Abstract

An improvement for holographic nondestructive testing in the field of information processing is proposed. It makes use of an optically generated zone plate for obtaining an interferometric hologram of an object suffering a deformation. This allows quick data acquisition and can be used outside laboratory conditions. Experimental results are discussed, and a brief mathematical analysis from the point of view of Fourier optics is also given.

© 1986 Optical Society of America

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References

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  1. R. Erf, Speckle Metrology (Academic, New York, 1978).
  2. R. Erf, Holographic Nondestructive Testing (Academic, New York, 1974).
  3. H. Glunder, R. Lenz, “Fault Detection in Nondestructive Testing (NDT) by an Optoelectronic Hybrid Processor,” in Holographic Data Nondestructive Testing, D. Vukicevic, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.370, 4 (1983).
    [CrossRef]
  4. W. Kock, Engineering Applications of Lasers and Holography (Plenum, New York, 1977), p. 49.
  5. M. H. Horman, H. H. M. Chau, “Zone Plate Theory Based on Holography,” Appl. Opt. 6, 317 (1967).
    [CrossRef] [PubMed]
  6. E. B. Champagne, “Optical Method for Producing Fresnel Zone Plates,” Appl. Opt. 7, 381 (1968).
    [CrossRef] [PubMed]
  7. H. H. M. Chau, “Zone Plates Produced Optically,” Appl. Opt. 8, 1209 (1969).
    [CrossRef] [PubMed]
  8. H. H. Barrett, F. A. Horrigan, “Fresnel Zone Plate Image of Gamma Rays; Theory,” Appl. Opt. 12, 2686 (1973).
    [CrossRef] [PubMed]
  9. G. B. Brandt, “Image Plane Holography,” Appl. Opt. 8, 1421 (1969).
    [CrossRef] [PubMed]
  10. M. Françon, La granularité laser (speckle) et ses applications en optique (Masson, Paris, 1968).
  11. M. Young, “Zone Plates and Their Aberrations,” J. Opt. Soc. Am. 62, 972 (1972).
    [CrossRef]
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

1973 (1)

1972 (1)

1969 (2)

1968 (1)

1967 (1)

Barrett, H. H.

Brandt, G. B.

Champagne, E. B.

Chau, H. H. M.

Erf, R.

R. Erf, Speckle Metrology (Academic, New York, 1978).

R. Erf, Holographic Nondestructive Testing (Academic, New York, 1974).

Françon, M.

M. Françon, La granularité laser (speckle) et ses applications en optique (Masson, Paris, 1968).

Glunder, H.

H. Glunder, R. Lenz, “Fault Detection in Nondestructive Testing (NDT) by an Optoelectronic Hybrid Processor,” in Holographic Data Nondestructive Testing, D. Vukicevic, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.370, 4 (1983).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Horman, M. H.

Horrigan, F. A.

Kock, W.

W. Kock, Engineering Applications of Lasers and Holography (Plenum, New York, 1977), p. 49.

Lenz, R.

H. Glunder, R. Lenz, “Fault Detection in Nondestructive Testing (NDT) by an Optoelectronic Hybrid Processor,” in Holographic Data Nondestructive Testing, D. Vukicevic, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.370, 4 (1983).
[CrossRef]

Young, M.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

Other (6)

R. Erf, Speckle Metrology (Academic, New York, 1978).

R. Erf, Holographic Nondestructive Testing (Academic, New York, 1974).

H. Glunder, R. Lenz, “Fault Detection in Nondestructive Testing (NDT) by an Optoelectronic Hybrid Processor,” in Holographic Data Nondestructive Testing, D. Vukicevic, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.370, 4 (1983).
[CrossRef]

W. Kock, Engineering Applications of Lasers and Holography (Plenum, New York, 1977), p. 49.

M. Françon, La granularité laser (speckle) et ses applications en optique (Masson, Paris, 1968).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (4)

Fig. 1
Fig. 1

Image formation of a point source by means of a zone plate. O.P.S., object point source; V.P.S., virtual image of the point source; R.P.S., real image of the point source; Z.P., zone plate.

Fig. 2
Fig. 2

Recording geometry: L, laser light; O, object under test; Z.P., zone plate; H.P., holographic plate placed where the object real image is formed. The unscattered light provides the reference beam needed for the holographic record.

Fig. 3
Fig. 3

Reconstructed virtual image of a loaded cantilever obtained with this method, where the equal deformation contours along the object can be seen.

Fig. 4
Fig. 4

Scheme showing the parameters used for the calculus of the field distribution: P0 is the object point source; d0 is the distance between the object plane and the zone plate plane; T is the zone plate; dR is the distance between the zone plate and the observation plane.

Equations (6)

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U R ( y R , z R ) = exp ( 2 π i λ d R ) i λ d R - U T ( y T , z T ) t ( y T , z T ) P ( y T , z T ) × exp { π i λ d R [ ( y R - y T ) 2 + ( z R - z T ) 2 } d y T d z T ,
U T ( y T , z T ) = A 0 i λ d 0 exp ( 2 π i λ d 0 ) × exp { i π λ d 0 [ ( y T - y 0 ) 2 + ( z T - z 0 ) 2 ] } .
t ( Y T , Z T ) = T 0 + B exp [ 2 π i λ C ( Y T 2 + Z T 2 ) ] + B * × exp [ - 2 π i λ C ( Y T 2 + Z T 2 ) ] ,
U R 0 ( y R , z R ) = A 0 ɛ exp { i π λ ( d 0 + d R ) [ ( y R - y 0 ) 2 + ( z R - z 0 ) 2 ] } , U R 1 ( y R , z R ) = A 0 γ exp { i π λ f p + d 0 f p ( d 0 + d R ) + d 0 d R [ ( y R - f p f p + d 0 y 0 ) 2 + ( z R - f p f p + d 0 z 0 ) 2 ] } , U R - 1 ( y R , z R ) = A 0 μ exp { i π λ f p - d 0 f p ( d 0 + d R ) - d 0 d R [ ( y R - f p f p - d 0 y 0 ) 2 + ( z R - f p f p - d 0 z 0 ) 2 ] } ,
f p ( d 0 + d R ) + d 0 d R f p + d 0 , f p ( d 0 + d R ) - d 0 d R f p - d 0 ,
f p f p + d 0 , f p f p - d 0 .

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