Abstract

The light spread function, the density variations due to granularity, and the shape of the density-vs-log-exposure curve are basic properties of a black-and-white photographic system that determine its effectiveness as a communication channel. The amount of information stored per unit area on a photographic material is analogous to the amount of information transmitted per unit time by an electrical communication system. Simple formulas, involving in one instance only the resolving power and in the other a cross-sectional area of the point spread function, the standard deviation of the density variations, and the density range, have been used with considerable success to predict experimentally determined information storage capacities for a variety of black-and-white photographic systems. The upper limit of storage capacity, attainable only if the input information is efficiently coded, can be calculated by the use of a two-dimensional version of Shannon’s formula for channel capacity. This method takes into account the shape of the modulation transfer function and also the shape of the granularity Wiener spectrum of the system. The contribution of color to information storage capacity is considered by D. L. MacAdam (in an appendix at the end of this paper), who finds that color photographs can provide a capacity approximately three times as great as that obtainable with corresponding black-and-white photographs.

© 1972 Optical Society of America

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References

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  1. J. Altman, H. Zweig, Photogr. Sci. Eng. 7, 173 (1963).
  2. C. S. McCamy, Appl. Opt. 4, 405 (1965).
    [CrossRef]
  3. C. E. Shannon, Bell Syst. Tech. J. 27, 379, 623 (1948).
  4. R. C. Jones, J. Opt. Soc. Am. 51, 1159 (1961).
    [CrossRef]
  5. P. B. Fellgett, E. H. Linfoot, Philos. Trans. Roy. Soc. London A247, 369 (1955).
  6. R. Shaw, Photogr. Sci. Eng. 6, 281 (1962).
  7. G. C. Higgins, Photogr. Sci. Eng. 15, 106 (1971).
  8. R. L. Lamberts, C. M. Straub, W. F. Garbe, Photogr. Sci. Eng. 9, 331 (1965).
  9. E. C. Doerner, J. Opt. Soc. Am. 52, 69 (1962).
    [CrossRef]
  10. R. C. Jones, J. Opt. Soc. Am. 45, 799 (1955).
    [CrossRef]
  11. E. W. H. Selwyn, Photogr. J. 75, 571 (1935).
  12. C. N. Nelson, Photogr. Sci. Eng. 15, 82 (1971).
  13. G. Hansen, A. Richter, Optik31 5, 488 (1970).
  14. A. Marriage, E. Pitts, J. Opt. Soc. Am. 46, 1019 (1956); J. Opt. Soc. Am. 47, 321 (1957).
    [CrossRef]
  15. H. Zweig, J. Opt. Soc. Am. 49, 238 (1959).
    [CrossRef]
  16. P. Baudry, R. Desprez, D. Preteseille, J. Photogr. Sci. 16, 132 (1968).
  17. E. Klein, G. Langer, J. Photogr. Sci. 11, 177 (1963).
  18. D. L. MacAdam, Rev. Opt. 28, 161 (1949); Doe. Ophthal. 3, 214 (1949).

1971 (2)

G. C. Higgins, Photogr. Sci. Eng. 15, 106 (1971).

C. N. Nelson, Photogr. Sci. Eng. 15, 82 (1971).

1970 (1)

G. Hansen, A. Richter, Optik31 5, 488 (1970).

1968 (1)

P. Baudry, R. Desprez, D. Preteseille, J. Photogr. Sci. 16, 132 (1968).

1965 (2)

R. L. Lamberts, C. M. Straub, W. F. Garbe, Photogr. Sci. Eng. 9, 331 (1965).

C. S. McCamy, Appl. Opt. 4, 405 (1965).
[CrossRef]

1963 (2)

E. Klein, G. Langer, J. Photogr. Sci. 11, 177 (1963).

J. Altman, H. Zweig, Photogr. Sci. Eng. 7, 173 (1963).

1962 (2)

R. Shaw, Photogr. Sci. Eng. 6, 281 (1962).

E. C. Doerner, J. Opt. Soc. Am. 52, 69 (1962).
[CrossRef]

1961 (1)

1959 (1)

1956 (1)

1955 (2)

P. B. Fellgett, E. H. Linfoot, Philos. Trans. Roy. Soc. London A247, 369 (1955).

R. C. Jones, J. Opt. Soc. Am. 45, 799 (1955).
[CrossRef]

1949 (1)

D. L. MacAdam, Rev. Opt. 28, 161 (1949); Doe. Ophthal. 3, 214 (1949).

1948 (1)

C. E. Shannon, Bell Syst. Tech. J. 27, 379, 623 (1948).

1935 (1)

E. W. H. Selwyn, Photogr. J. 75, 571 (1935).

Altman, J.

J. Altman, H. Zweig, Photogr. Sci. Eng. 7, 173 (1963).

Baudry, P.

P. Baudry, R. Desprez, D. Preteseille, J. Photogr. Sci. 16, 132 (1968).

Desprez, R.

P. Baudry, R. Desprez, D. Preteseille, J. Photogr. Sci. 16, 132 (1968).

Doerner, E. C.

E. C. Doerner, J. Opt. Soc. Am. 52, 69 (1962).
[CrossRef]

Fellgett, P. B.

P. B. Fellgett, E. H. Linfoot, Philos. Trans. Roy. Soc. London A247, 369 (1955).

Garbe, W. F.

R. L. Lamberts, C. M. Straub, W. F. Garbe, Photogr. Sci. Eng. 9, 331 (1965).

Hansen, G.

G. Hansen, A. Richter, Optik31 5, 488 (1970).

Higgins, G. C.

G. C. Higgins, Photogr. Sci. Eng. 15, 106 (1971).

Jones, R. C.

Klein, E.

E. Klein, G. Langer, J. Photogr. Sci. 11, 177 (1963).

Lamberts, R. L.

R. L. Lamberts, C. M. Straub, W. F. Garbe, Photogr. Sci. Eng. 9, 331 (1965).

Langer, G.

E. Klein, G. Langer, J. Photogr. Sci. 11, 177 (1963).

Linfoot, E. H.

P. B. Fellgett, E. H. Linfoot, Philos. Trans. Roy. Soc. London A247, 369 (1955).

MacAdam, D. L.

D. L. MacAdam, Rev. Opt. 28, 161 (1949); Doe. Ophthal. 3, 214 (1949).

Marriage, A.

McCamy, C. S.

Nelson, C. N.

C. N. Nelson, Photogr. Sci. Eng. 15, 82 (1971).

Pitts, E.

Preteseille, D.

P. Baudry, R. Desprez, D. Preteseille, J. Photogr. Sci. 16, 132 (1968).

Richter, A.

G. Hansen, A. Richter, Optik31 5, 488 (1970).

Selwyn, E. W. H.

E. W. H. Selwyn, Photogr. J. 75, 571 (1935).

Shannon, C. E.

C. E. Shannon, Bell Syst. Tech. J. 27, 379, 623 (1948).

Shaw, R.

R. Shaw, Photogr. Sci. Eng. 6, 281 (1962).

Straub, C. M.

R. L. Lamberts, C. M. Straub, W. F. Garbe, Photogr. Sci. Eng. 9, 331 (1965).

Zweig, H.

J. Altman, H. Zweig, Photogr. Sci. Eng. 7, 173 (1963).

H. Zweig, J. Opt. Soc. Am. 49, 238 (1959).
[CrossRef]

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

C. E. Shannon, Bell Syst. Tech. J. 27, 379, 623 (1948).

J. Opt. Soc. Am. (5)

J. Photogr. Sci. (2)

P. Baudry, R. Desprez, D. Preteseille, J. Photogr. Sci. 16, 132 (1968).

E. Klein, G. Langer, J. Photogr. Sci. 11, 177 (1963).

Optik (1)

G. Hansen, A. Richter, Optik31 5, 488 (1970).

Philos. Trans. Roy. Soc. London (1)

P. B. Fellgett, E. H. Linfoot, Philos. Trans. Roy. Soc. London A247, 369 (1955).

Photogr. J. (1)

E. W. H. Selwyn, Photogr. J. 75, 571 (1935).

Photogr. Sci. Eng. (5)

C. N. Nelson, Photogr. Sci. Eng. 15, 82 (1971).

R. Shaw, Photogr. Sci. Eng. 6, 281 (1962).

G. C. Higgins, Photogr. Sci. Eng. 15, 106 (1971).

R. L. Lamberts, C. M. Straub, W. F. Garbe, Photogr. Sci. Eng. 9, 331 (1965).

J. Altman, H. Zweig, Photogr. Sci. Eng. 7, 173 (1963).

Rev. Opt. (1)

D. L. MacAdam, Rev. Opt. 28, 161 (1949); Doe. Ophthal. 3, 214 (1949).

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Equations (11)

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

C = 100 r 2 bits / cm 2 ,
I = N log 2 M ,
M = 1 + ( D max - D min ) / k ( 2 σ ) ,
C = Δ f log 2 ( 1 + P / N ) ,
C = Δ 1 f log 2 ( 1 + P 1 / N 1 ) + Δ 2 f log 2 ( 1 + P 2 / N 2 ) .
C = 0 log 2 [ 1 + P ( f ) / N ( f ) ] d f ,
C = 1 2 - - log 2 [ 1 + P ( u , v ) / N ( u , v ) ] d u d v ,
C = π 0 f log 2 [ 1 + P ( f ) / N ( f ) ] d f ,
P ( f ) N ( f ) = [ Δ T ( f ) ] 2 W T ( f ) = [ Δ T ( f ) / T ¯ ] 2 W T ( f ) / T ¯ 2 = ( 0.43 ) 2 [ Δ E ( f ) / E ] 2 γ 2 H 2 ( f ) W D ( f ) ,
C = π 0 f log 2 [ 1 + K ( f ) γ 2 H 2 ( f ) W D ( f ) ] d f ,
C = h Δ f log 2 { 1 + [ P ( f ) / k N ( f ) ] } ,

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