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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 68, Iss. 7 — Jul. 1, 1978
  • pp: 972–978

A model for reciprocity failure in photographic materials and its asymptotic behavior at low and high intensities

William J. Anderson  »View Author Affiliations

JOSA, Vol. 68, Issue 7, pp. 972-978 (1978)

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A model which combines both low- and high-intensity reciprocity failure in photographic materials is described. The asymptotic behavior of the resulting isodense curves at high and low intensities is investigated and characterized in terms of the model parameters.

© 1978 Optical Society of America

William J. Anderson, "A model for reciprocity failure in photographic materials and its asymptotic behavior at low and high intensities," J. Opt. Soc. Am. 68, 972-978 (1978)

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  1. W. J. Anderson, "On a model for reciprocity failure in photographic materials," Can. J. Statist. 3, 223–234 (1975).
  2. B. E. Bayer and J. F. Hamilton, "Computer investigation of a latent image model," J. Opt. Soc. Am. 55, 439–452 (1965).
  3. J. F. Hamilton and B. E. Bayer, "Investigation of a latent image model: recombination of trapped electrons and free holes," J. Opt. Soc. Am. 55, 528–533 (1965).
  4. J. F. Hamilton, "Latent image formation as a probabilistic process," Photogr. Sci. Eng. 12, 143–145 (1968).
  5. W. J. Albersheim, J. Soc. Mot. Pict. Engrs. 32, 73 (1939).
  6. L. Silberstein, "A theoretical treatment of the two-quanta hypothesis as applied to the photographic reciprocity law failure," J. Opt. Soc. Am. 29, 432–477 (1939).
  7. E. Katz, "On the photographic reciprocity law failure and related effects. II. The low intensity sequence effect," J. Chem. Phys. 18, 499–506 (1950).
  8. Pr{} denotes the probability of the event in parentheses.
  9. As discussed in Ref. 10, pp. 135-6, the dead time is not the only source of high-intensity reciprocity failure. However, the effects of alternative causes, such as competitive nucleation and topographic effects cannot be included in a single trap model.
  10. C. E. K. Mees and T. H. James, The Theory of the Photographic Process (Macmillan, New York, 1966).
  11. Except when P(0) > 0 is assumed, in which case the silver ion has probability P(0) of remaining in the trap and 1 -P(0) of being ejected (forever).
  12. J. H. B. Kemperman (private communication, 1976).
  13. The notation for transforms should not be confused with the convolution operator.
  14. W. Feller, An Introduction to Probability Theory and its Applications, Volume II (Wiley, New York, 1966).
  15. E. Cinlar, Introduction to Stochastic Processes (Prentice-Hall, New Jersey, 1975).
  16. S. Karlin and H. M. Taylor, A First Course in Stochastic Processes, 2nd ed. (Academic, New York, 1975).
  17. J. F. Hamilton, W. H. Lawton, and E. A. Trabka, "Some spatial and temporal point processes in photographic science," in Stochastic Point Processes: Statistical Analysis, Theory, and Applications, edited by P. A. W. Lewis (Wiley, New York, 1972).

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