Abstract

A modification of a previously described model of photographic latent-image formation (see preceding paper) is in closer agreement with the absolute sensitivity of actual emulsion systems. The modification includes, in addition to recombination of a free electron with a trapped hole, the complementary process: namely, the recombination of a free hole with a trapped electron. When the cross sections for trapping of an electron, for trapping of a hole, and for recombination by either process are all equal, the number of adjustable parameters of the model reduces to only three. These parameters may be assigned reasonable values such that the response of the model closely approximates that of an experimental emulsion system. Effects of changes in various physical properties of the model system are predictable.

© 1965 Optical Society of America

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References

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  1. B. E. Bayer and J. F. Hamilton, J. Opt. Soc. Am. 55, 439 (1965).
    [Crossref]
  2. H. E. Spencer and R. E. Atwell, J. Opt. Soc. Am. 54, 498 (1964).
    [Crossref]
  3. H. E. Spencer, L. E. Brady, and J. F. Hamilton, J. Opt. Soc. Am. 54, 492 (1964).
    [Crossref]
  4. H. E. Spencer (private communication).
  5. A. Marriage, J. Phot. Sci. 9, 93 (1961).
  6. E. Klein, J. Phot. Sci. 10, 26 (1962).
  7. J. F. Hamilton and L. E. Brady, J. Phys. Chem. 66, 2384 (1962).
    [Crossref]
  8. A. L. Kartuzhanskii, Zh. Eksperim. i Teor. Fiz. 26, 763 (1954).
  9. S. Fujisawa and E. Mizuki, Sci. Publ. Fuji Photo Film Co., Ltd. 2, 35 (1954).
  10. Y. Wakabayashi and Y. Kobayashi, J. Soc. Sci. Phot. Japan 20, 102 (1957).
  11. J. W. Mitchell, J. Phot. Sci. 6, 57 (1958).

1965 (1)

1964 (2)

1962 (2)

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

J. F. Hamilton and L. E. Brady, J. Phys. Chem. 66, 2384 (1962).
[Crossref]

1961 (1)

A. Marriage, J. Phot. Sci. 9, 93 (1961).

1958 (1)

J. W. Mitchell, J. Phot. Sci. 6, 57 (1958).

1957 (1)

Y. Wakabayashi and Y. Kobayashi, J. Soc. Sci. Phot. Japan 20, 102 (1957).

1954 (2)

A. L. Kartuzhanskii, Zh. Eksperim. i Teor. Fiz. 26, 763 (1954).

S. Fujisawa and E. Mizuki, Sci. Publ. Fuji Photo Film Co., Ltd. 2, 35 (1954).

Atwell, R. E.

Bayer, B. E.

Brady, L. E.

Fujisawa, S.

S. Fujisawa and E. Mizuki, Sci. Publ. Fuji Photo Film Co., Ltd. 2, 35 (1954).

Hamilton, J. F.

Kartuzhanskii, A. L.

A. L. Kartuzhanskii, Zh. Eksperim. i Teor. Fiz. 26, 763 (1954).

Klein, E.

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

Kobayashi, Y.

Y. Wakabayashi and Y. Kobayashi, J. Soc. Sci. Phot. Japan 20, 102 (1957).

Marriage, A.

A. Marriage, J. Phot. Sci. 9, 93 (1961).

Mitchell, J. W.

J. W. Mitchell, J. Phot. Sci. 6, 57 (1958).

Mizuki, E.

S. Fujisawa and E. Mizuki, Sci. Publ. Fuji Photo Film Co., Ltd. 2, 35 (1954).

Spencer, H. E.

Wakabayashi, Y.

Y. Wakabayashi and Y. Kobayashi, J. Soc. Sci. Phot. Japan 20, 102 (1957).

J. Opt. Soc. Am. (3)

J. Phot. Sci. (3)

A. Marriage, J. Phot. Sci. 9, 93 (1961).

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

J. W. Mitchell, J. Phot. Sci. 6, 57 (1958).

J. Phys. Chem. (1)

J. F. Hamilton and L. E. Brady, J. Phys. Chem. 66, 2384 (1962).
[Crossref]

J. Soc. Sci. Phot. Japan (1)

Y. Wakabayashi and Y. Kobayashi, J. Soc. Sci. Phot. Japan 20, 102 (1957).

Sci. Publ. Fuji Photo Film Co., Ltd. (1)

S. Fujisawa and E. Mizuki, Sci. Publ. Fuji Photo Film Co., Ltd. 2, 35 (1954).

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

A. L. Kartuzhanskii, Zh. Eksperim. i Teor. Fiz. 26, 763 (1954).

Other (1)

H. E. Spencer (private communication).

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Figures (6)

Fig. 1
Fig. 1

Energy-level diagrams illustrating the two types of recombination considered: (a) capture of a free electron by a trapped hole; (b) capture of a free hole by a trapped electron.

Fig. 2
Fig. 2

Simulated “D–logE” curves for the unsensitized (●) and the sensitized (▲) forms of the model at optimum intensity. Open symbols (○,△) represent the same forms, with hole removal included. Developable centers, five or more atoms.

Fig. 3
Fig. 3

Simulated reciprocity curves for unsensitized (●) and sensitized (▲) forms of the model, taken at 50% developability, five-atom developable centers.

Fig. 4
Fig. 4

Simulated reciprocity curves for the sensitized form of the model, at 50% developability. Developable centers are five or more (▲), four or more (■), and three or more atoms (▼).

Fig. 5
Fig. 5

Simulated reciprocity curves for the unsensitized form of the model without (●) and with (○) hole removal, taken at 50% developability, five-atom developable centers.

Fig. 6
Fig. 6

Simulated reciprocity curves for the unsensitized (○) and sensitized (△) forms of the model, with hole removal, taken at 50% developability, five-atom developable centers.

Tables (1)

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Table I Parameter values for simulation.

Equations (26)

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ψ = ( ρ r / b ρ b p ) / [ 1 + ( ρ r / b ρ b p ) ]
γ = [ 1 + ( ρ r / b ρ b p ) ] - 1
p = ψ h ,
r = γ h .
λ rec ( a ) = ϕ c γ h ρ n r ,
λ rec ( b ) = β c ψ h ρ d p .
ρ n s = σ s v n V - 1 ,
ρ n s ρ b p ρ n r ρ d p ρ .
λ nucl = ϕ c α ( c - 1 ) ρ .
λ rec = λ r ( a ) + λ r ( b ) = ( ϕ γ + β ψ ) c h ρ .
λ gr = ϕ c a k ρ .
λ rem = h ρ h .
λ nucl λ gr = ϕ a ρ [ c ( c - 1 ) ] ϕ ρ [ c a k ] = α f ( N ) .
λ rec λ gr = ( ϕ γ + β ψ ) ρ [ c h ] ϕ ρ [ c a k ] = ( γ + β ψ ϕ ) f ( N ) .
λ gr intensity = ϕ ρ [ c a k ] λ q = ϕ ρ λ q f ( N ) .
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 ) ] .
ϕ ( ρ d / s ρ n s ) / [ 1 + ( i ρ d i / ρ a ) ] ,
β [ 1 + ( i ρ d i / ρ a ) ] - 1 ,
α ( i ρ d i / ρ a ) / [ 1 + ( i ρ d i / ρ a ) ] .
γ + β ψ ϕ = 1 1 + ( ρ r / b ρ b p ) + [ 1 1 + ( i ρ d i / ρ a ) · ( ρ r / b ρ b p ) 1 + ( ρ r / b ρ a p ) · 1 + ( i ρ d i / ρ a ) ( ρ d / s ρ n s ) ] ,
= 1 1 + ( ρ r / b ρ b p ) + ρ r ρ d · s ρ n s b ρ b p · 1 1 + ( ρ r / b ρ b p ) ,
γ + β ψ / ϕ 1 + ρ r s / ρ d b .
ϕ ρ = { ( ρ d / s ρ n s ) / [ 1 + ( i ρ d i / ρ a ) ] } ρ ,
ϕ ρ = ( ρ d / s ) / [ 1 + ( i ρ d i / ρ a ) ] .