Abstract

A theoretical formulation of diffuse reflection density of a glossy color print under perfectly diffuse illumination has been developed by taking into consideration the first-surface reflection from a gelatin layer and multiple internal reflections in a gelatin layer. The diffuse reflection density of a glossy color print under perfectly diffuse illumination is approximately equal to the specular reflection density of a color print adjusted for 5% surface reflection from the gelatin. The color gamuts obtainable in glossy color prints under perfectly diffuse illumination and under specular illumination (perpendicular to color prints) with 5% surface reflection are shown in comparison with those obtainable in color transparencies.

© 1972 Optical Society of America

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References

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  1. N. Ohta, Phot. Sci. Eng. 15, 487 (1971).
  2. F. C. Williams and F. R. Clapper, J. Opt. Soc. Am. 43, 595 (1953).
    [Crossref] [PubMed]
  3. N. Ohta, J. Opt. Soc. Am. 62, 129 (1972).
    [Crossref]
  4. J. A. C. Yule, Principles of Color Reproduction (Wiley, New York, 1967), p. 156.
  5. C. J. Bartleson (private communication).
  6. R. S. Longhurst, Geometrical and Physical Optics (Longmans, Green, London, 1957), p. 370.
  7. Reference 4, p. 209.
  8. D. B. Judd, J. Res. Natl. Bur. Std. (U.S.) 25, 329 (1942).
    [Crossref]
  9. R. M. Evans, W. T. Hanson, and W. L. Brewer, Principles of Color Photography (Wiley, New York, 1953).
  10. N. Ohta, paper presented at the Annual Symposium of the SPSE on Color Photography System, 21–24 Oct. 1970. Information is available from the author.
  11. N. Ohta, Phot. Sci. Eng. 15, 399 (1971).

1972 (1)

1971 (2)

N. Ohta, Phot. Sci. Eng. 15, 487 (1971).

N. Ohta, Phot. Sci. Eng. 15, 399 (1971).

1953 (1)

1942 (1)

D. B. Judd, J. Res. Natl. Bur. Std. (U.S.) 25, 329 (1942).
[Crossref]

Bartleson, C. J.

C. J. Bartleson (private communication).

Brewer, W. L.

R. M. Evans, W. T. Hanson, and W. L. Brewer, Principles of Color Photography (Wiley, New York, 1953).

Clapper, F. R.

Evans, R. M.

R. M. Evans, W. T. Hanson, and W. L. Brewer, Principles of Color Photography (Wiley, New York, 1953).

Hanson, W. T.

R. M. Evans, W. T. Hanson, and W. L. Brewer, Principles of Color Photography (Wiley, New York, 1953).

Judd, D. B.

D. B. Judd, J. Res. Natl. Bur. Std. (U.S.) 25, 329 (1942).
[Crossref]

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics (Longmans, Green, London, 1957), p. 370.

Ohta, N.

N. Ohta, J. Opt. Soc. Am. 62, 129 (1972).
[Crossref]

N. Ohta, Phot. Sci. Eng. 15, 487 (1971).

N. Ohta, Phot. Sci. Eng. 15, 399 (1971).

N. Ohta, paper presented at the Annual Symposium of the SPSE on Color Photography System, 21–24 Oct. 1970. Information is available from the author.

Williams, F. C.

Yule, J. A. C.

J. A. C. Yule, Principles of Color Reproduction (Wiley, New York, 1967), p. 156.

J. Opt. Soc. Am. (2)

J. Res. Natl. Bur. Std. (U.S.) (1)

D. B. Judd, J. Res. Natl. Bur. Std. (U.S.) 25, 329 (1942).
[Crossref]

Phot. Sci. Eng. (2)

N. Ohta, Phot. Sci. Eng. 15, 487 (1971).

N. Ohta, Phot. Sci. Eng. 15, 399 (1971).

Other (6)

R. M. Evans, W. T. Hanson, and W. L. Brewer, Principles of Color Photography (Wiley, New York, 1953).

N. Ohta, paper presented at the Annual Symposium of the SPSE on Color Photography System, 21–24 Oct. 1970. Information is available from the author.

J. A. C. Yule, Principles of Color Reproduction (Wiley, New York, 1967), p. 156.

C. J. Bartleson (private communication).

R. S. Longhurst, Geometrical and Physical Optics (Longmans, Green, London, 1957), p. 370.

Reference 4, p. 209.

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Figures (12)

Fig. 1
Fig. 1

Luminous intensity I of an element of area ds in direction θ.

Fig. 2
Fig. 2

Multiple internal reflections of diffuse light in a gelatin layer.

Fig. 3
Fig. 3

External and internal Fresnel reflectances Rθ and rθ vs angle of incidence θ.

Fig. 4
Fig. 4

Values of definite integrals I1 and I2 vs transmittance T.

Fig. 5
Fig. 5

Diffuse reflection density (lower solid curve), specular reflection density (upper solid curve), and specular reflection density+surface reflection (lower dotted curve) vs transmission density Dt.

Fig. 6
Fig. 6

Diffuse reflection density Dr vs transmission density Dt for a series of base reflectance RB.

Fig. 7
Fig. 7

Specular reflection density Dr′ with 5% surface reflection vs transmission density Dt for a series of base reflectance RB.

Fig. 8
Fig. 8

Spectral transmission-density distributions of typical cyan, magenta, and yellow dyes.

Fig. 9
Fig. 9

Color gamut obtainable by use of three dyes of Fig. 8 in a color film.

Fig. 10
Fig. 10

Color gamut obtainable by use of three dyes of Fig. 8 in a color print under perfectly diffuse unpolarized illumination.—— 80%, – – – 40%, – ×× – 20%, and – Δ — Δ – 10% luminous reflectance level.

Fig. 11
Fig. 11

Color gamut obtainable by use of three dyes of Fig. 8 in a color print with 5% surface reflectance. See legend, caption of Fig. 10.

Fig. 12
Fig. 12

Color gamut obtainable by use of three dyes of Fig. 8 in a color print without surface reflection. See legend, caption of Fig. 10.

Tables (2)

Tables Icon

Table I Areas of color gamuts in Fig. 10 S1, and in Fig. 11 S2, and the ratio r(= S1/S2) at each luminous-reflectance level L (%).

Tables Icon

Table II Areas of color gamuts in Fig. 9 S3, and in Fig. 12 S4, and the ratio r(= S4/S3) at each luminous-reflectance level L (%).

Equations (34)

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I = L d s cos θ ,
d F = 2 π L d s sin θ cos θ d θ .
F = 0 θ 2 π L d s sin θ cos θ d θ = π L d s sin 2 θ ,
F t = π L d s .
d F = 2 F t sin θ cos θ d θ .
D r = - log ( 10 - D r + S ) + log ( 1 + S ) ,
d F = 2 F t sin Φ cos Φ d Φ ,
d F 0 = 2 F t R Ω sin Ω cos Ω d Ω ,
d f 1 = d F ( 1 - R Φ ) T sec ϕ ,
d F 1 = 2 d f 1 sin ω cos ω T sec ω ( 1 - r ω ) R B d ω ,
sin Ω = n sin ω , sin Φ = n sin ϕ ,
d f 1 = 2 R B d f 1 sin θ 1 cos θ 1 d θ 1 .
d f 2 = d f 1 T 2 sec θ 1 r θ 1 = 2 R B d f 1 T 2 sec θ 1 r θ 1 sin θ 1 cos θ 1 d θ 1 .
d F 2 = 2 d f 2 sin ω cos ω T sec ω ( 1 - r ω ) R B d ω .
d F 3 = 2 d f 3 sin ω cos ω T sec ω ( 1 - r ω ) R B d ω , d F n = 2 d f n sin ω cos ω T sec ω ( 1 - r ω ) R B d ω .
F 1 = 2 R B d F T sec ϕ + sec ω sin ω cos ω ( 1 - r ω ) ( 1 - R Φ ) d ω = 2 R B A ,
A = d F T sec ϕ + sin ω sin ω cos ω ( 1 - r ω ) ( 1 - R Φ ) d ω ,
F 2 = 0 π / 2 d F 2 = ( 2 R B ) 2 A 0 π / 2 T 2 sec θ 1 r θ 1 sin θ 1 cos θ 1 d θ 1 = ( 2 R B ) 2 A I 1 ,
I 1 = 0 π / 2 T 2 sec θ r θ sin θ cos θ d θ ,
F 3 = 0 π / 2 0 π / 2 d F 2 = ( 2 R B ) 3 A 0 π / 2 0 π / 2 T 2 sec θ 1 r θ 1 sin θ 1 cos θ 1 T 2 sec θ 2 r θ 2 × sin θ 2 cos θ 2 d θ 1 d θ 2 = ( 2 R B ) 3 A ( I 1 ) 2 , F n = ( 2 R B ) n A ( I 1 ) n - 1 .
f t ( Φ ) = A lim n i = 1 n ( 2 R B ) i I 1 i - 1 = 2 R B A lim n { [ 1 - ( 2 R B I 1 ) n ] / ( 1 - 2 R B I 1 ) } .
2 R B I 1 = 2 R B 0 π / 2 T 2 sec θ r θ sin θ cos θ d θ 2 0 π / 2 r θ sin θ cos θ d θ
f t ( Φ ) = 2 R B A / ( 1 - 2 R B I 1 ) .
F g = d F 0 + 0 π / 2 f t ( Φ ) = d F 0 + 2 R B 1 - 2 R B I 1 T sec ω sin ω cos ω ( 1 - r ω ) d ω × 0 π / 2 T sec ϕ ( 1 - R Φ ) d F .
F g = 2 F t R Ω sin Ω cos Ω d Ω + [ 4 R B F t / ( 1 - 2 R B I 1 ) ] × T sec ω sin ω cos ω ( 1 - r ω ) d ω I 2 ,
I 2 = 0 π / 2 T sec ϕ ( 1 - R Φ ) sin Φ cos Φ d Φ .
F b = 2 F t sin Ω cos Ω d Ω .
R = F g / F b = R Ω + 2 R B 1 - 2 R B I 1 T sec ω ( 1 - r ω ) sin ω cos ω d ω sin Ω cos Ω d Ω I 2 .
sin Ω = n sin ω , cos Ω d Ω = n cos ω d ω .
R = R Ω + [ 2 R B / ( 1 - 2 R B I 1 ) ] T sec ω ( 1 - r ω ) ( I 2 / n 2 ) .
R S S = 0.193 T 2.13 ( 1 2 R B - 0 π / 2 T 2 sec θ r θ sin θ cos θ d θ ) - 1 = 0.193 T 2.13 [ ( 1 / 2 R B ) - I 1 ] - 1 .
R D S = R Ω + [ 2 R B / ( 1 - 2 R B I 1 ) ] T sec ω ( 1 - r ω ) ( I 2 / n 2 ) .
I 2 0.45 T .
R D S ( R S S + R Ω ) / ( 1 + R Ω ) .