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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 63, Iss. 7 — Jul. 1, 1973
  • pp: 820–825

Alternating renewal model of photographic granularity

P. E. Castro, J. H. B. Kemperman, and E. A. Trabka  »View Author Affiliations

JOSA, Vol. 63, Issue 7, pp. 820-825 (1973)

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A crowded-monolayer emulsion is viewed in one dimension as an alternating renewal process. The model presented is sufficiently general to include the effects of arbitrary distributions of halide grain sizes and gap sizes and further arbitrary dependence of developability of the grains on grain size and exposure. In an example, we calculate the increase of granularity that accompanies the increased exposure latitude obtained by broadening the size distribution of maximally sensitized grains.

P. E. Castro, J. H. B. Kemperman, and E. A. Trabka, "Alternating renewal model of photographic granularity," J. Opt. Soc. Am. 63, 820-825 (1973)

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  1. E. A. Trabka, J. Opt. Soc. Am. 61, 800 (1971).
  2. J. F. Hamilton, W. H. Lawton, and E. A. Trabka, in Stochastic Point Processes: Statistical Analysis, Theory and Applications, edited by P. A. W. Lewis (Wiley, New York, 1972), pp. 817–867.
  3. See J. Feller, An Introduction to Probability Theory and Its Applications, Vol. II (Wiley, New York, 1966), Ch. XI, for modifications in the lattice case.
  4. Reference 3, p. 366.
  5. The Stieltjes convolution G * H(t) of two functions G(t), H(t) of locally bounded variation is defined as ∫-∞H (t - u) dG(u), where the integral is interpreted in the Lebesque-Stieltjes sense. When G,H vanish for negative arguments, this becomes ∫t0H (t - u) dG(u), again interpreted in the Lebesque—Stieltjes sense.
  6. In all Laplace-Stieltjes integrals, the functions are to be interpreted as vanishing for all arguments less than 0 and the integral replaced by an integral extending from - ∞ to + ∞.
  7. Reference 2, p. 849.
  8. Reference 1.
  9. E. F. Haugh, J. Photogr. Sci. 11, 65 (1963).
  10. W. H. Lawton, E. A. Trabka, and D. R. Wilder, J. Opt. Soc. Am. 65, 659 (1972).
  11. Reference 3, p. 355.
  12. Reference 3, p. 182.

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