Abstract

A bismuth silicon oxide crystal is used in the diffusion regime as a dynamic recording medium in a real-time holographic interferometer based on anisotropic self-diffraction. This device is connected with an interferogram-analysis method that uses the phase-shifting technique for quantitative measurement of diffusive-reflecting object deformations. In addition to the usual error sources in phase shifting, the temporal interferogram erasure is studied and is found weakly perturbative for the measured phase. It is shown that quantitative measurements are possible for low-intensity object beams (8 μW/cm2) and a large observed area. A practical situation of defect monitoring in a composite structure is presented.

© 1995 Optical Society of America

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References

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  1. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  2. P. K. Rastogi, ed., Holographic interferometry: Principles and Methods, Vol. 68 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1994).
  3. P. Smigielski, Holographie Industrielle (Teknea, Toulouse, 1994).
  4. P. Hariharan, Optical Holography: Principles, Techniques and Applications, Vol. 2 of Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, UK, 1986).
  5. P. Günter, J.-P. Huignard, eds., Photorefractive Materials and Their Applications: Survey of Applications, Vol. 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1989).
  6. M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, Vol. 59 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1991).
  7. S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Prog. Phys. 57, 39–116 (1994).
    [CrossRef]
  8. P. Günter, J.-P. Huignard, eds., Photorefractive Materials and Their Applications: Fundamental Phenomena, Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988).
    [CrossRef]
  9. H. J. Tiziani, “Real-time metrology with BSO crystals,” Opt. Acta 29, 463–470 (1982).
    [CrossRef]
  10. R. C. Troth, J. C. Dainty, “Holographic interferometry using anisotropic self-diffraction in Bi12SiO20,” Opt. Lett. 16, 53–55 (1991).
    [CrossRef] [PubMed]
  11. V. I. Vlad, D. Popa, M. P. Petrov, A. A. Kamshilin, “Optical testing by dynamic holographic interferometry with photorefractive crystals and computer image processing,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1332, 237–244 (1990).
  12. D. Dirksen, G. von Bally, “Holographic double-exposure interferometry in near real time with photorefractive crystals,” J. Opt. Soc. Am. B 11, 1858–1863 (1994).
    [CrossRef]
  13. H. J. Tiziani, “Fringe analysis in holography with BSO applications,” in Second French-German Congress on Applications of Holography, P. Smigielski, ed. (HOLO3, Saint-Louis, France, 1988).
  14. A. A. Kamshilin, M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
    [CrossRef]
  15. H. Kogelnik, “Coupled-wave theory of thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  16. S. Mallick, D. Rouède, A. G. Apostolidis, “Efficiency and polarization characteristics of photorefractive diffraction in a Bi12SiO20 crystal,” J. Opt. Soc. Am. B 4, 1247–1259 (1987).
    [CrossRef]
  17. A. Marrakchi, R. V. Johnson, A. R. Tanguay, “Polarization properties of photorefractive diffraction in electro-optic and optically active sillenite crystals (Bragg regime),” J. Opt. Soc. Am. B 3, 321–336 (1986).
    [CrossRef]
  18. D. W. Robinson, G. T. Reid, eds., Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, London, 1993).
  19. T. M. Kreis, “Review of digital processing of holographic interferograms,” in Third French-German Congress on Applications of Holography, P. Smigielski, ed. (HOLO3, Saint-Louis, France, 1991).

1994 (2)

1991 (1)

1987 (1)

1986 (1)

1985 (1)

A. A. Kamshilin, M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

1982 (1)

H. J. Tiziani, “Real-time metrology with BSO crystals,” Opt. Acta 29, 463–470 (1982).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled-wave theory of thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Apostolidis, A. G.

Dainty, J. C.

Dirksen, D.

Hariharan, P.

P. Hariharan, Optical Holography: Principles, Techniques and Applications, Vol. 2 of Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, UK, 1986).

Johnson, R. V.

Kamshilin, A. A.

A. A. Kamshilin, M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

V. I. Vlad, D. Popa, M. P. Petrov, A. A. Kamshilin, “Optical testing by dynamic holographic interferometry with photorefractive crystals and computer image processing,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1332, 237–244 (1990).

Khomenko, A. V.

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, Vol. 59 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1991).

Kogelnik, H.

H. Kogelnik, “Coupled-wave theory of thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Kreis, T. M.

T. M. Kreis, “Review of digital processing of holographic interferograms,” in Third French-German Congress on Applications of Holography, P. Smigielski, ed. (HOLO3, Saint-Louis, France, 1991).

Mallick, S.

Marrakchi, A.

Petrov, M. P.

A. A. Kamshilin, M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

V. I. Vlad, D. Popa, M. P. Petrov, A. A. Kamshilin, “Optical testing by dynamic holographic interferometry with photorefractive crystals and computer image processing,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1332, 237–244 (1990).

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, Vol. 59 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1991).

Popa, D.

V. I. Vlad, D. Popa, M. P. Petrov, A. A. Kamshilin, “Optical testing by dynamic holographic interferometry with photorefractive crystals and computer image processing,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1332, 237–244 (1990).

Rouède, D.

Smigielski, P.

P. Smigielski, Holographie Industrielle (Teknea, Toulouse, 1994).

Stepanov, S. I.

S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Prog. Phys. 57, 39–116 (1994).
[CrossRef]

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, Vol. 59 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1991).

Tanguay, A. R.

Tiziani, H. J.

H. J. Tiziani, “Real-time metrology with BSO crystals,” Opt. Acta 29, 463–470 (1982).
[CrossRef]

H. J. Tiziani, “Fringe analysis in holography with BSO applications,” in Second French-German Congress on Applications of Holography, P. Smigielski, ed. (HOLO3, Saint-Louis, France, 1988).

Troth, R. C.

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

Vlad, V. I.

V. I. Vlad, D. Popa, M. P. Petrov, A. A. Kamshilin, “Optical testing by dynamic holographic interferometry with photorefractive crystals and computer image processing,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1332, 237–244 (1990).

von Bally, G.

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled-wave theory of thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

J. Opt. Soc. Am. B (3)

Opt. Acta (1)

H. J. Tiziani, “Real-time metrology with BSO crystals,” Opt. Acta 29, 463–470 (1982).
[CrossRef]

Opt. Commun. (1)

A. A. Kamshilin, M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

Opt. Lett. (1)

Rep. Prog. Phys. (1)

S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Prog. Phys. 57, 39–116 (1994).
[CrossRef]

Other (11)

P. Günter, J.-P. Huignard, eds., Photorefractive Materials and Their Applications: Fundamental Phenomena, Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988).
[CrossRef]

V. I. Vlad, D. Popa, M. P. Petrov, A. A. Kamshilin, “Optical testing by dynamic holographic interferometry with photorefractive crystals and computer image processing,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1332, 237–244 (1990).

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

P. K. Rastogi, ed., Holographic interferometry: Principles and Methods, Vol. 68 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1994).

P. Smigielski, Holographie Industrielle (Teknea, Toulouse, 1994).

P. Hariharan, Optical Holography: Principles, Techniques and Applications, Vol. 2 of Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, UK, 1986).

P. Günter, J.-P. Huignard, eds., Photorefractive Materials and Their Applications: Survey of Applications, Vol. 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1989).

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, Vol. 59 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1991).

H. J. Tiziani, “Fringe analysis in holography with BSO applications,” in Second French-German Congress on Applications of Holography, P. Smigielski, ed. (HOLO3, Saint-Louis, France, 1988).

D. W. Robinson, G. T. Reid, eds., Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, London, 1993).

T. M. Kreis, “Review of digital processing of holographic interferograms,” in Third French-German Congress on Applications of Holography, P. Smigielski, ed. (HOLO3, Saint-Louis, France, 1991).

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Figures (10)

Fig. 1
Fig. 1

BSO crystal configuration used for real-time holographic interferometry, with grating vector K parallel to the 〈110〉 direction.

Fig. 2
Fig. 2

Orientations of the linear polarizations of the different object beams involved with respect to the principal axis x of the crystal. Vectors P i , P d , and P t are drawn with different lengths that are qualitatively proportional to the intensities of the corresponding beams.

Fig. 3
Fig. 3

Holographic interferometer setup that uses a BSO crystal. DPZT, deformation piezoelectric translator.

Fig. 4
Fig. 4

Plot of the modulation m as a function of t/τ compared with the diffracted-intensity exponential decrease.

Fig. 5
Fig. 5

Computed rms error (as a fraction of a wave) made on the calculated phase in the presence of a modulation decrease.

Fig. 6
Fig. 6

Erasure time in seconds measured as a function of the intensity ratio R for an object-beam intensity of 8 μW/cm2.

Fig. 7
Fig. 7

Certification experiment: sequence of operations.

Fig. 8
Fig. 8

Certification experiment: (a) one of the interferograms obtained after deformation of the plate (the zones corresponding to the central mirror and the attachment points are masked), (b) the corresponding phase calculated modulo 2π by phase shifting, (c) the phase map after unwrapping of (b).

Fig. 9
Fig. 9

Phase profile along the line passing through the lower-left and the upper-right attachment points. The solid curve represents the polynomial fit of the data to obtain the phase in the masked area.

Fig. 10
Fig. 10

Application to defects detection: (a) one of the interferograms obtained after thermal infrared stimulation of the composite sample, (b) the corresponding phase calculated modulo 2π by phase shifting, and (c) a three-dimensional view of the global deformation including defects (ordinates in radians).

Tables (1)

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Table 1 Results of Elongation Obtained by Holographic Interferometry and by a Michelson Interferometer

Equations (11)

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η 0 = exp ( - α l / cos θ ) sin 2 ( π Δ n l λ cos θ ) ,
η = η 0 sinc 2 ( ρ l ) ,
I ( u , v ) = I 0 ( u , v ) { 1 + m ( u , v ) cos [ ϕ ( u , v ) ] } ,
I k ( u , v ) = I 0 ( u , v ) { 1 + m ( u , v ) cos [ ϕ ( u , v ) + Δ ϕ k ( u , v ) ] } ,
ϕ ( u , v ) = tan - 1 ( I 4 - I 2 I 1 - I 3 ) .
ϕ ( u , v ) = tan - 1 ( { ( I 1 - I 4 + I 2 - I 3 ) [ 3 ( I 2 - I 3 ) - ( I 1 - I 4 ) ] } 1 / 2 ( I 2 + I 3 ) - ( I 1 + I 4 ) ) .
m = I max - I min I max + I min = 2 ( I d I t ) 1 / 2 I d + I t ,
I d = I d ( t ) = I d , 0 exp ( - t / τ ) .
m = m ( t ) = 2 exp ( - t / 2 τ ) 1 + exp ( - t / τ ) .
e ϕ = [ ( e md ) 2 + ( e nld ) 2 + ( e q ) 2 + ( e vib ) 2 ] 1 / 2 e vib = λ / 40.
L = ϕ c λ 2 π [ cos ( θ 1 ) + cos ( θ 2 ) ] ,

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