Abstract

This paper reports on the application of phase shifting interferometry to comparative holography. The method here enables the measurement of phase distributions corresponding to the difference in displacements of two nominally identical specimens subjected to similar loading steps. Different aspects of the method are discussed, and experimental results are presented to demonstrate the feasibility and versatility of the technique in flaw detection.

© 1991 Optical Society of America

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References

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  1. D. B. Neumann, “Comparative Holography: A Technique For Eliminating Background Fringes in Holographic Interferometry,” Opt. Eng. 24, 625–627 (1985).
  2. Z. Füzessy, F. Gyimesi, “Difference Holographic Interferometry: Displacement Measurement,” Opt. Eng. 23, 780–783 (1984).
  3. P. K. Rastogi, “Comparative Holographic Moire Interferometry,” Appl. Opt. 23, 924–927 (1984).
    [CrossRef] [PubMed]
  4. P. K. Rastogi, “Comparative Holographic Interferometry: A Nondestructive Inspection System For Detection of Flaws,” Exp. Mech. 25, 325–337 (1985).
    [CrossRef]
  5. P. K. Rastogi, “Observation of Difference Displacement Fringes Using Comparative Holography and Its Application to the Detection of Concealed Flaws,” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 16–25 (1986).
  6. E. Simova, V. Sainov, “Comparative Holographic Moire Interferometry For Nondestructive Testing: Comparison With Conventional Holographic Interferometry,” Opt. Eng. 28, 261–266 (1989).
    [CrossRef]
  7. E. Simova, V. Sainov, “Comparative Holographic Moire Interferometry: Separation of Moire Fringes From the Carrier Interference Pattern,” Opt. Eng. 28, 550–555 (1989).
  8. P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase Measurement System For Real-Time Holographic Interferometry,” Opt. Commun. 41, 393–396 (1982).
    [CrossRef]
  9. K. Creath, “Phase-Measurement Interferometry Techniques,” in Progress in Optics, Vol. 26, E. Wolf, Ed. (North-Holland, Amsterdam, 1988), p. 349.
    [CrossRef]
  10. C. A. Sciammarella, J. A. Gilbert, “A Holographic Moire Technique to Obtain Separate Patterns For Components of Displacement,” Exp. Mech. 16, 215–220 (1976).
    [CrossRef]

1989

E. Simova, V. Sainov, “Comparative Holographic Moire Interferometry For Nondestructive Testing: Comparison With Conventional Holographic Interferometry,” Opt. Eng. 28, 261–266 (1989).
[CrossRef]

E. Simova, V. Sainov, “Comparative Holographic Moire Interferometry: Separation of Moire Fringes From the Carrier Interference Pattern,” Opt. Eng. 28, 550–555 (1989).

1986

P. K. Rastogi, “Observation of Difference Displacement Fringes Using Comparative Holography and Its Application to the Detection of Concealed Flaws,” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 16–25 (1986).

1985

P. K. Rastogi, “Comparative Holographic Interferometry: A Nondestructive Inspection System For Detection of Flaws,” Exp. Mech. 25, 325–337 (1985).
[CrossRef]

D. B. Neumann, “Comparative Holography: A Technique For Eliminating Background Fringes in Holographic Interferometry,” Opt. Eng. 24, 625–627 (1985).

1984

Z. Füzessy, F. Gyimesi, “Difference Holographic Interferometry: Displacement Measurement,” Opt. Eng. 23, 780–783 (1984).

P. K. Rastogi, “Comparative Holographic Moire Interferometry,” Appl. Opt. 23, 924–927 (1984).
[CrossRef] [PubMed]

1982

P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase Measurement System For Real-Time Holographic Interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

1976

C. A. Sciammarella, J. A. Gilbert, “A Holographic Moire Technique to Obtain Separate Patterns For Components of Displacement,” Exp. Mech. 16, 215–220 (1976).
[CrossRef]

Brown, N.

P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase Measurement System For Real-Time Holographic Interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

Creath, K.

K. Creath, “Phase-Measurement Interferometry Techniques,” in Progress in Optics, Vol. 26, E. Wolf, Ed. (North-Holland, Amsterdam, 1988), p. 349.
[CrossRef]

Füzessy, Z.

Z. Füzessy, F. Gyimesi, “Difference Holographic Interferometry: Displacement Measurement,” Opt. Eng. 23, 780–783 (1984).

Gilbert, J. A.

C. A. Sciammarella, J. A. Gilbert, “A Holographic Moire Technique to Obtain Separate Patterns For Components of Displacement,” Exp. Mech. 16, 215–220 (1976).
[CrossRef]

Gyimesi, F.

Z. Füzessy, F. Gyimesi, “Difference Holographic Interferometry: Displacement Measurement,” Opt. Eng. 23, 780–783 (1984).

Hariharan, P.

P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase Measurement System For Real-Time Holographic Interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

Neumann, D. B.

D. B. Neumann, “Comparative Holography: A Technique For Eliminating Background Fringes in Holographic Interferometry,” Opt. Eng. 24, 625–627 (1985).

Oreb, B. F.

P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase Measurement System For Real-Time Holographic Interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

Rastogi, P. K.

P. K. Rastogi, “Observation of Difference Displacement Fringes Using Comparative Holography and Its Application to the Detection of Concealed Flaws,” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 16–25 (1986).

P. K. Rastogi, “Comparative Holographic Interferometry: A Nondestructive Inspection System For Detection of Flaws,” Exp. Mech. 25, 325–337 (1985).
[CrossRef]

P. K. Rastogi, “Comparative Holographic Moire Interferometry,” Appl. Opt. 23, 924–927 (1984).
[CrossRef] [PubMed]

Sainov, V.

E. Simova, V. Sainov, “Comparative Holographic Moire Interferometry For Nondestructive Testing: Comparison With Conventional Holographic Interferometry,” Opt. Eng. 28, 261–266 (1989).
[CrossRef]

E. Simova, V. Sainov, “Comparative Holographic Moire Interferometry: Separation of Moire Fringes From the Carrier Interference Pattern,” Opt. Eng. 28, 550–555 (1989).

Sciammarella, C. A.

C. A. Sciammarella, J. A. Gilbert, “A Holographic Moire Technique to Obtain Separate Patterns For Components of Displacement,” Exp. Mech. 16, 215–220 (1976).
[CrossRef]

Simova, E.

E. Simova, V. Sainov, “Comparative Holographic Moire Interferometry: Separation of Moire Fringes From the Carrier Interference Pattern,” Opt. Eng. 28, 550–555 (1989).

E. Simova, V. Sainov, “Comparative Holographic Moire Interferometry For Nondestructive Testing: Comparison With Conventional Holographic Interferometry,” Opt. Eng. 28, 261–266 (1989).
[CrossRef]

Appl. Opt.

Exp. Mech.

P. K. Rastogi, “Comparative Holographic Interferometry: A Nondestructive Inspection System For Detection of Flaws,” Exp. Mech. 25, 325–337 (1985).
[CrossRef]

C. A. Sciammarella, J. A. Gilbert, “A Holographic Moire Technique to Obtain Separate Patterns For Components of Displacement,” Exp. Mech. 16, 215–220 (1976).
[CrossRef]

Opt. Commun.

P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase Measurement System For Real-Time Holographic Interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

Opt. Eng.

E. Simova, V. Sainov, “Comparative Holographic Moire Interferometry For Nondestructive Testing: Comparison With Conventional Holographic Interferometry,” Opt. Eng. 28, 261–266 (1989).
[CrossRef]

E. Simova, V. Sainov, “Comparative Holographic Moire Interferometry: Separation of Moire Fringes From the Carrier Interference Pattern,” Opt. Eng. 28, 550–555 (1989).

D. B. Neumann, “Comparative Holography: A Technique For Eliminating Background Fringes in Holographic Interferometry,” Opt. Eng. 24, 625–627 (1985).

Z. Füzessy, F. Gyimesi, “Difference Holographic Interferometry: Displacement Measurement,” Opt. Eng. 23, 780–783 (1984).

Proc. Soc. Photo-Opt. Instrum. Eng.

P. K. Rastogi, “Observation of Difference Displacement Fringes Using Comparative Holography and Its Application to the Detection of Concealed Flaws,” Proc. Soc. Photo-Opt. Instrum. Eng. 661, 16–25 (1986).

Other

K. Creath, “Phase-Measurement Interferometry Techniques,” in Progress in Optics, Vol. 26, E. Wolf, Ed. (North-Holland, Amsterdam, 1988), p. 349.
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

(a) Modulo 2π phase ψ calculated by phase shifting interferometry. (b) Reconstruction of the actual phase ϕ.

Fig. 2
Fig. 2

Schematic of the principle involved in the objective approach to obtain the comparative phase function ψc: (a) modulo 2π phase distribution ψt; (b) modulo 2π phase distribution ψm; (c) difference between (a) and (b); (d) variation of K; and (e) reconstruction of ψc obtained from (c) and (d).

Fig. 3
Fig. 3

Layout of the experimental arrangement.

Fig. 4
Fig. 4

Moire fringes resulting from the numerical (a) subtraction and (b) multiplication of sinusoidal interferograms.

Fig. 5
Fig. 5

Moire phase distribution resulting from the numerical subtraction of the sawtooth phase functions ψt and ψm.

Fig. 6
Fig. 6

(a) Display of the absolute value of |ψtψm|. The thin lines indicate the setting of the threshold levels. (b) The resulting gray-level display.

Fig. 7
Fig. 7

Phase map obtained by gray-level windowing of Fig. 5.

Fig. 8
Fig. 8

Moire phase distribution corresponding to the difference in displacements of two plates, one flaw-free and the other with a flaw, subjected to slightly different loadings. (b) Result obtained after thresholding the interferogram shown in (a).

Fig. 9
Fig. 9

Interference phase distributions ψc corresponding to the difference in displacements: (a) two plates, one flaw-free and the other with a flaw, subjected to identical loadings; (b) two identical flaw-free plates subjected to unequal loadings; and (c) two plates, one flaw-free and the other with a flaw, subjected to unequal loadings.

Fig. 10
Fig. 10

Three-dimensional plot of the difference phase distribution obtained in Fig. 9(b).

Equations (9)

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ϕ m [ S ( P ) , U 1 ( P ) ] = 2 N 1 π ,
ϕ t [ S ( P ) , U 2 ( P ) ] = 2 N 2 π .
ϕ m [ S ( P ) , U 1 ( P ) ] ϕ t [ S ( P ) , U 2 ( P ) ] = 2 N m π
ψ i = ϕ i 2 π Int ( ϕ i 2 π ) ,
ψ c = ϕ t ϕ m 2 π Int ( ϕ t ϕ m 2 π ) .
ψ c = ψ t ψ m + 2 π K ,
K = Int ( ϕ t 2 π ) Int ( ϕ m 2 π ) Int ( ϕ t ϕ m 2 π ) .
K = { 1 if ψ t ψ m < 0 , 0 otherwise .
ψ i = tan 1 3 ( I 1 I 3 ) 2 I 2 I 1 I 3 ,

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