Abstract

We extend a previously proposed spectral reflectance and transmittance prediction model for recto-verso prints to the case of multi-ink halftones. The model takes into account the multiple reflections and the lateral propagation of light within the paper substrate (optical dot gain) as well as the spreading of the inks according to their superposition conditions (mechanical dot gain). The model accounts for the orientation of the incident and exiting lights when traversing the halftone ink layers, which enables modeling the measuring geometry. The equations for the calibration of the model and for the predictions are presented in detail. Several experiments with inkjet prints show that the multi-ink halftone transmittance model is as accurate as the actually most performing reflectance models for halftone prints.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. D. Hersch, P. Emmel, F. Collaud, and F. Crété, “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 33001-33012 (2005).
    [CrossRef]
  2. M. Hébert and R. D. Hersch, “A reflectance and transmittance model for recto-verso halftone prints,” J. Opt. Soc. Am. A 22, 1952-1967 (2006).
    [CrossRef]
  3. F. R. Clapper and J. A. C. Yule, “The effect of multiple internal reflections on the densities of halftone prints on paper,” J. Opt. Soc. Am. 43, 600-603 (1953).
    [CrossRef]
  4. F. C. Williams and F. R. Clapper, “Multiple internal reflections in photographic color prints,” J. Opt. Soc. Am. 29, 595-599 (1953).
    [CrossRef]
  5. M. Hébert, R. D. Hersch, and J.-M. Becker, “Compositional reflectance and transmittance model for multilayer specimens,” J. Opt. Soc. Am. A 24, 2628-2644 (2007).
    [CrossRef]
  6. H.-H. Perkampus, Encyclopedia of Spectroscopy (VCH, 1995).
  7. J. W. Ryde, “The scattering of light by turbid media,” Proc. R. Soc. London, Ser. A 131, 451-475 (1931).
    [CrossRef]
  8. G. Kortüm, “Phenomenological theories of absorption and scattering of tightly packed particles,” in Reflectance Spectroscopy (Springer Verlag, 1969), Chap. 4, pp. 103-168.
  9. M. Born and E. Wolf, Principle of Optics, 7th ed. (Pergamon, 1999), p. 40.
  10. M. Hébert and R. D. Hersch, “Classical print reflection models: a radiometric approach,” J. Imaging Sci. Technol. 48, 363-374 (2004).
  11. W. R. McCluney, Introduction to Radiometry and Photometry (Artech, 1994), pp. 7-13.
  12. D. B. Judd, “Fresnel reflection of diffusely incident light,” J. Res. Natl. Bur. Stand. 29, 329-332 (1942).
  13. P. Emmel and R. D. Hersch, “Modeling ink spreading for color prediction,” J. Imaging Sci. Technol. 46, 237-246 (2002).
  14. M. E. Demichel, Procédé 26, 17-21 (1924), see also .
  15. D. R. Wyble and R. S. Berns, “A critical review of spectral models applied to binary color printing,” Color Res. Appl. 25, 4-19 (2000).
    [CrossRef]
  16. G. Sharma, “Color fundamentals for digital imaging,” in Digital Color Imaging Handbook, G.Sharma, ed. (CRC, 2003), pp. 30-36.

2007 (1)

2006 (1)

2005 (1)

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété, “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 33001-33012 (2005).
[CrossRef]

2004 (1)

M. Hébert and R. D. Hersch, “Classical print reflection models: a radiometric approach,” J. Imaging Sci. Technol. 48, 363-374 (2004).

2002 (1)

P. Emmel and R. D. Hersch, “Modeling ink spreading for color prediction,” J. Imaging Sci. Technol. 46, 237-246 (2002).

2000 (1)

D. R. Wyble and R. S. Berns, “A critical review of spectral models applied to binary color printing,” Color Res. Appl. 25, 4-19 (2000).
[CrossRef]

1953 (2)

F. R. Clapper and J. A. C. Yule, “The effect of multiple internal reflections on the densities of halftone prints on paper,” J. Opt. Soc. Am. 43, 600-603 (1953).
[CrossRef]

F. C. Williams and F. R. Clapper, “Multiple internal reflections in photographic color prints,” J. Opt. Soc. Am. 29, 595-599 (1953).
[CrossRef]

1942 (1)

D. B. Judd, “Fresnel reflection of diffusely incident light,” J. Res. Natl. Bur. Stand. 29, 329-332 (1942).

1931 (1)

J. W. Ryde, “The scattering of light by turbid media,” Proc. R. Soc. London, Ser. A 131, 451-475 (1931).
[CrossRef]

1924 (1)

M. E. Demichel, Procédé 26, 17-21 (1924), see also .

Becker, J.-M.

Berns, R. S.

D. R. Wyble and R. S. Berns, “A critical review of spectral models applied to binary color printing,” Color Res. Appl. 25, 4-19 (2000).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principle of Optics, 7th ed. (Pergamon, 1999), p. 40.

Clapper, F. R.

F. R. Clapper and J. A. C. Yule, “The effect of multiple internal reflections on the densities of halftone prints on paper,” J. Opt. Soc. Am. 43, 600-603 (1953).
[CrossRef]

F. C. Williams and F. R. Clapper, “Multiple internal reflections in photographic color prints,” J. Opt. Soc. Am. 29, 595-599 (1953).
[CrossRef]

Collaud, F.

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété, “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 33001-33012 (2005).
[CrossRef]

Crété, F.

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété, “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 33001-33012 (2005).
[CrossRef]

Demichel, M. E.

M. E. Demichel, Procédé 26, 17-21 (1924), see also .

Emmel, P.

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété, “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 33001-33012 (2005).
[CrossRef]

P. Emmel and R. D. Hersch, “Modeling ink spreading for color prediction,” J. Imaging Sci. Technol. 46, 237-246 (2002).

Hébert, M.

Hersch, R. D.

M. Hébert, R. D. Hersch, and J.-M. Becker, “Compositional reflectance and transmittance model for multilayer specimens,” J. Opt. Soc. Am. A 24, 2628-2644 (2007).
[CrossRef]

M. Hébert and R. D. Hersch, “A reflectance and transmittance model for recto-verso halftone prints,” J. Opt. Soc. Am. A 22, 1952-1967 (2006).
[CrossRef]

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété, “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 33001-33012 (2005).
[CrossRef]

M. Hébert and R. D. Hersch, “Classical print reflection models: a radiometric approach,” J. Imaging Sci. Technol. 48, 363-374 (2004).

P. Emmel and R. D. Hersch, “Modeling ink spreading for color prediction,” J. Imaging Sci. Technol. 46, 237-246 (2002).

Judd, D. B.

D. B. Judd, “Fresnel reflection of diffusely incident light,” J. Res. Natl. Bur. Stand. 29, 329-332 (1942).

Kortüm, G.

G. Kortüm, “Phenomenological theories of absorption and scattering of tightly packed particles,” in Reflectance Spectroscopy (Springer Verlag, 1969), Chap. 4, pp. 103-168.

McCluney, W. R.

W. R. McCluney, Introduction to Radiometry and Photometry (Artech, 1994), pp. 7-13.

Perkampus, H.-H.

H.-H. Perkampus, Encyclopedia of Spectroscopy (VCH, 1995).

Ryde, J. W.

J. W. Ryde, “The scattering of light by turbid media,” Proc. R. Soc. London, Ser. A 131, 451-475 (1931).
[CrossRef]

Sharma, G.

G. Sharma, “Color fundamentals for digital imaging,” in Digital Color Imaging Handbook, G.Sharma, ed. (CRC, 2003), pp. 30-36.

Williams, F. C.

F. C. Williams and F. R. Clapper, “Multiple internal reflections in photographic color prints,” J. Opt. Soc. Am. 29, 595-599 (1953).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principle of Optics, 7th ed. (Pergamon, 1999), p. 40.

Wyble, D. R.

D. R. Wyble and R. S. Berns, “A critical review of spectral models applied to binary color printing,” Color Res. Appl. 25, 4-19 (2000).
[CrossRef]

Yule, J. A. C.

Color Res. Appl. (1)

D. R. Wyble and R. S. Berns, “A critical review of spectral models applied to binary color printing,” Color Res. Appl. 25, 4-19 (2000).
[CrossRef]

J. Electron. Imaging (1)

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété, “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 33001-33012 (2005).
[CrossRef]

J. Imaging Sci. Technol. (2)

M. Hébert and R. D. Hersch, “Classical print reflection models: a radiometric approach,” J. Imaging Sci. Technol. 48, 363-374 (2004).

P. Emmel and R. D. Hersch, “Modeling ink spreading for color prediction,” J. Imaging Sci. Technol. 46, 237-246 (2002).

J. Opt. Soc. Am. (2)

F. C. Williams and F. R. Clapper, “Multiple internal reflections in photographic color prints,” J. Opt. Soc. Am. 29, 595-599 (1953).
[CrossRef]

F. R. Clapper and J. A. C. Yule, “The effect of multiple internal reflections on the densities of halftone prints on paper,” J. Opt. Soc. Am. 43, 600-603 (1953).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Res. Natl. Bur. Stand. (1)

D. B. Judd, “Fresnel reflection of diffusely incident light,” J. Res. Natl. Bur. Stand. 29, 329-332 (1942).

Proc. R. Soc. London, Ser. A (1)

J. W. Ryde, “The scattering of light by turbid media,” Proc. R. Soc. London, Ser. A 131, 451-475 (1931).
[CrossRef]

Procédé (1)

M. E. Demichel, Procédé 26, 17-21 (1924), see also .

Other (5)

H.-H. Perkampus, Encyclopedia of Spectroscopy (VCH, 1995).

G. Kortüm, “Phenomenological theories of absorption and scattering of tightly packed particles,” in Reflectance Spectroscopy (Springer Verlag, 1969), Chap. 4, pp. 103-168.

M. Born and E. Wolf, Principle of Optics, 7th ed. (Pergamon, 1999), p. 40.

W. R. McCluney, Introduction to Radiometry and Photometry (Artech, 1994), pp. 7-13.

G. Sharma, “Color fundamentals for digital imaging,” in Digital Color Imaging Handbook, G.Sharma, ed. (CRC, 2003), pp. 30-36.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Reflection and transmission of directional light at the air-side and paper-side of a colored interface.

Fig. 2
Fig. 2

Nominal-to-effective surface coverage function representing the effective surface coverage of a halftone ink as a function of the nominal surface coverage a.

Tables (4)

Tables Icon

Table 1 Expressions for T in

Tables Icon

Table 2 Expressions for T ex

Tables Icon

Table 3 Average Color Difference between Measured and Predicted Transmission Spectra

Tables Icon

Table 4 Average Color Difference between Measured and Predicted Transmission Spectra

Equations (56)

Equations on this page are rendered with MathJax. Learn more.

t = k = 1 2 N a k t k .
k = 1 2 N a k t k 1 cos θ .
R = T in T ex ρ r 2 ( ρ 2 τ 2 ) ( 1 r 1 ρ ) ( 1 r 2 ρ ) r 1 r 2 τ 2 ,
T = T in T ex τ ( 1 r 1 ρ ) ( 1 r 2 ρ ) r 1 r 2 τ 2 ,
R 01 ( θ 0 ) + T 01 ( θ 0 ) = 1 .
R 10 ( θ 1 ) + T 10 ( θ 1 ) = 1 .
T 01 ( θ 0 ) = T 10 ( θ 1 ) ,
R 01 ( θ 0 ) = R 10 ( θ 1 ) .
r 01 = θ 0 = 0 π 2 R 01 ( θ 0 ) sin 2 θ 0 d θ 0 ,
r 10 = θ 1 = 0 π 2 R 10 ( θ 1 ) sin 2 θ 1 d θ 1 ,
t 01 = θ 0 = 0 π 2 T 01 ( θ 0 ) sin 2 θ 0 d θ 0 = 1 r 01 ,
t 10 = θ 1 = 0 π 2 T 10 ( θ 1 ) sin 2 θ 1 d θ 1 = 1 r 10 .
r 10 ( t ) = θ 1 = 0 π 2 R 10 ( θ 1 ) t 2 cos θ 1 sin 2 θ 1 d θ 1 .
t 01 ( t ) = θ 0 = 0 π 2 T 01 ( θ 0 ) t 1 cos θ 1 sin 2 θ 0 d θ 0 ,
t 10 ( t ) = θ 1 = 0 π 2 T 10 ( θ 1 ) t 1 cos θ 1 sin 2 θ 1 d θ 1 .
r 10 ( t ) r 10 e t β 1 e 1 ,
t 01 ( t ) t 01 t μ ,
t 10 ( t ) t 10 t μ ,
T 01 ( θ i ) k = 1 2 N a k t k 1 cos θ i ,
t 01 ( a k , t k ) = k a k t 01 ( t k ) t 01 k a k t k μ .
t 10 ( a k , t k ) = k a k t 10 ( t k ) t 10 k a k t k μ .
r 10 ( a k , t k ) = k a k r 10 ( t k ) .
r 10 ( t ) = r 10 t 2 .
R = t 01 T 10 ( 0 ) n p 2 ρ r 10 ( ρ 2 τ 2 ) ( 1 r 10 ρ ) 2 r 10 2 τ 2 .
T = t 01 T 10 ( 0 ) n p 2 τ ( 1 r 10 ρ ) 2 r 10 2 τ 2 .
R = R t 01 T 10 ( 0 ) n p 2
T = T t 01 T 10 ( 0 ) n p 2 ,
ρ = R + r 10 ( R 2 T 2 ) ( 1 + r 10 R ) 2 r 10 2 T 2 ,
τ = T ( 1 + r 10 R ) 2 r 10 2 T 2 .
T = t u t 01 T 10 ( 0 ) n p 2 τ [ 1 r 10 ( t u ) ρ ] [ 1 r 10 ρ ] r 10 ( t u ) r 10 τ 2 .
T = t u μ t 01 T 10 ( 0 ) n p 2 τ [ 1 r 10 ρ ] [ 1 r 10 ( t u ) ρ ] r 10 r 10 ( t u ) τ 2 .
r 1 = a u v r 10 ( t u + v ) + ( 1 a u v ) r 10 ( t v ) ,
T ex = [ a u v t u + v + ( 1 a u v ) t v ] T 10 ( 0 ) n p 2 .
T = [ a u v t u + v + ( 1 a u v ) t v ] t 01 T 10 ( 0 ) n p 2 τ ( 1 r 1 ρ ) ( 1 r 10 ρ ) r 1 r 10 τ 2
a u v = min 0 a 1 λ = 380 nm 730 nm { T ̃ t 01 T 10 ( 0 ) n p 2 τ ̃ [ a t ̃ u + v + ( 1 a ) t ̃ v ] ( 1 r 10 ρ ̃ ) ( 1 r ̃ 1 ρ ̃ ) r 10 r ̃ 1 τ ̃ 2 } 2 ,
T in = t 10 [ ( 1 a u v ) t u + v μ + a u v t v μ ] ,
T ex = T 10 ( 0 ) n p 2 ,
r 1 = r 10 ,
r 2 = a u v r 10 ( t u + v ) + ( 1 a u v ) r 10 ( t v ) .
c = ( 1 m ) ( 1 y ) f c ( c 0 ) + m ( 1 y ) f c m ( c 0 ) + ( 1 m ) y f c y ( c 0 ) + m y f c m + y ( c 0 ) ,
m = ( 1 c ) ( 1 y ) f m ( m 0 ) + c ( 1 y ) f m c ( m 0 ) + ( 1 c ) y f m y ( m 0 ) + c y f m c + y ( m 0 ) ,
y = ( 1 c ) ( 1 m ) f y ( y 0 ) + c ( 1 m ) f y c ( y 0 ) + ( 1 c ) m f y m ( y 0 ) + c m f y c + m ( y 0 ) .
a w = ( 1 c ) ( 1 m ) ( 1 y ) ,
a c = c ( 1 m ) ( 1 y ) ,
a m = ( 1 c ) m ( 1 y ) ,
a y = ( 1 c ) ( 1 m ) y ,
a m + y = ( 1 c ) m y ,
a c + y = c ( 1 m ) y ,
a c + m = c m ( 1 y ) ,
a c + m + y = c m y .
T in = t 01 k a k t k μ , T ex = T 10 ( 0 ) n p 2 k a k t k ,
r 1 = k a k r 10 ( t k ) , and r 2 = k a k r 10 ( t k ) ,
T = t 01 T 10 ( 0 ) n p 2 τ ( a k t k μ ) ( a k t k ) [ 1 ρ a k r 10 ( t k ) ] [ 1 ρ a k r 10 ( t k ) ] [ a k r 10 ( t k ) ] [ a k r 10 ( t k ) ] τ 2 .
T in = t 01 k a k t k μ .
R = t 01 T 10 ( 0 ) n p 2 ( a k t k μ ) ( a k t k ) [ ρ ( ρ 2 τ 2 ) a k r 10 ( t k ) ] [ 1 ρ a k r 10 ( t k ) ] [ 1 ρ a k r 10 ( t k ) ] [ a k r 10 ( t k ) ] [ a k r 10 ( t k ) ] τ 2 .
R = t 01 T 10 ( 0 ) n p 2 ( a k t k μ ) ( a k t k ) ρ B 1 ρ B a k r 10 ( t k ) ,

Metrics