Abstract

An analysis of an idealized film-grain model suggests that any photographic emulsion may be significantly more sensitive in holographic imagery than in conventional imagery. Experiments with Kodak Plus-X emulsion show that such an improvement of sensitivity can indeed be realized.

© 1968 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. J. Zweig, G. C. Higgins, and D. L. MacAdam, J. Opt. Soc. Am. 48, 926 (1958).
    [Crossref]
  2. D. Gabor and W. P. Goss, J. Opt. Soc. Am. 56, 849 (1966).
    [Crossref]
  3. D. Gabor, in Progress in Optics, Vol. I, E. Wolf, Ed. (North-Holland Publishing Co., Amsterdam, 1961), p. 122.
  4. In some cases it may also be desired to measure the phase of the light transmitted by a coherently illuminated object, but we do not consider this problem here.
  5. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).
    [Crossref]
  6. G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic Press Inc., New York, 1966).
  7. L. Silberstein, Phil. Mag. 44, 257 (1922).
    [Crossref]
  8. L. Silberstein, J. Opt. Soc. Am. 31, 343 (1941).
    [Crossref]
  9. E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Co., Reading, Mass., 1963).
  10. The presence of light in the original aerial image is indicated by a drop in the transmittance of the resulting negative transparency. Thus the “signal” amplitude is taken to be 1−t¯, while the noise amplitude is σt.
  11. J. W. Goodman, J. Opt. Soc. Am. 57, 493 (1967).
    [Crossref] [PubMed]
  12. The possibility was considered that aberrations might be present in the holographic case, thus yielding more photons per resolution-cell than would be calculated under the assumption of diffraction-limited operation. However, comparison of the granularities caused by the so-called speckle effect demonstrated that the conventional and holographic images were of roughly the same resolution.

1967 (1)

1966 (1)

1962 (1)

1958 (1)

1941 (1)

1922 (1)

L. Silberstein, Phil. Mag. 44, 257 (1922).
[Crossref]

Gabor, D.

D. Gabor and W. P. Goss, J. Opt. Soc. Am. 56, 849 (1966).
[Crossref]

D. Gabor, in Progress in Optics, Vol. I, E. Wolf, Ed. (North-Holland Publishing Co., Amsterdam, 1961), p. 122.

Goodman, J. W.

Goss, W. P.

Higgins, G. C.

Leith, E. N.

MacAdam, D. L.

O’Neill, E. L.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Co., Reading, Mass., 1963).

Silberstein, L.

Stroke, G. W.

G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic Press Inc., New York, 1966).

Upatnieks, J.

Zweig, H. J.

J. Opt. Soc. Am. (5)

Phil. Mag. (1)

L. Silberstein, Phil. Mag. 44, 257 (1922).
[Crossref]

Other (6)

The possibility was considered that aberrations might be present in the holographic case, thus yielding more photons per resolution-cell than would be calculated under the assumption of diffraction-limited operation. However, comparison of the granularities caused by the so-called speckle effect demonstrated that the conventional and holographic images were of roughly the same resolution.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Co., Reading, Mass., 1963).

The presence of light in the original aerial image is indicated by a drop in the transmittance of the resulting negative transparency. Thus the “signal” amplitude is taken to be 1−t¯, while the noise amplitude is σt.

G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic Press Inc., New York, 1966).

D. Gabor, in Progress in Optics, Vol. I, E. Wolf, Ed. (North-Holland Publishing Co., Amsterdam, 1961), p. 122.

In some cases it may also be desired to measure the phase of the light transmitted by a coherently illuminated object, but we do not consider this problem here.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Conventional method of image measurement: (a) Recording the images, (b) Measuring the image irradiance.

Fig. 2
Fig. 2

Holographic method of image measurement: (a) Recording the hologram, (b) Measuring the image irradiance.

Fig. 3
Fig. 3

Conventionally recorded image, no flashing, 9000 photons per resolution cell.

Fig. 4
Fig. 4

Conventionally recorded image, no flashing, 4500 photons per resolution cell.

Fig. 5
Fig. 5

Conventionally recorded image, no flashing, 3000 photons per resolution cell.

Fig. 6
Fig. 6

Holographic image, 120 photons per resolution cell, of which about 90 are copolarized with the reference wave.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

U i ( x , y ) = s ( x , y ; ξ , η ) U 0 ( ξ , η ) d ξ d η .
Prob ( t = 1 ) = k = 0 m 1 ( N ¯ ) k k ! e N ¯
Prob ( t = 0 ) = k = m ( N ¯ ) k k ! e N ¯ ,
t ¯ = 0 · Prob ( t = 0 ) + 1 · Prob ( t = 1 ) = k = 0 m 1 ( N ¯ ) k k ! e N ¯ ,
σ t = [ t ¯ ( 1 t ¯ ) ] 1 2 .
χ = [ ( N ¯ ) m 1 / ( m 1 ) ! ] e N ¯ .
S N = 1 t ¯ σ t = ( 1 t ¯ t ¯ ) 1 2 ,
( 1 t ¯ ) / t ¯ = 1 or t ¯ = 1 2 .
S / m .
Δ t ¯ = χ max Δ ( N ¯ ) = χ max N ¯ 0 = [ ( m 1 ) m 1 / ( m 1 ) ! ] e ( m 1 ) N ¯ 0 ,
S / N 2 [ ( m 1 ) m 1 / ( m 1 ) ! ] e ( m 1 ) N ¯ 0 .
S 2 [ ( m 1 ) m 1 / ( m 1 ) ! ] e ( m 1 ) .
K m = 2 [ ( m 1 ) m 1 / ( m 1 ) ! ] e ( m 1 )
S N = Q m N ¯ 0 ( 1 + 2 Q m N ¯ 0 ) 1 2 ,
Q m = ( N ¯ r ) 2 m 1 e 2 N ¯ r ( m 1 ) ! ( m 1 ) ! t ¯ ( 1 t ¯ ) .
N ¯ r = m 1 2 ,
S N ( 2 / π ) N ¯ 0 [ 1 + ( 4 / π ) N ¯ 0 ] 1 2 .
S = / 1.2 π .
E TOTAL = E r + E 0 + 2 ( E r E 0 ) 1 2 cos [ ω x + θ ( x ) ] ,
A R = λ 2 D 2 / A p ,