Abstract

The practical use of holographic interferometry in nondestructive testing leads to many situations in which the characteristics of the fringe patterns make the observation and subsequent interpretation of the fringes difficult. Fringe control may then be employed to correct the troublesome parameters, the most commonly treated of which is fringe spacing. To gain more powerful control, a novel method is presented here that also permits one to change the localization of the fringe pattern. General vectorial expressions are derived that relate a tilt in the reference beam to a change in the fringe localization. Moreover the changes introduced into the fringe vector by this tilt can be suppressed by an adequate shift of the illumination beam focus. Some illustrative examples for a plane object are presented.

© 1992 Optical Society of America

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References

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  1. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  2. J. P. Waters, “Interferometric Holography,” in Holographic Nondestructive Testing, R. K. Erf, ed. (Academic, San Diego, Calif., 1974).
  3. O. D. D. Soares, J. F. Fernandez, “Moire Evaluation Holography,” in International Conference on Holography Applications, ed., Proc. Soc. Photo-Opt. Instrum. Eng.673, 198–206 (1986).
    [CrossRef]
  4. O. D. D. Soares, A. L. V. S. Lage, L. M. Bernardo, “Moiré evaluation with fringe patterns of interferograms, holograms, moirégrams and specklegrams,” in Optical Metrology, O. D. D. Soares, ed. (Nijhoff, Dordrecht, The Netherlands, 1987).
  5. J. Blanco-García, J. L. Fernández, C. Lopez, A. F. Doval, M. Pérez-Amor, “Annulling parasitic fringes in real-time holographic interferometry: a new method,” Appl. Opt. 30, 1588–1590 (1991).
    [CrossRef] [PubMed]
  6. P. K. Rastogi, P. Jacquot, L. Pflug, “Holographic interferometry applied at subfreezing temperatures: study of damage in concrete exposed to frost action,” Opt. Eng. 27, 172–178 (1988).
    [CrossRef]
  7. C. A. Sciammarella, “Holographic moire, an optical tool for determination of displacements, strains, contours and slopes of surfaces,” Opt. Eng. 21, 447–457 (1982).
    [CrossRef]
  8. M. Yonemura, “Holographic contour generation by spatial frequency modulation,” Appl. Opt. 21, 3652–3658 (1982).
    [CrossRef] [PubMed]
  9. K. A. Stetson, “A rigourous treatment of the fringes of hologram interferometry,” Optik 29, 386–400 (1969).
  10. S. Walles, “Visibility and localization of fringes in holographic interferometry of diffusely reflecting surfaces,” Ark. Fys. 40, 299–403 (1970).
  11. W. Schumann, M. Dubas, Holographic Interferometry (Springer-Verlag, Berlin, 1979).
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  13. T. Tsuruta, N. Shiotake, Y. Itoh, “Formation and localization of holographically produced interference fringes,” Opt. Acta 16, 723–733 (1969).
    [CrossRef]
  14. W. Schumann, “Some aspects of the optical techniques for strain determination,” Exp. Mech. 13, 225–231 (1973).
    [CrossRef]
  15. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971).
  16. I. S. Sokolnikoff, Tensor Analysis: Theory and Applications (Wiley, New York, 1951).
  17. K. A. Stetson, “Matrix methods in hologram interferometry,” in Optical Metrology, O. D. D. Soares, ed. (Nijhoff, Dordrecht, The Netherlands, 1987).

1991 (1)

1988 (1)

P. K. Rastogi, P. Jacquot, L. Pflug, “Holographic interferometry applied at subfreezing temperatures: study of damage in concrete exposed to frost action,” Opt. Eng. 27, 172–178 (1988).
[CrossRef]

1982 (2)

C. A. Sciammarella, “Holographic moire, an optical tool for determination of displacements, strains, contours and slopes of surfaces,” Opt. Eng. 21, 447–457 (1982).
[CrossRef]

M. Yonemura, “Holographic contour generation by spatial frequency modulation,” Appl. Opt. 21, 3652–3658 (1982).
[CrossRef] [PubMed]

1973 (1)

W. Schumann, “Some aspects of the optical techniques for strain determination,” Exp. Mech. 13, 225–231 (1973).
[CrossRef]

1970 (1)

S. Walles, “Visibility and localization of fringes in holographic interferometry of diffusely reflecting surfaces,” Ark. Fys. 40, 299–403 (1970).

1969 (2)

T. Tsuruta, N. Shiotake, Y. Itoh, “Formation and localization of holographically produced interference fringes,” Opt. Acta 16, 723–733 (1969).
[CrossRef]

K. A. Stetson, “A rigourous treatment of the fringes of hologram interferometry,” Optik 29, 386–400 (1969).

Bernardo, L. M.

O. D. D. Soares, A. L. V. S. Lage, L. M. Bernardo, “Moiré evaluation with fringe patterns of interferograms, holograms, moirégrams and specklegrams,” in Optical Metrology, O. D. D. Soares, ed. (Nijhoff, Dordrecht, The Netherlands, 1987).

Blanco-García, J.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971).

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971).

Doval, A. F.

Dubas, M.

W. Schumann, M. Dubas, Holographic Interferometry (Springer-Verlag, Berlin, 1979).

Fernandez, J. F.

O. D. D. Soares, J. F. Fernandez, “Moire Evaluation Holography,” in International Conference on Holography Applications, ed., Proc. Soc. Photo-Opt. Instrum. Eng.673, 198–206 (1986).
[CrossRef]

Fernández, J. L.

Itoh, Y.

T. Tsuruta, N. Shiotake, Y. Itoh, “Formation and localization of holographically produced interference fringes,” Opt. Acta 16, 723–733 (1969).
[CrossRef]

Jacquot, P.

P. K. Rastogi, P. Jacquot, L. Pflug, “Holographic interferometry applied at subfreezing temperatures: study of damage in concrete exposed to frost action,” Opt. Eng. 27, 172–178 (1988).
[CrossRef]

Lage, A. L. V. S.

O. D. D. Soares, A. L. V. S. Lage, L. M. Bernardo, “Moiré evaluation with fringe patterns of interferograms, holograms, moirégrams and specklegrams,” in Optical Metrology, O. D. D. Soares, ed. (Nijhoff, Dordrecht, The Netherlands, 1987).

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971).

Lopez, C.

Pérez-Amor, M.

Pflug, L.

P. K. Rastogi, P. Jacquot, L. Pflug, “Holographic interferometry applied at subfreezing temperatures: study of damage in concrete exposed to frost action,” Opt. Eng. 27, 172–178 (1988).
[CrossRef]

Rastogi, P. K.

P. K. Rastogi, P. Jacquot, L. Pflug, “Holographic interferometry applied at subfreezing temperatures: study of damage in concrete exposed to frost action,” Opt. Eng. 27, 172–178 (1988).
[CrossRef]

Schumann, W.

W. Schumann, “Some aspects of the optical techniques for strain determination,” Exp. Mech. 13, 225–231 (1973).
[CrossRef]

W. Schumann, M. Dubas, Holographic Interferometry (Springer-Verlag, Berlin, 1979).

Sciammarella, C. A.

C. A. Sciammarella, “Holographic moire, an optical tool for determination of displacements, strains, contours and slopes of surfaces,” Opt. Eng. 21, 447–457 (1982).
[CrossRef]

Shiotake, N.

T. Tsuruta, N. Shiotake, Y. Itoh, “Formation and localization of holographically produced interference fringes,” Opt. Acta 16, 723–733 (1969).
[CrossRef]

Soares, O. D. D.

O. D. D. Soares, J. F. Fernandez, “Moire Evaluation Holography,” in International Conference on Holography Applications, ed., Proc. Soc. Photo-Opt. Instrum. Eng.673, 198–206 (1986).
[CrossRef]

O. D. D. Soares, A. L. V. S. Lage, L. M. Bernardo, “Moiré evaluation with fringe patterns of interferograms, holograms, moirégrams and specklegrams,” in Optical Metrology, O. D. D. Soares, ed. (Nijhoff, Dordrecht, The Netherlands, 1987).

Sokolnikoff, I. S.

I. S. Sokolnikoff, Tensor Analysis: Theory and Applications (Wiley, New York, 1951).

Stetson, K. A.

K. A. Stetson, “A rigourous treatment of the fringes of hologram interferometry,” Optik 29, 386–400 (1969).

K. A. Stetson, “Matrix methods in hologram interferometry,” in Optical Metrology, O. D. D. Soares, ed. (Nijhoff, Dordrecht, The Netherlands, 1987).

Tsuruta, T.

T. Tsuruta, N. Shiotake, Y. Itoh, “Formation and localization of holographically produced interference fringes,” Opt. Acta 16, 723–733 (1969).
[CrossRef]

Vest, C. M.

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

Walles, S.

S. Walles, “Visibility and localization of fringes in holographic interferometry of diffusely reflecting surfaces,” Ark. Fys. 40, 299–403 (1970).

Waters, J. P.

J. P. Waters, “Interferometric Holography,” in Holographic Nondestructive Testing, R. K. Erf, ed. (Academic, San Diego, Calif., 1974).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Yonemura, M.

Appl. Opt. (2)

Ark. Fys. (1)

S. Walles, “Visibility and localization of fringes in holographic interferometry of diffusely reflecting surfaces,” Ark. Fys. 40, 299–403 (1970).

Exp. Mech. (1)

W. Schumann, “Some aspects of the optical techniques for strain determination,” Exp. Mech. 13, 225–231 (1973).
[CrossRef]

Opt. Acta (1)

T. Tsuruta, N. Shiotake, Y. Itoh, “Formation and localization of holographically produced interference fringes,” Opt. Acta 16, 723–733 (1969).
[CrossRef]

Opt. Eng. (2)

P. K. Rastogi, P. Jacquot, L. Pflug, “Holographic interferometry applied at subfreezing temperatures: study of damage in concrete exposed to frost action,” Opt. Eng. 27, 172–178 (1988).
[CrossRef]

C. A. Sciammarella, “Holographic moire, an optical tool for determination of displacements, strains, contours and slopes of surfaces,” Opt. Eng. 21, 447–457 (1982).
[CrossRef]

Optik (1)

K. A. Stetson, “A rigourous treatment of the fringes of hologram interferometry,” Optik 29, 386–400 (1969).

Other (9)

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

J. P. Waters, “Interferometric Holography,” in Holographic Nondestructive Testing, R. K. Erf, ed. (Academic, San Diego, Calif., 1974).

O. D. D. Soares, J. F. Fernandez, “Moire Evaluation Holography,” in International Conference on Holography Applications, ed., Proc. Soc. Photo-Opt. Instrum. Eng.673, 198–206 (1986).
[CrossRef]

O. D. D. Soares, A. L. V. S. Lage, L. M. Bernardo, “Moiré evaluation with fringe patterns of interferograms, holograms, moirégrams and specklegrams,” in Optical Metrology, O. D. D. Soares, ed. (Nijhoff, Dordrecht, The Netherlands, 1987).

W. Schumann, M. Dubas, Holographic Interferometry (Springer-Verlag, Berlin, 1979).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971).

I. S. Sokolnikoff, Tensor Analysis: Theory and Applications (Wiley, New York, 1951).

K. A. Stetson, “Matrix methods in hologram interferometry,” in Optical Metrology, O. D. D. Soares, ed. (Nijhoff, Dordrecht, The Netherlands, 1987).

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Figures (10)

Fig. 1
Fig. 1

Rays contributing to the complex amplitude at any point K: O.S., observation system; P, and P′, points on the undeformed and deformed surfaces, respectively.

Fig. 2
Fig. 2

Variation of the optical path difference with the observation direction from any observation point O.

Fig. 3
Fig. 3

Variation of the illumination length with the displacement of the illumination source.

Fig. 4
Fig. 4

Mechanical and optical displacements by tilting the reference beam. H.P. is the hologram plate.

Fig. 5
Fig. 5

Optical arrangement described in Section IV. D. S. is the plane diffusing surface; R. B. is the reference beam.

Fig. 6
Fig. 6

Relationship between elementary vectors on the hologram plate and the vectors on the object plane surface.

Fig. 7
Fig. 7

Schematic of the examples examined in special cases.

Fig. 8
Fig. 8

Fringe pattern caused by an in-plane translation of the object, u = 0.05 mm: (a) The fringe pattern is focused 1 m behind the object surface. (b) The fringe pattern is carried to the object surface by tilting the reference beam. (c) The fringe pattern is a few centimeters in front of the object surface.

Fig. 9
Fig. 9

Fringe pattern caused by an out-of-plane translation of the object, u = 0.15 mm: (a) The fringes are focused on the right-hand side of the object 20 cm behind the surface. (b) The same fringes are carried to the surface. (c) The fringes are focused 10 cm in front of the surface on its left side. (d) The same fringes are carried to the surface.

Fig. 10
Fig. 10

Object rotated at an angle of 2 arcmin about a vertical axis located 2 cm behind the surface and 5 cm to the right from the center of the cross. (The width of the cross lines is 5 mm.) (a) The fringes are as close to the surface as they appear. (b) The fringes are carried to infinity; is not compensated for the fringe vector

Equations (56)

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U ( K ) = A S L S | L | κ ( γ, β ) G ( P ) exp [ 2 π i λ ( L S L ) ] d A ,
U ( K ) = exp ( 2 π i λ D ) A S L S | L | κ ( γ , β ) G ( P ) × exp [ 2 π i λ ( L S L d D K ) ] d A ,
I ( K ) = E [ U U * ] + E [ U U * ] + E [ U U * ] + E [ U * U ] .
I ( K ) = 2 { I 0 + | Γ | cos [ 2 π λ ( D + δ ) ] } ,
Γ = exp ( 2 π i λ D ) A C | S | 2 L S 2 L 2 | κ ( λ , β ) | 2 exp ( 2 π i λ d D K ) d A = | r | exp [ 2 π i λ ( D + δ ) ] ,
V = I max I min I max + I min = | Γ | I 0 = | A C | S | 2 L S 2 L 2 | κ ( γ , β ) | 2 exp ( 2 π i λ d D K ) d A | A C | S | 2 L S 2 L 2 | κ ( γ , β ) | 2 d A .
V = 2 | J 1 ( 2 π λ L L + L 0 r ° | n D K | ) 2 π λ L L + L 0 r ° | n D K | | ,
d D K = d r · n D K ,
d V d L = 0 .
d d L | L L + L 0 | n D K | | = 0 .
d D o = d r · n D o ,
d D o d s = e ˆ · n D o .
Δ s = λ | n D o | .
Δ s L = L 0 L L 0 λ | n D o | .
D = u · g ,
D = ( L S L ) ( L S L ) = ( L S L S ) ( L L ) ,
L S = | d + L S h ˆ + u | = ( d 2 + L S 2 + u 2 2 L S d · h ˆ 2 d · h ˆ + 2 L S u · h ˆ ) 1 / 2 ,
L S L S = L S L S ( 1 + d 2 L S 2 + u 2 L S 2 2 d · h ˆ L S 2 d · u L S 2 + 2 u · h ˆ L S ) 1 / 2 .
L S L S d · h ˆ u · h ˆ .
L L = u · k ˆ .
D = d · h ˆ u · h ˆ + u · k ˆ = u · g + d · h ˆ .
D = ( L S * L * ) ( L S L ) .
2 π λ p * + ϕ S * 2 π λ c ˆ * · r ψ* = 2 π λ p + ϕ S 2 π λ c ˆ · r ψ,
L S * = λ 2 π ϕ S * = ( p p * ) ( c ˆ c ˆ * ) · r λ 2 π ( ψ ψ* ) + L S .
D = ( L S L S ) ( L * L ) + ( p p * ) ( c ˆ c ˆ * ) · r λ 2 π ( ϕ ϕ * ) .
D = u · h ˆ + u * · k ˆ + v · k ˆ Δ c ˆ · r λ 2 π ( ψ ψ* ) = u · g Δ c ˆ · r λ 2 π ( ψ ψ* ) .
D = u · g + d · h ˆ Δ c ˆ · r λ 2 π ( ψ ψ* ) ,
n D K = n ( u · g ) + n ( d · h ˆ ) n ( Δ c ˆ · r ) .
n ( u · g ) = N ( u · g ) = N [ u · g + g · u ] = N ( w + 1 L K u ) ,
w = u · g 1 L S H u .
n ( d · h ) = N ( d · h ˆ + h ˆ · d ) = 1 L S N H d ,
n ( Δ c ˆ · r ) = n Δ c ˆ · r + n r · Δ c ˆ ,
d r p + L = d r ° L .
r = L + p L I .
n D k = N w + 1 L N H u + 1 L S N H d L + p L N Δ c .
d d L | L L + L o × [ ( N w + 1 L N H u + 1 L S N H d L + p L N Δ c ˆ ) 2 ] 1 / 2 | = 0 ,
L = ( N H u p N Δ c ) · ( N w 1 L 0 N H u + 1 L S N H d L 0 p L 0 N Δ c ˆ ) ( N w + 1 L N H d N Δ c ) · ( N w 1 L 0 N H u + 1 L S N H d L 0 p L 0 N Δ c ˆ ) .
n D 0 = N w 1 L 0 N H u + 1 L S N H d L 0 p L 0 N Δ c ˆ .
L = ( N H u p N Δ c ˆ ) · n D 0 ( N w + 1 L S N H d N Δ c ) · n D 0 .
p N Δ c = N H u .
K v = p M Δ c ,
N K v = p N Δ c ˆ .
N K v = N K u .
Δ ϑ N m = N K u p .
n D K = N w N K u p + 1 L S N H d ,
N H d = L S L o p L o N Δ c .
Δ s Δ s L = L o L o + L .
L = sin ( α + ϕ ) cos α sin ( ϕ β ) cos β L S .
Δ ϑ cos ϑ = u p sin ( ϕ + α ) cos α .
L a L S cos 2 β ,
Δ ϑ = u p cos ϑ ,
L = sin 2 α sin 2 β 2 ( x a ) sin 2 β L S L o .
Δ ϑ = u sin 2 α 2 p cos ϑ ( x a ) L o cos ϑ u p .
u = γ x ˆ j ˆ + t i ˆ ,
L = ( a + L o sin α ) sin 2 α 2 t γ cos 2 α 2 ( cos α + cos β ) + ( a + L o sin α ) sin 2 β + 2 t γ cos 2 β L S .
Δ ϑ = 1 2 γ ( a + L o sin α ) sin 2 α + t cos 2 α p cos ϑ .

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