Abstract

A new method of phase determination in hologram interferometry is described. The Fresnel holograms, which represent the undeformed and the deformed states of the object, are generated on a CCD target and stored electronically. No lens or other imaging device is used. The reconstruction is done from the digitally stored holograms with mathematical methods. It is shown that the intensity as well as the phase can be calculated from the digitally sampled holograms. A comparison of the phases of the undeformed and the deformed states permits direct determination of the interference phase.

© 1994 Optical Society of America

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References

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  1. W. Jüptner, “Automatisierte Auswertung holografischer Interferogramme mit dem Zeilen-Scan-Verfahren,” presented at the Deutsche Physikalische Gesellschaft/Deutsche Gesellschaft für Angewandte Optik-Frühjahrsschule, Holografische Interferometrie in Technik und Medizin, Hannover, April 4–7, 1978.
  2. W. Jüptner, Th. Kreis, H. Kreitlow, “Automatic evaluation of holographic interferograms by reference beam phase shifting,” in Industrial Applications of Laser Technology,W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.398, 22–29 (1983).
    [CrossRef]
  3. C. L. Koliopoulos, “Interferometric optical phase measurement techniques,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz.; University Microfilms, Ann Arbor, Mich.).
  4. R. Dändliker, B. Ineichen, F. M. Mottier, “High resolution hologram interferometry by electronic phase measurement,” Opt. Commun. 9, 412–416 (1973).
    [CrossRef]
  5. Th. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A 3, 847–855 (1986).
    [CrossRef]
  6. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985).
    [CrossRef] [PubMed]
  7. K. A. Stetson, W. R. Brohinsky, “Electrooptic holography and its application to hologram interferometry,” Appl. Opt. 24, 3631–3637 (1985).
    [CrossRef] [PubMed]
  8. P. Das, Lasers and Optical Engineering (Springer, New York, 1991), Chap. 2.4, p. 81.
  9. L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography, translated from Russian by D. Parsons (Consultants Bureau, New York, 1989), Chap. 1, p. 14.
  10. Y. Ostrovsky, M. M. Butusov, G. V. Ostrovskaya, Interferometry by Holography, Springer Series in Optical Sciences (Springer, New York, 1980), Chap. 1, p. 11.
  11. A. Ettemeyer, U. Neupert, H. Rottenkolber, C. Winter, “Schnelle und robuste Analyse von Streifenmustern—Ein wichtiger Schritt der Automation von holografischen Prozessen,” in Proceedings of the 2nd International Workshop on Automatic Processing of Fringe Patterns (Akademie-Verlag, Berlin, 1989), pp. 23–31.
  12. Th. Kreis, W. Jüptner, “Fourier-transform evaluation of interference patterns: demodulation and sign ambiguity,” in Laser Interferometry TV: Computer-Aided Interferometry,R. J. Pryputniewiez, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 263–273 (1991).
    [CrossRef]

1986 (1)

1985 (2)

1973 (1)

R. Dändliker, B. Ineichen, F. M. Mottier, “High resolution hologram interferometry by electronic phase measurement,” Opt. Commun. 9, 412–416 (1973).
[CrossRef]

Brohinsky, W. R.

Butusov, M. M.

Y. Ostrovsky, M. M. Butusov, G. V. Ostrovskaya, Interferometry by Holography, Springer Series in Optical Sciences (Springer, New York, 1980), Chap. 1, p. 11.

Creath, K.

Dändliker, R.

R. Dändliker, B. Ineichen, F. M. Mottier, “High resolution hologram interferometry by electronic phase measurement,” Opt. Commun. 9, 412–416 (1973).
[CrossRef]

Das, P.

P. Das, Lasers and Optical Engineering (Springer, New York, 1991), Chap. 2.4, p. 81.

Ettemeyer, A.

A. Ettemeyer, U. Neupert, H. Rottenkolber, C. Winter, “Schnelle und robuste Analyse von Streifenmustern—Ein wichtiger Schritt der Automation von holografischen Prozessen,” in Proceedings of the 2nd International Workshop on Automatic Processing of Fringe Patterns (Akademie-Verlag, Berlin, 1989), pp. 23–31.

Ineichen, B.

R. Dändliker, B. Ineichen, F. M. Mottier, “High resolution hologram interferometry by electronic phase measurement,” Opt. Commun. 9, 412–416 (1973).
[CrossRef]

Jüptner, W.

Th. Kreis, W. Jüptner, “Fourier-transform evaluation of interference patterns: demodulation and sign ambiguity,” in Laser Interferometry TV: Computer-Aided Interferometry,R. J. Pryputniewiez, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 263–273 (1991).
[CrossRef]

W. Jüptner, “Automatisierte Auswertung holografischer Interferogramme mit dem Zeilen-Scan-Verfahren,” presented at the Deutsche Physikalische Gesellschaft/Deutsche Gesellschaft für Angewandte Optik-Frühjahrsschule, Holografische Interferometrie in Technik und Medizin, Hannover, April 4–7, 1978.

W. Jüptner, Th. Kreis, H. Kreitlow, “Automatic evaluation of holographic interferograms by reference beam phase shifting,” in Industrial Applications of Laser Technology,W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.398, 22–29 (1983).
[CrossRef]

Koliopoulos, C. L.

C. L. Koliopoulos, “Interferometric optical phase measurement techniques,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz.; University Microfilms, Ann Arbor, Mich.).

Kreis, Th.

Th. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A 3, 847–855 (1986).
[CrossRef]

Th. Kreis, W. Jüptner, “Fourier-transform evaluation of interference patterns: demodulation and sign ambiguity,” in Laser Interferometry TV: Computer-Aided Interferometry,R. J. Pryputniewiez, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 263–273 (1991).
[CrossRef]

W. Jüptner, Th. Kreis, H. Kreitlow, “Automatic evaluation of holographic interferograms by reference beam phase shifting,” in Industrial Applications of Laser Technology,W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.398, 22–29 (1983).
[CrossRef]

Kreitlow, H.

W. Jüptner, Th. Kreis, H. Kreitlow, “Automatic evaluation of holographic interferograms by reference beam phase shifting,” in Industrial Applications of Laser Technology,W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.398, 22–29 (1983).
[CrossRef]

Merzlyakov, N. S.

L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography, translated from Russian by D. Parsons (Consultants Bureau, New York, 1989), Chap. 1, p. 14.

Mottier, F. M.

R. Dändliker, B. Ineichen, F. M. Mottier, “High resolution hologram interferometry by electronic phase measurement,” Opt. Commun. 9, 412–416 (1973).
[CrossRef]

Neupert, U.

A. Ettemeyer, U. Neupert, H. Rottenkolber, C. Winter, “Schnelle und robuste Analyse von Streifenmustern—Ein wichtiger Schritt der Automation von holografischen Prozessen,” in Proceedings of the 2nd International Workshop on Automatic Processing of Fringe Patterns (Akademie-Verlag, Berlin, 1989), pp. 23–31.

Ostrovskaya, G. V.

Y. Ostrovsky, M. M. Butusov, G. V. Ostrovskaya, Interferometry by Holography, Springer Series in Optical Sciences (Springer, New York, 1980), Chap. 1, p. 11.

Ostrovsky, Y.

Y. Ostrovsky, M. M. Butusov, G. V. Ostrovskaya, Interferometry by Holography, Springer Series in Optical Sciences (Springer, New York, 1980), Chap. 1, p. 11.

Rottenkolber, H.

A. Ettemeyer, U. Neupert, H. Rottenkolber, C. Winter, “Schnelle und robuste Analyse von Streifenmustern—Ein wichtiger Schritt der Automation von holografischen Prozessen,” in Proceedings of the 2nd International Workshop on Automatic Processing of Fringe Patterns (Akademie-Verlag, Berlin, 1989), pp. 23–31.

Stetson, K. A.

Winter, C.

A. Ettemeyer, U. Neupert, H. Rottenkolber, C. Winter, “Schnelle und robuste Analyse von Streifenmustern—Ein wichtiger Schritt der Automation von holografischen Prozessen,” in Proceedings of the 2nd International Workshop on Automatic Processing of Fringe Patterns (Akademie-Verlag, Berlin, 1989), pp. 23–31.

Yaroslavskii, L. P.

L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography, translated from Russian by D. Parsons (Consultants Bureau, New York, 1989), Chap. 1, p. 14.

Appl. Opt. (2)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

R. Dändliker, B. Ineichen, F. M. Mottier, “High resolution hologram interferometry by electronic phase measurement,” Opt. Commun. 9, 412–416 (1973).
[CrossRef]

Other (8)

P. Das, Lasers and Optical Engineering (Springer, New York, 1991), Chap. 2.4, p. 81.

L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography, translated from Russian by D. Parsons (Consultants Bureau, New York, 1989), Chap. 1, p. 14.

Y. Ostrovsky, M. M. Butusov, G. V. Ostrovskaya, Interferometry by Holography, Springer Series in Optical Sciences (Springer, New York, 1980), Chap. 1, p. 11.

A. Ettemeyer, U. Neupert, H. Rottenkolber, C. Winter, “Schnelle und robuste Analyse von Streifenmustern—Ein wichtiger Schritt der Automation von holografischen Prozessen,” in Proceedings of the 2nd International Workshop on Automatic Processing of Fringe Patterns (Akademie-Verlag, Berlin, 1989), pp. 23–31.

Th. Kreis, W. Jüptner, “Fourier-transform evaluation of interference patterns: demodulation and sign ambiguity,” in Laser Interferometry TV: Computer-Aided Interferometry,R. J. Pryputniewiez, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 263–273 (1991).
[CrossRef]

W. Jüptner, “Automatisierte Auswertung holografischer Interferogramme mit dem Zeilen-Scan-Verfahren,” presented at the Deutsche Physikalische Gesellschaft/Deutsche Gesellschaft für Angewandte Optik-Frühjahrsschule, Holografische Interferometrie in Technik und Medizin, Hannover, April 4–7, 1978.

W. Jüptner, Th. Kreis, H. Kreitlow, “Automatic evaluation of holographic interferograms by reference beam phase shifting,” in Industrial Applications of Laser Technology,W. F. Fagan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.398, 22–29 (1983).
[CrossRef]

C. L. Koliopoulos, “Interferometric optical phase measurement techniques,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz.; University Microfilms, Ann Arbor, Mich.).

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Figures (13)

Fig. 1
Fig. 1

Off-axis holography with a plane reference wave: (a) recording, (b) reconstruction.

Fig. 2
Fig. 2

Coordinate system used for reconstruction.

Fig. 3
Fig. 3

Diagram of the reconstruction process. FRT denotes Fresnel transformation. The reconstruction of the superimposed holograms leads to an interferogram (double-exposure holography). If the phases of each individual object state are reconstructed, the interference phase can be calculated directly.

Fig. 4
Fig. 4

Experimental setup: BS, beam splitter; M, mirror; L, lens.

Fig. 5
Fig. 5

Digitally sampled hologram, undeformed object.

Fig. 6
Fig. 6

Digitally sampled hologram, deformed object.

Fig. 7
Fig. 7

Numerically reconstructed holographic interferogram.

Fig. 8
Fig. 8

Numerically reconstructed phase, undeformed object.

Fig. 9
Fig. 9

Numerically reconstructed phase, deformed object.

Fig. 10
Fig. 10

Interference phase modulo 2π calculated directly from the holograms.

Fig. 11
Fig. 11

Interference phase modulo 2π, smoothed by a 3 × 3 median filter.

Fig. 12
Fig. 12

Phase unwrapping for one row: (a) interference phase modulo 2π, (b) filtered interference phase modulo 2π, (c) unwrapped interference phase.

Fig. 13
Fig. 13

Plot of continuous interference-phase distribution.

Equations (10)

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d 3 π 4 λ [ ( x ξ ) 2 + ( y η ) 2 ] max 2 .
Γ ( ξ , η ) = i a λ d exp [ i π λ d ( ξ 2 + η 2 ) ] × t ( x , y ) exp [ i π λ d ( x 2 + y 2 ) ] × exp [ i 2 π λ d ( x ξ + y η ) ] d x d y ,
Γ ( m , n ) = exp [ i π λ d ( m 2 Δ ξ 2 + n 2 Δ η 2 ) ] × k = 0 N 1 l = 0 N 1 t ( k , l ) exp [ i π λ d ( k 2 Δ x 2 + l 2 Δ y 2 ) ] × exp [ i 2 π λ d ( k Δ x m Δ ξ + l Δ y n Δ η ) ] , m = 0 , 1 , , N 1 ; n = 0 , 1 , , N 1.
Δ ξ = λ d / N Δ x , Δ η = λ d / N Δ y .
Γ ( m , n ) = exp [ i π λ d ( m 2 N 2 Δ x 2 + n 2 N 2 Δ y 2 ) ] × k = 0 N 1 l = 0 N 1 t ( k , l ) exp [ i π λ d ( k 2 Δ x 2 + l 2 Δ y 2 ) ] × exp [ i 2 π ( k m N + l n N ) ] .
I ( ξ , η ) = | Γ ( ξ , η ) | 2 = Re 2 [ Γ ( ξ , η ) ] + Im 2 [ Γ ( ξ , η ) ] .
Φ ( ξ , η ) = arctan Im [ Γ ( ξ , η ) ] Re [ Γ ( ξ , η ) ] .
t ( k , l ) = t 1 ( k , l ) + t 2 ( k , l ) ,
Δ Φ ( ξ , η ) = { Φ 1 Φ 2 if Φ 1 Φ 2 Φ 1 Φ 2 + 2 π if Φ 1 < Φ 2 .
f max = 2 / λ sin θ max / 2.

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