Abstract

Spectral prediction models for halftone prints generally assume homogeneously thick and sharply edged ink dots, i.e., bilevel halftones. In real prints, the ink thickness often decreases at the boundaries of the ink dots, thereby forming continuous-level halftones. The present study aims at verifying to what extent the classical Clapper–Yule and Yule–Nielsen models are able to predict the reflectance of single-ink continuous-level halftone prints. First we model the reflectance of continuous-level halftones by developing variable thickness extensions of both the Clapper–Yule and the Yule–Nielsen spectral prediction models. We consider continuous halftones whose thickness profiles are obtained by Gaussian filtering of the bilevel halftone image. Then we predict the reflectance spectra defined by the continuous-level models by fitting the bilevel models’ effective ink surface coverages. Since dot blurring tends to increase the absorption of light by the ink, the effective ink surface coverage is larger than the nominal one, i.e., dot blurring induces its own contribution to dot gain. Dot blurring can also be accurately modeled by an increased n-value of the classical Yule–Nielsen model.

© 2009 Optical Society of America

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References

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  1. A. Murray, “Monochrome reproduction in photoengraving,” J. Franklin Inst. 221, 721-744 (1936).
    [CrossRef]
  2. J. A. C. Yule and W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” in Proceedings of TAGA (Technical Association of the Graphic Arts, 1951), Vol. 3, 65-76.
  3. J. A. S. Viggiano, “The color of halftone tints,” in Proceedings of TAGA (Technical Association of the Graphic Arts, 1985), Vol. 37, pp. 647-661.
  4. F. R. Ruckdeschel and O. G. Hauser, “Yule-Nielsen effect in printing: a physical analysis,” Appl. Opt. 17, 3376-3383 (1978).
    [CrossRef] [PubMed]
  5. J. Arney and S. Yamaguchi, “The physics behind the Yule-Nielsen equation,” in Proceedings of PICS 1999: Image Processing, Image Quality, Image Capture, Systems Conference (Society for Imaging Science and Technology, 1999), pp. 381-385.
  6. A. Lewandowski, M. Ludl, G. Byrne, and G. Dorffner, “Applying the Yule-Nielsen equation with negative n,” J. Opt. Soc. Am. A 23, 1827-1834 (2006).
    [CrossRef]
  7. 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]
  8. D. B. Judd, “Fresnel reflection of diffusely incident light,” J. Res. Natl. Bur. Stand. 29, 329-332 (1942).
  9. M. Hébert and R. D. Hersch, “Classical print reflection models: a radiometric approach,” J. Imaging Sci. Technol. 48, 363-374 (2004).
  10. K. Iino and R. Berns, “Building color management modules using linear optimization. I. Desktop color system,” J. Imaging Sci. Technol. 42, 79-94 (1998).
  11. K. Iino and R. Berns, “Building color management modules using linear optimization. II. Prepress system for offset printing,” J. Imaging Sci. Technol. 42, 99-114 (1998).
  12. R. Balasubramanian, “Optimization of the spectral Neugebauer model for printer characterization,” J. Electron. Imaging 8, 156-166 (1999).
    [CrossRef]
  13. P. Emmel and R. D. Hersch, “Modeling ink spreading for color prediction,” J. Imaging Sci. Technol. 46, 237-246 (2002).
  14. R. D. Hersch, P. Emmel, F. Collaud, and F. Crété (2005), “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 33001-12.
    [CrossRef]
  15. G. Rogers, “Optical dot gain in a halftone print,” J. Imaging Sci. Technol. 41, 643-656 (1997).
  16. G. Rogers, “Optical dot gain: lateral scattering probabilities,” J. Imaging Sci. Technol. 42, 341-345 (1998).
  17. J. S. Arney and M. L. Alber, “A probability description of the Yule-Nielsen effect I,” J. Imaging Sci. Technol. 41, 633-636 (1997).
  18. J. S. Arney and M. L. Alber, “Optical effects of ink spread and penetration on halftones printed by thermal ink jet,” J. Imaging Sci. Technol. 42, 331-334 (1998).
  19. L. Yang, R. Lenz, and B. Kruse, “Light scattering and ink penetration effects on tone reproduction,” J. Opt. Soc. Am. A 18, 360-366 (2001).
    [CrossRef]
  20. G. Sharma, “Color fundamentals for digital imaging,” in Digital Color Imaging Handbook, G.Sharma, ed. (CRC Press, 2003), pp. 30-36.

2006 (1)

2005 (1)

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété (2005), “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 33001-12.
[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).

2001 (1)

1999 (1)

R. Balasubramanian, “Optimization of the spectral Neugebauer model for printer characterization,” J. Electron. Imaging 8, 156-166 (1999).
[CrossRef]

1998 (4)

K. Iino and R. Berns, “Building color management modules using linear optimization. I. Desktop color system,” J. Imaging Sci. Technol. 42, 79-94 (1998).

K. Iino and R. Berns, “Building color management modules using linear optimization. II. Prepress system for offset printing,” J. Imaging Sci. Technol. 42, 99-114 (1998).

J. S. Arney and M. L. Alber, “Optical effects of ink spread and penetration on halftones printed by thermal ink jet,” J. Imaging Sci. Technol. 42, 331-334 (1998).

G. Rogers, “Optical dot gain: lateral scattering probabilities,” J. Imaging Sci. Technol. 42, 341-345 (1998).

1997 (2)

J. S. Arney and M. L. Alber, “A probability description of the Yule-Nielsen effect I,” J. Imaging Sci. Technol. 41, 633-636 (1997).

G. Rogers, “Optical dot gain in a halftone print,” J. Imaging Sci. Technol. 41, 643-656 (1997).

1978 (1)

1953 (1)

1942 (1)

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

1936 (1)

A. Murray, “Monochrome reproduction in photoengraving,” J. Franklin Inst. 221, 721-744 (1936).
[CrossRef]

Alber, M. L.

J. S. Arney and M. L. Alber, “Optical effects of ink spread and penetration on halftones printed by thermal ink jet,” J. Imaging Sci. Technol. 42, 331-334 (1998).

J. S. Arney and M. L. Alber, “A probability description of the Yule-Nielsen effect I,” J. Imaging Sci. Technol. 41, 633-636 (1997).

Arney, J.

J. Arney and S. Yamaguchi, “The physics behind the Yule-Nielsen equation,” in Proceedings of PICS 1999: Image Processing, Image Quality, Image Capture, Systems Conference (Society for Imaging Science and Technology, 1999), pp. 381-385.

Arney, J. S.

J. S. Arney and M. L. Alber, “Optical effects of ink spread and penetration on halftones printed by thermal ink jet,” J. Imaging Sci. Technol. 42, 331-334 (1998).

J. S. Arney and M. L. Alber, “A probability description of the Yule-Nielsen effect I,” J. Imaging Sci. Technol. 41, 633-636 (1997).

Balasubramanian, R.

R. Balasubramanian, “Optimization of the spectral Neugebauer model for printer characterization,” J. Electron. Imaging 8, 156-166 (1999).
[CrossRef]

Berns, R.

K. Iino and R. Berns, “Building color management modules using linear optimization. II. Prepress system for offset printing,” J. Imaging Sci. Technol. 42, 99-114 (1998).

K. Iino and R. Berns, “Building color management modules using linear optimization. I. Desktop color system,” J. Imaging Sci. Technol. 42, 79-94 (1998).

Byrne, G.

Clapper, F. R.

Collaud, F.

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété (2005), “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 33001-12.
[CrossRef]

Crété, F.

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété (2005), “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 33001-12.
[CrossRef]

Dorffner, G.

Emmel, P.

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété (2005), “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 33001-12.
[CrossRef]

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

Hauser, O. G.

Hébert, M.

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

Hersch, R. D.

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété (2005), “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 33001-12.
[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).

Iino, K.

K. Iino and R. Berns, “Building color management modules using linear optimization. I. Desktop color system,” J. Imaging Sci. Technol. 42, 79-94 (1998).

K. Iino and R. Berns, “Building color management modules using linear optimization. II. Prepress system for offset printing,” J. Imaging Sci. Technol. 42, 99-114 (1998).

Judd, D. B.

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

Kruse, B.

Lenz, R.

Lewandowski, A.

Ludl, M.

Murray, A.

A. Murray, “Monochrome reproduction in photoengraving,” J. Franklin Inst. 221, 721-744 (1936).
[CrossRef]

Nielsen, W. J.

J. A. C. Yule and W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” in Proceedings of TAGA (Technical Association of the Graphic Arts, 1951), Vol. 3, 65-76.

Rogers, G.

G. Rogers, “Optical dot gain: lateral scattering probabilities,” J. Imaging Sci. Technol. 42, 341-345 (1998).

G. Rogers, “Optical dot gain in a halftone print,” J. Imaging Sci. Technol. 41, 643-656 (1997).

Ruckdeschel, F. R.

Sharma, G.

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

Viggiano, J. A. S.

J. A. S. Viggiano, “The color of halftone tints,” in Proceedings of TAGA (Technical Association of the Graphic Arts, 1985), Vol. 37, pp. 647-661.

Yamaguchi, S.

J. Arney and S. Yamaguchi, “The physics behind the Yule-Nielsen equation,” in Proceedings of PICS 1999: Image Processing, Image Quality, Image Capture, Systems Conference (Society for Imaging Science and Technology, 1999), pp. 381-385.

Yang, L.

Yule, J. A. C.

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. A. C. Yule and W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” in Proceedings of TAGA (Technical Association of the Graphic Arts, 1951), Vol. 3, 65-76.

Appl. Opt. (1)

J. Electron. Imaging (2)

R. D. Hersch, P. Emmel, F. Collaud, and F. Crété (2005), “Spectral reflection and dot surface prediction models for color halftone prints,” J. Electron. Imaging 14, 33001-12.
[CrossRef]

R. Balasubramanian, “Optimization of the spectral Neugebauer model for printer characterization,” J. Electron. Imaging 8, 156-166 (1999).
[CrossRef]

J. Franklin Inst. (1)

A. Murray, “Monochrome reproduction in photoengraving,” J. Franklin Inst. 221, 721-744 (1936).
[CrossRef]

J. Imaging Sci. Technol. (8)

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

K. Iino and R. Berns, “Building color management modules using linear optimization. I. Desktop color system,” J. Imaging Sci. Technol. 42, 79-94 (1998).

K. Iino and R. Berns, “Building color management modules using linear optimization. II. Prepress system for offset printing,” J. Imaging Sci. Technol. 42, 99-114 (1998).

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

G. Rogers, “Optical dot gain in a halftone print,” J. Imaging Sci. Technol. 41, 643-656 (1997).

G. Rogers, “Optical dot gain: lateral scattering probabilities,” J. Imaging Sci. Technol. 42, 341-345 (1998).

J. S. Arney and M. L. Alber, “A probability description of the Yule-Nielsen effect I,” J. Imaging Sci. Technol. 41, 633-636 (1997).

J. S. Arney and M. L. Alber, “Optical effects of ink spread and penetration on halftones printed by thermal ink jet,” J. Imaging Sci. Technol. 42, 331-334 (1998).

J. Opt. Soc. Am. (1)

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).

Other (4)

J. A. C. Yule and W. J. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” in Proceedings of TAGA (Technical Association of the Graphic Arts, 1951), Vol. 3, 65-76.

J. A. S. Viggiano, “The color of halftone tints,” in Proceedings of TAGA (Technical Association of the Graphic Arts, 1985), Vol. 37, pp. 647-661.

J. Arney and S. Yamaguchi, “The physics behind the Yule-Nielsen equation,” in Proceedings of PICS 1999: Image Processing, Image Quality, Image Capture, Systems Conference (Society for Imaging Science and Technology, 1999), pp. 381-385.

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

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Figures (7)

Fig. 1
Fig. 1

(a) Blurred halftone function F ( x , y ) for a surface coverage a = 0.6 and various blurring coefficients σ and (b) the ink thickness of a single dot along the x axis.

Fig. 2
Fig. 2

Reflectances of the paper, R p , of the solid cyan ink print, R i , of a 50% bilevel halftone, R, and of the blurred halftone obtained with σ = 0.1 , R σ . R p and R i are measured. R and R σ are predicted by the classical and the continuous Clapper–Yule model, respectively..

Fig. 3
Fig. 3

Dot gain curves predicted by the Clapper–Yule model for various blurring coefficients.

Fig. 4
Fig. 4

Dot gain curves predicted by the Yule–Nielsen model for various blurring coefficients and for n b = n c = 3.5 .

Fig. 5
Fig. 5

Influence of the blurring coefficient on the n-factor fitted from three blurred halftone patches with ink surface coverages 0.25, 0.5, and 0.75 by considering the effective surface coverages equal to the nominal ones.

Fig. 6
Fig. 6

Dot gain curves calculated using the bilevel Yule–Nielsen model with various n b -values, from print reflectances simulated by the continuous-level Yule–Nielsen model with n c = 3.5 for a blurring coefficient σ = 0.1 .

Fig. 7
Fig. 7

Fitted optimal dot gain for the 0.5 surface coverage halftone with a blurring coefficient σ = 0.1 .

Equations (23)

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R ( λ ) = ( 1 a ) R p ( λ ) + a R i ( λ ) .
R ( λ ) = [ a R i 1 n ( λ ) + ( 1 a ) R p 1 n ( λ ) ] n .
R ( λ ) = T in T ex r g ( λ ) [ 1 a + a t ( λ ) ] 2 1 r i r g ( λ ) [ 1 a + a t 2 ( λ ) ] ,
F ( x , y ) = i j f ( x i , y j ) .
f 0 ( x , y ) = { 1 if x 2 + y 2 < a π 0 else } .
g σ ( x , y ) = 1 2 π σ 2 exp ( x 2 + y 2 2 σ 2 ) .
f σ ( x , y ) = f 0 ( u , v ) g σ ( x u , y v ) d u d v ,
F σ ( x , y ) = f σ ( x , y ) + f σ ( x 1 , y ) + f σ ( x , y 1 ) + f σ ( x 1 , y 1 ) .
g σ ( x , y ) d x d y = 1 ,
T ( x , y ) = t F ( x , y ) ,
R i ( λ ) = R p ( λ ) t y n 2 ( λ ) .
R i ( γ ) ( λ ) = R p ( λ ) t y n 2 γ ( λ ) = R p ( λ ) [ R i ( λ ) R p ( λ ) ] γ .
R i ( λ ) = T in T ex r g ( λ ) t 2 ( λ ) 1 r i r g ( λ ) t 2 ( λ ) .
r g ( λ ) = R p ( λ ) T in T ex + r i R p ( λ ) .
t ( λ ) = R i ( λ ) r g ( λ ) [ T in T ex + r i R i ( λ ) ] .
R YN ( λ ) = [ k = 1 N a k R k 1 n ( λ ) ] n .
R YN = R p [ x = 0 1 y = 0 1 ( R i R p ) F ( x , y ) n c d x d y ] n c .
R CY ( λ ) = T in T ex r g ( λ ) [ k = 1 N a k t k ( λ ) ] 2 1 r i r g ( λ ) k = 1 N a k t k 2 ( λ ) ,
R CY = T in T ex r g [ x = 0 1 y = 0 1 t F ( x , y ) d x d y ] 2 1 r i r g x = 0 1 y = 0 1 t 2 F ( x , y ) d x d y .
a = arg min x λ = 380 730 [ P x ( λ ) M ( λ ) ] 2 .
a = arg min x λ = 380 730 { T in T ex r g ( λ ) [ 1 x + x t ( λ ) ] 2 1 r i r g ( λ ) [ 1 x + x t 2 ( λ ) ] M ( λ ) } 2 .
a = arg min x λ = 380 730 { [ x R i 1 n b ( λ ) + ( 1 x ) R p 1 n b ( λ ) ] n b M ( λ ) } 2 .
n b = arg min u k [ λ = 380 730 { [ a k R i 1 u ( λ ) + ( 1 a k ) R p 1 u ( λ ) ] u M k ( λ ) } 2 ] .

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