Abstract

The paper describes a method for computing the response of a hypothetical photographic emulsion, given a detailed model for latent-image formation and development. A digital computer generates a random sequence of events simulating those which occur during and after exposure of a photographic grain. The computer records all of the active centers which form as a result of these events, and gives as a final result the number of silver specks of each size. The application of some developability criterion to these data determines whether or not the grain is developable and how many development centers it contains. The process is repeated until an adequate sampling of grains is represented, and the results are compared with data from actual emulsions. The method yields D–log E, reciprocity-failure, or development-center distribution characteristics. The authors propose a model as a working hypothesis to explain the response characteristics of a simple photographic emulsion [ H. E. Spencer and R. E. Atwell, J. Opt. Soc. Am. 54, 498 ( 1964); H. E. Spencer, L. E. Brady, and J. F. Hamilton, ibid. 54,492 ( 1964)]. This model contains many features in common with the Gurney–Mott mechanism of latent-image formation, including: reversible electron-trapping; ionic neutralization of trapped electrons; recombination; thermal decay of single silver atoms; permanent hole-trapping; permanent electron-trapping at silver aggregates, etc. The effects of changes in various physical parameters on photographic response are determined. The study shows that the observed effects of sulfur sensitization of this emulsion can be simulated by moderate increases in the depth of electron traps and in the stability of single silver atoms.

© 1965 Optical Society of America

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References

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  1. H. E. Spencer and R. E. Atwell, J. Opt. Soc. Am. 54, 498 (1964).
    [Crossref]
  2. H. E. Spencer, L. E. Brady, and J. F. Hamilton, J. Opt. Soc. Am. 54, 492 (1964).
    [Crossref]
  3. N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Oxford University Press, New York, 1948), 2nd ed., Chap. VII.
  4. E. A. Baker, Proc. Roy. Soc. Edinburgh 48, 106 (1927–1928).
  5. W. J. Albersheim, J. Soc. Motion Picture Engrs. 32, 73 (1939).
  6. G. C. Sprague, J. Appl. Phys. 32, 2410 (1961).
    [Crossref]
  7. P. C. Burton and W. F. Berg, Phot. J. 86B2, (1946).
  8. J. H. Webb, J. Opt. Soc. Am. 40, 3, 197 (1950); E. Katz, J. Chem. Phys. 17, 1132 (1949); P. V. Meĭklyar, Zh. Nauchn. i Prikl. Fotogr. i Kinematogr. 4, 62 (1959).
    [Crossref]
  9. A. Hautot and H. Sauvenier, Sci. Ind. Phot. 28, 1 (1957); ibid. 31, 137 (1960).
  10. J. Eggert and R. von Wartburg, Z. Elektrochem. 61, 693 (1957).
  11. F. Seitz, Rev. Mod. Phys. 23, 328 (1951).
    [Crossref]
  12. R. S. Van Heyningen and F. C. Brown, Phys. Rev. 111, 462 (1958).
    [Crossref]
  13. J. W. Mitchell, J. Phot. Sci. 6, 57 (1958); Rept. Progr. Phys. 22, 433 (1957).
  14. J. F. Hamilton and L. E. Brady, J. Appl. Phys. 30, 1893 (1959); J. Phys. Chem. 66, 2384 (1962).
    [Crossref]
  15. J. H. Webb, J. Opt. Soc. Am. 31, 348, 559 (1941); ibid. 38, 312 (1948).
    [Crossref]
  16. E. Klein, J. Phot. Sci. 10, 26 (1962).
  17. G. C. Farnell, J. Phot. Sci. 6, 83 (1958); G. C. Farnell and P. G. Powell, ibid. 11, 57 (1963); E. Mizuki and S. Fujisawa, Photographic Sensitivity, Hakone Symposium 1953, edited by S. Fujisawa (Maruzen Co., Ltd., Tokyo, 1956), p. 97, Vol. 1; S. Tutihasi, J. Opt. Soc. Am. 45, 15 (1955).
    [Crossref]
  18. W. F. Berg, Trans. Faraday Soc. 44, 783 (1948).
    [Crossref]
  19. E. A. Baker, J. Phot. Sci. 4, 101 (1956).
  20. A. L. Kartuzhanskii, Zh. Eksperim. i Teor. Fiz. 26, 763 (1954); S. Fujisawa and E. Mizuki, Sci. Publ. Fuji Photo Film Company, Ltd. 2, 35 (1954); Y. Wakabayashi and Y. Kobayashi, J. Soc. Sci. Phot., Japan 20, 102 (1957).

1964 (2)

1962 (1)

E. Klein, J. Phot. Sci. 10, 26 (1962).

1961 (1)

G. C. Sprague, J. Appl. Phys. 32, 2410 (1961).
[Crossref]

1959 (1)

J. F. Hamilton and L. E. Brady, J. Appl. Phys. 30, 1893 (1959); J. Phys. Chem. 66, 2384 (1962).
[Crossref]

1958 (3)

G. C. Farnell, J. Phot. Sci. 6, 83 (1958); G. C. Farnell and P. G. Powell, ibid. 11, 57 (1963); E. Mizuki and S. Fujisawa, Photographic Sensitivity, Hakone Symposium 1953, edited by S. Fujisawa (Maruzen Co., Ltd., Tokyo, 1956), p. 97, Vol. 1; S. Tutihasi, J. Opt. Soc. Am. 45, 15 (1955).
[Crossref]

R. S. Van Heyningen and F. C. Brown, Phys. Rev. 111, 462 (1958).
[Crossref]

J. W. Mitchell, J. Phot. Sci. 6, 57 (1958); Rept. Progr. Phys. 22, 433 (1957).

1957 (2)

A. Hautot and H. Sauvenier, Sci. Ind. Phot. 28, 1 (1957); ibid. 31, 137 (1960).

J. Eggert and R. von Wartburg, Z. Elektrochem. 61, 693 (1957).

1956 (1)

E. A. Baker, J. Phot. Sci. 4, 101 (1956).

1954 (1)

A. L. Kartuzhanskii, Zh. Eksperim. i Teor. Fiz. 26, 763 (1954); S. Fujisawa and E. Mizuki, Sci. Publ. Fuji Photo Film Company, Ltd. 2, 35 (1954); Y. Wakabayashi and Y. Kobayashi, J. Soc. Sci. Phot., Japan 20, 102 (1957).

1951 (1)

F. Seitz, Rev. Mod. Phys. 23, 328 (1951).
[Crossref]

1950 (1)

1948 (1)

W. F. Berg, Trans. Faraday Soc. 44, 783 (1948).
[Crossref]

1946 (1)

P. C. Burton and W. F. Berg, Phot. J. 86B2, (1946).

1941 (1)

1939 (1)

W. J. Albersheim, J. Soc. Motion Picture Engrs. 32, 73 (1939).

Albersheim, W. J.

W. J. Albersheim, J. Soc. Motion Picture Engrs. 32, 73 (1939).

Atwell, R. E.

Baker, E. A.

E. A. Baker, J. Phot. Sci. 4, 101 (1956).

E. A. Baker, Proc. Roy. Soc. Edinburgh 48, 106 (1927–1928).

Berg, W. F.

W. F. Berg, Trans. Faraday Soc. 44, 783 (1948).
[Crossref]

P. C. Burton and W. F. Berg, Phot. J. 86B2, (1946).

Brady, L. E.

H. E. Spencer, L. E. Brady, and J. F. Hamilton, J. Opt. Soc. Am. 54, 492 (1964).
[Crossref]

J. F. Hamilton and L. E. Brady, J. Appl. Phys. 30, 1893 (1959); J. Phys. Chem. 66, 2384 (1962).
[Crossref]

Brown, F. C.

R. S. Van Heyningen and F. C. Brown, Phys. Rev. 111, 462 (1958).
[Crossref]

Burton, P. C.

P. C. Burton and W. F. Berg, Phot. J. 86B2, (1946).

Eggert, J.

J. Eggert and R. von Wartburg, Z. Elektrochem. 61, 693 (1957).

Farnell, G. C.

G. C. Farnell, J. Phot. Sci. 6, 83 (1958); G. C. Farnell and P. G. Powell, ibid. 11, 57 (1963); E. Mizuki and S. Fujisawa, Photographic Sensitivity, Hakone Symposium 1953, edited by S. Fujisawa (Maruzen Co., Ltd., Tokyo, 1956), p. 97, Vol. 1; S. Tutihasi, J. Opt. Soc. Am. 45, 15 (1955).
[Crossref]

Gurney, R. W.

N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Oxford University Press, New York, 1948), 2nd ed., Chap. VII.

Hamilton, J. F.

H. E. Spencer, L. E. Brady, and J. F. Hamilton, J. Opt. Soc. Am. 54, 492 (1964).
[Crossref]

J. F. Hamilton and L. E. Brady, J. Appl. Phys. 30, 1893 (1959); J. Phys. Chem. 66, 2384 (1962).
[Crossref]

Hautot, A.

A. Hautot and H. Sauvenier, Sci. Ind. Phot. 28, 1 (1957); ibid. 31, 137 (1960).

Kartuzhanskii, A. L.

A. L. Kartuzhanskii, Zh. Eksperim. i Teor. Fiz. 26, 763 (1954); S. Fujisawa and E. Mizuki, Sci. Publ. Fuji Photo Film Company, Ltd. 2, 35 (1954); Y. Wakabayashi and Y. Kobayashi, J. Soc. Sci. Phot., Japan 20, 102 (1957).

Klein, E.

E. Klein, J. Phot. Sci. 10, 26 (1962).

Mitchell, J. W.

J. W. Mitchell, J. Phot. Sci. 6, 57 (1958); Rept. Progr. Phys. 22, 433 (1957).

Mott, N. F.

N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Oxford University Press, New York, 1948), 2nd ed., Chap. VII.

Sauvenier, H.

A. Hautot and H. Sauvenier, Sci. Ind. Phot. 28, 1 (1957); ibid. 31, 137 (1960).

Seitz, F.

F. Seitz, Rev. Mod. Phys. 23, 328 (1951).
[Crossref]

Spencer, H. E.

Sprague, G. C.

G. C. Sprague, J. Appl. Phys. 32, 2410 (1961).
[Crossref]

Van Heyningen, R. S.

R. S. Van Heyningen and F. C. Brown, Phys. Rev. 111, 462 (1958).
[Crossref]

von Wartburg, R.

J. Eggert and R. von Wartburg, Z. Elektrochem. 61, 693 (1957).

Webb, J. H.

J. Appl. Phys. (2)

G. C. Sprague, J. Appl. Phys. 32, 2410 (1961).
[Crossref]

J. F. Hamilton and L. E. Brady, J. Appl. Phys. 30, 1893 (1959); J. Phys. Chem. 66, 2384 (1962).
[Crossref]

J. Opt. Soc. Am. (4)

J. Phot. Sci. (4)

E. Klein, J. Phot. Sci. 10, 26 (1962).

G. C. Farnell, J. Phot. Sci. 6, 83 (1958); G. C. Farnell and P. G. Powell, ibid. 11, 57 (1963); E. Mizuki and S. Fujisawa, Photographic Sensitivity, Hakone Symposium 1953, edited by S. Fujisawa (Maruzen Co., Ltd., Tokyo, 1956), p. 97, Vol. 1; S. Tutihasi, J. Opt. Soc. Am. 45, 15 (1955).
[Crossref]

E. A. Baker, J. Phot. Sci. 4, 101 (1956).

J. W. Mitchell, J. Phot. Sci. 6, 57 (1958); Rept. Progr. Phys. 22, 433 (1957).

J. Soc. Motion Picture Engrs. (1)

W. J. Albersheim, J. Soc. Motion Picture Engrs. 32, 73 (1939).

Phot. J. (1)

P. C. Burton and W. F. Berg, Phot. J. 86B2, (1946).

Phys. Rev. (1)

R. S. Van Heyningen and F. C. Brown, Phys. Rev. 111, 462 (1958).
[Crossref]

Proc. Roy. Soc. Edinburgh (1)

E. A. Baker, Proc. Roy. Soc. Edinburgh 48, 106 (1927–1928).

Rev. Mod. Phys. (1)

F. Seitz, Rev. Mod. Phys. 23, 328 (1951).
[Crossref]

Sci. Ind. Phot. (1)

A. Hautot and H. Sauvenier, Sci. Ind. Phot. 28, 1 (1957); ibid. 31, 137 (1960).

Trans. Faraday Soc. (1)

W. F. Berg, Trans. Faraday Soc. 44, 783 (1948).
[Crossref]

Z. Elektrochem. (1)

J. Eggert and R. von Wartburg, Z. Elektrochem. 61, 693 (1957).

Zh. Eksperim. i Teor. Fiz. (1)

A. L. Kartuzhanskii, Zh. Eksperim. i Teor. Fiz. 26, 763 (1954); S. Fujisawa and E. Mizuki, Sci. Publ. Fuji Photo Film Company, Ltd. 2, 35 (1954); Y. Wakabayashi and Y. Kobayashi, J. Soc. Sci. Phot., Japan 20, 102 (1957).

Other (1)

N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Oxford University Press, New York, 1948), 2nd ed., Chap. VII.

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the simplified model of latent-image formation used in the analysis. Actors are indicated by circles, events by rectangular blocks.

Fig. 2
Fig. 2

Comparison of a simulated D–logE curve with an experimental curve for an unsensitized emulsion. Points represent the results of simulation; solid curve from experimental results of Spencer and Atwell.1 Intermediate intensity and a 6-atom development criterion were used in the simulation.

Fig. 3
Fig. 3

Simulated reciprocity curves for the unsensitized case at three reference densities: 0.1, 0.5, and 0.9. Time t of exposure is in seconds. The figure above each curve represents the fraction of grains developed. The curves and the solid circles are those for a 6-atom development criterion; the open circles for a 4-atom criterion.

Fig. 4
Fig. 4

Simulated reciprocity curves for the sensitized case (solid lines) in comparison with those for the unsensitized case (broken lines) at three reference densities: 0.1, 0.5, and 0.9. A 6-atom development criterion was used.

Fig. 5
Fig. 5

Simulated distribution of development centers of 6 or more atoms (open circles) for the sensitized case, exposed at very high intensity, compared with the Poisson probabilities (solid circles).

Fig. 6
Fig. 6

The effect of changing the development criterion on simulated reciprocity curves for the sensitized case. The figure above each curve represents the minimum size of a developable aggregate. The reference density is D/Dmax=0.5.

Fig. 7
Fig. 7

The effect of changing the development criterion on the fraction of developable grains, plotted for various high-intensity exposure levels, for the sensitized (S) and unsensitized (U) emulsions.

Fig. 8
Fig. 8

Simulated reciprocity curves for three states of sensitization, unsensitized (U), partially sensitized (P), and fully sensitized (S), using a reference density of D/Dmax=0.5 and a 6-atom development criterion.

Tables (2)

Tables Icon

Table I Parameter values used for simulation.

Tables Icon

Table II Formulas for estimating the number of quanta required to form a latent image.

Equations (34)

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X + Y Z ,
Z X + Y .
λ x y = x y ρ x y ,
λ z = z ρ z ,
ϕ = ( ρ d / s ρ n s ) 1 + ( ρ d / s ρ n s ) + ( i ρ d i / ρ a ) ,
β = [ 1 + ( ρ d / s ρ n s ) + ( i ρ d i / ρ a ) ] - 1 ,
α = ( i ρ d i / ρ a ) 1 + ( ρ d / s ρ n s ) + ( i ρ d i / ρ a ) .
G ( t ) = 1 - e - λ t .
G ( t ) = 1 - e - λ t ,
λ q > ϕ ρ n a .
[ r / ( c - 1 ) ] ( ϕ ρ n r / α ϕ ρ n a ) .
( 1 / α ) ( ϕ ρ n r / ϕ ρ n a ) .
ϕ ρ n r / ϕ ρ n a 3 × 10 - 2 .
( r / A 2 ) ( ϕ ρ n r / ϕ ρ n a ) .
τ = ( ϕ ρ n r ) - 1 .
ϕ ρ n r / ρ r = ( ϕ ρ n r / λ q ) ( 4 ϕ ρ n r / 2 α ϕ ρ n a ) .
ρ = σ 0 v n V - 1 ,
σ 0 = σ 1 = σ 2 = = σ k .
ρ n s 2.5 × 10 7 sec - 1 .
λ d = d ρ d = d ν d e - E / k T ,
λ a = a ρ a = a ν a e - W / k T .
( ρ d ) U = ν d e - E / k T = 2 × 10 8 sec - 1 ,
( ρ a ) U = ν a e - W / k T = 1 2 × 10 10 sec - 1 .
( ρ d ) S = ν d e - ( E + S ) / k T = 10 6 sec - 1 ,
( ρ a ) S = ν a e - ( W + S ) / k T = 2 × 10 7 sec - 1 .
E = W = 0.098 eV .
λ n r = n r ρ n r = n r σ r v n V - 1 .
λ p g = p g ρ p g = ( ψ h ) g ρ p g .
λ r = r ρ r = ( γ h ) ν r e - W / k T .
Recombination ( λ n r ) Absorption ( λ q ) ϕ c r ρ n r λ q c r ( ϕ ρ n r λ q )
Recombination ( λ n r ) Hole removal ( λ r ) ϕ c r ρ n r r ρ r c ( ϕ ρ n r ρ r )
Recombination ( λ n r ) Nucleation ( λ n a ) ϕ c r ρ n r ϕ c α ( c - 1 ) ρ n a r c - 1 ( ϕ ρ n r α ρ n a )
Recombination ( λ n r ) Growth ( λ n a ) ϕ c r ρ n r ϕ c A 2 ρ n a r A 2 ( ϕ ρ n r ϕ ρ n a )
Nucleation ( λ n a ) Growth ( λ n a ) ϕ c α ( c - 1 ) ρ n a ϕ c A 2 ρ n a c - 1 A 2 ( α )