Abstract

The known techniques for making incoherent holograms succeed for an object containing a small number of points; however, they fail in practice for an object with a great many discrete points or for an object with a continuous intensity distribution. This results because the intensity pattern generated in incoherent holography in a superposition of random intensity patterns generated by the individual object points. Thus, the intensity pattern contains a large bias level which masks the relatively small spatial variations of the pattern in the recording film grain noise. This paper describes a technique for eliminating the bias. By introducing a narrow band time modulation of the light in one path of an interferometer used to generate the hologram intensity pattern, the spatially varying part of the hologram intensity pattern is modulated at the time frequency, while the bias part is unmodulated. The bias part can then be eliminated by performing a point-by-point time correlation over the hologram plane. Experimental results are presented.

© 1969 Optical Society of America

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References

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  1. L. Mertz, N. O. Young, Proceedings of the ICO Conference on Optical Instruments (Chapman and Hall, London, 1961), p. 305.
  2. G. Cochran, J. Opt. Soc. Amer. 56, 1513 (1966).
    [Crossref]
  3. A. Lohmann, J. Opt. Soc. Amer. 55, 1556 (1965).
    [Crossref]
  4. P. J. Peters, Appl. Phys. Lett. 8, 209 (1966).
    [Crossref]
  5. J. T. Winthrop, C. R. Worthington, Phys. Lett. 15, 124 (1965).
    [Crossref]
  6. G. W. Stroke, R. C. Restrick, Appl. Phys. Lett. 7, 9 (1965).
  7. H. R. Worthington, J. Opt. Soc. Amer. 56, 1397 (1966).
    [Crossref]
  8. W. D. Montgomery, J. Opt. Soc. Amer. 56, 1769 (1967).
  9. O. Bryngdahl, A. Lohmann, J. Opt. Soc. Amer. 57, 1412A (1967).
  10. A. Kozma, J. Opt. Soc. Amer. 58, 436 (1968).
    [Crossref]
  11. C. N. Burckhardt, Appl. Opt. 6, 1359 (1967).
    [Crossref] [PubMed]
  12. M. Ryle, Proc. Roy. Soc. London A211, 351 (1952).
  13. L. Mertz, J. Opt. Soc. Amer. p. vii, May1964.

1968 (1)

A. Kozma, J. Opt. Soc. Amer. 58, 436 (1968).
[Crossref]

1967 (3)

W. D. Montgomery, J. Opt. Soc. Amer. 56, 1769 (1967).

O. Bryngdahl, A. Lohmann, J. Opt. Soc. Amer. 57, 1412A (1967).

C. N. Burckhardt, Appl. Opt. 6, 1359 (1967).
[Crossref] [PubMed]

1966 (3)

H. R. Worthington, J. Opt. Soc. Amer. 56, 1397 (1966).
[Crossref]

G. Cochran, J. Opt. Soc. Amer. 56, 1513 (1966).
[Crossref]

P. J. Peters, Appl. Phys. Lett. 8, 209 (1966).
[Crossref]

1965 (3)

J. T. Winthrop, C. R. Worthington, Phys. Lett. 15, 124 (1965).
[Crossref]

G. W. Stroke, R. C. Restrick, Appl. Phys. Lett. 7, 9 (1965).

A. Lohmann, J. Opt. Soc. Amer. 55, 1556 (1965).
[Crossref]

1964 (1)

L. Mertz, J. Opt. Soc. Amer. p. vii, May1964.

1952 (1)

M. Ryle, Proc. Roy. Soc. London A211, 351 (1952).

Bryngdahl, O.

O. Bryngdahl, A. Lohmann, J. Opt. Soc. Amer. 57, 1412A (1967).

Burckhardt, C. N.

Cochran, G.

G. Cochran, J. Opt. Soc. Amer. 56, 1513 (1966).
[Crossref]

Kozma, A.

A. Kozma, J. Opt. Soc. Amer. 58, 436 (1968).
[Crossref]

Lohmann, A.

O. Bryngdahl, A. Lohmann, J. Opt. Soc. Amer. 57, 1412A (1967).

A. Lohmann, J. Opt. Soc. Amer. 55, 1556 (1965).
[Crossref]

Mertz, L.

L. Mertz, J. Opt. Soc. Amer. p. vii, May1964.

L. Mertz, N. O. Young, Proceedings of the ICO Conference on Optical Instruments (Chapman and Hall, London, 1961), p. 305.

Montgomery, W. D.

W. D. Montgomery, J. Opt. Soc. Amer. 56, 1769 (1967).

Peters, P. J.

P. J. Peters, Appl. Phys. Lett. 8, 209 (1966).
[Crossref]

Restrick, R. C.

G. W. Stroke, R. C. Restrick, Appl. Phys. Lett. 7, 9 (1965).

Ryle, M.

M. Ryle, Proc. Roy. Soc. London A211, 351 (1952).

Stroke, G. W.

G. W. Stroke, R. C. Restrick, Appl. Phys. Lett. 7, 9 (1965).

Winthrop, J. T.

J. T. Winthrop, C. R. Worthington, Phys. Lett. 15, 124 (1965).
[Crossref]

Worthington, C. R.

J. T. Winthrop, C. R. Worthington, Phys. Lett. 15, 124 (1965).
[Crossref]

Worthington, H. R.

H. R. Worthington, J. Opt. Soc. Amer. 56, 1397 (1966).
[Crossref]

Young, N. O.

L. Mertz, N. O. Young, Proceedings of the ICO Conference on Optical Instruments (Chapman and Hall, London, 1961), p. 305.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

P. J. Peters, Appl. Phys. Lett. 8, 209 (1966).
[Crossref]

G. W. Stroke, R. C. Restrick, Appl. Phys. Lett. 7, 9 (1965).

J. Opt. Soc. Amer. (7)

H. R. Worthington, J. Opt. Soc. Amer. 56, 1397 (1966).
[Crossref]

W. D. Montgomery, J. Opt. Soc. Amer. 56, 1769 (1967).

O. Bryngdahl, A. Lohmann, J. Opt. Soc. Amer. 57, 1412A (1967).

A. Kozma, J. Opt. Soc. Amer. 58, 436 (1968).
[Crossref]

G. Cochran, J. Opt. Soc. Amer. 56, 1513 (1966).
[Crossref]

A. Lohmann, J. Opt. Soc. Amer. 55, 1556 (1965).
[Crossref]

L. Mertz, J. Opt. Soc. Amer. p. vii, May1964.

Phys. Lett. (1)

J. T. Winthrop, C. R. Worthington, Phys. Lett. 15, 124 (1965).
[Crossref]

Proc. Roy. Soc. London (1)

M. Ryle, Proc. Roy. Soc. London A211, 351 (1952).

Other (1)

L. Mertz, N. O. Young, Proceedings of the ICO Conference on Optical Instruments (Chapman and Hall, London, 1961), p. 305.

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Figures (7)

Fig. 1
Fig. 1

The reconstruction from an incoherent hologram made on the triangular interferometer. The object, which was transparent lettering, was illuminated by the green line of a broad Hg vapor source.

Fig. 2
Fig. 2

The modified Linnik interferometer. L1 and L2 are lenses of focal length f1 and f2. M are mirrors placed at the back focal plane of the lenses. O is the object, H the hologram plane, and BS a beam splitter.

Fig. 3
Fig. 3

The effect of increasing the object size on the brightness of the reconstruction: (a) shows the composite object photographed through one path of the interferometer and (b) shows the reconstruction from an incoherent hologram made from the entire object. (c) and (d) are reconstructions made from holograms where only parts of the object were used.

Fig. 4
Fig. 4

The object (left) and the reconstruction (right) from an incoherent hologram.

Fig. 5
Fig. 5

A continuous tone object (left) and the resulting reconstruction (right) made from an incoherent hologram.

Fig. 6
Fig. 6

Block diagram of the apparatus used in the time modulation experiment. O is the object, I is the interferometer, H the hologram plane, P a pinhole, PM a photomultipler, psd a phase sensitive detector or a chopper stabilized dc voltmeter, and C a chart recorder.

Fig. 7
Fig. 7

Results of the time modulation experiment.

Equations (2)

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I ( x , y , t ) = a i 2 [ 1 + J 0 ( u ) cos ( ψ i 1 - ψ i 2 ) + 2 cos ( ψ i 1 - ψ i 2 ) k = 1 ( - 1 ) k J 2 k ( u ) cos 2 k p t - 2 sin ( ψ i 1 - ψ i 2 ) k = 0 ( - 1 ) k J 2 k + 1 ( u ) cos ( 2 k + 1 ) p t ] + high frequency terms ,
I ( x 0 , y 0 , t ) = 2 a i 2 sin [ ψ i 1 - ψ i 2 ] J 1 ( u ) cos p t .

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