Abstract

A new method of measuring the scattered light to determine the noise spectral power density is described. The technique is shown to be useful at the high spatial frequencies used in holography, beyond the range of the former methods of noise power measurement. Measurements of the grain noise of several photographic emulsions used for holography are presented; they are consistent with a model of emulsions characterized by a transmission correlation length. The measured correlation length of several of the emulsions fit experimentally observed spatial frequency responses. Data on noise power of several other photosensitive materials suitable for holography are also presented.

© 1970 Optical Society of America

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References

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  1. R. Clark Jones, J. Opt. Soc. Amer. 45, 799 (1955).
    [CrossRef]
  2. A. Marriage, E. Pitts, J. Opt. Soc. Amer. 46, 1019 (1956).
    [CrossRef]
  3. E. N. Leith, Soc. Phot. Sci. Eng. 6, 75 (1962).
  4. H. S. Stark et al., Appl. Opt. 8, 11 (1969).
    [CrossRef]
  5. D. H. R. Vilkomerson, Ph.D. dissertation, Columbia University, July1969.
  6. T. Shankoff, Appl. Opt. 7, 2101 (1968).
    [CrossRef] [PubMed]
  7. E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), p. 113.
  8. A. Friesem et al., Appl. Opt. 6, 851 (1967).
    [CrossRef] [PubMed]
  9. B. Picinbono, Compt. Rend. 246, 3605 (1958).

1969 (1)

H. S. Stark et al., Appl. Opt. 8, 11 (1969).
[CrossRef]

1968 (1)

1967 (1)

1962 (1)

E. N. Leith, Soc. Phot. Sci. Eng. 6, 75 (1962).

1958 (1)

B. Picinbono, Compt. Rend. 246, 3605 (1958).

1956 (1)

A. Marriage, E. Pitts, J. Opt. Soc. Amer. 46, 1019 (1956).
[CrossRef]

1955 (1)

R. Clark Jones, J. Opt. Soc. Amer. 45, 799 (1955).
[CrossRef]

Clark Jones, R.

R. Clark Jones, J. Opt. Soc. Amer. 45, 799 (1955).
[CrossRef]

Friesem, A.

Leith, E. N.

E. N. Leith, Soc. Phot. Sci. Eng. 6, 75 (1962).

Marriage, A.

A. Marriage, E. Pitts, J. Opt. Soc. Amer. 46, 1019 (1956).
[CrossRef]

O’Neill, E. L.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), p. 113.

Picinbono, B.

B. Picinbono, Compt. Rend. 246, 3605 (1958).

Pitts, E.

A. Marriage, E. Pitts, J. Opt. Soc. Amer. 46, 1019 (1956).
[CrossRef]

Shankoff, T.

Stark, H. S.

H. S. Stark et al., Appl. Opt. 8, 11 (1969).
[CrossRef]

Vilkomerson, D. H. R.

D. H. R. Vilkomerson, Ph.D. dissertation, Columbia University, July1969.

Appl. Opt. (3)

Compt. Rend. (1)

B. Picinbono, Compt. Rend. 246, 3605 (1958).

J. Opt. Soc. Amer. (2)

R. Clark Jones, J. Opt. Soc. Amer. 45, 799 (1955).
[CrossRef]

A. Marriage, E. Pitts, J. Opt. Soc. Amer. 46, 1019 (1956).
[CrossRef]

Soc. Phot. Sci. Eng. (1)

E. N. Leith, Soc. Phot. Sci. Eng. 6, 75 (1962).

Other (2)

D. H. R. Vilkomerson, Ph.D. dissertation, Columbia University, July1969.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), p. 113.

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Figures (9)

Fig. 1
Fig. 1

Apparatus to measure scattered light.

Fig. 2
Fig. 2

Scattering S, as a function of frequency for differing angles to the horizontal. The transmission, .7; 649F emulsion, uniform exposure.

Fig. 3
Fig. 3

Representation of scattering, S, as height over the spatial frequency space, and the S measured by moving the detector off the horizontal axis, shown by the measurement trace.

Fig. 4
Fig. 4

Scattering S vs spatial frequency with differing transmissions; Kodak 649F.

Fig. 5
Fig. 5

Scattering S at 37° horizontal, 20° vertical of fifteen point holograms of different modulations, and one complex subject hologram.

Fig. 6
Fig. 6

Scattering S as a function of frequency.

Fig. 7
Fig. 7

Comparison of theoretical scattering spectrum and experimental Kodak 649F.

Fig. 8
Fig. 8

Comparison of theoretical and experimental scattering Agfa 10E70.

Fig. 9
Fig. 9

Diagram to determine power received by detector.

Tables (1)

Tables Icon

Table I Scattering Factor for Different Materials

Equations (15)

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sin θ i + sin θ 0 = λ f .
f = sin θ / λ ,
area of freq . plane P scat d ω x d ω y = P i n · S · ( B W 1 · B W 2 ) ,
S theory ( ω x , ω y ) = T ( 1 T ) l 2 [ sinc ( ω x l / 2 ) ] 2 [ sinc ( ω y l / 2 ) ] 2 ,
P ( ω ) = D ( ω 0 ) A ( ω ω 0 ) d ω 0 .
P meas = P ( ω ) d ω = D ( ω 0 ) A ( ω ω 0 ) d ω 0 d ω .
f ( x + x 0 ) d x = f ( x ) d x ,
D ( ω 0 ) A ( ω ω 0 ) d ω 0 d ω = D ( ω 0 ) d ω 0 × A ( ω ) d ω .
P meas = 2 ω 2 · P / cycle · 2 ω 1 .
P / cycle = P t o t / B W ,
f = sin θ / λ , Δ f ( cos θ / λ ) Δ θ ,
Δ θ = d / D ,
B W = ( cos θ / λ 2 ) ( π / 4 ) ( d 2 / D ) ( cycles / mm ) 2 .
S P / cycle 2 / P in .
S = P scatt meas / P in × 1 / B W .

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