Abstract

Light scattering, or the so-called Yule–Nielsen effect, and ink penetration into the substrate paper play important roles in tone reproduction. We develop a framework in which the influences of both of these effects on the reflectance and tristimulus values of a halftone sample are investigated. The properties of the paper and the ink and their bilateral interaction can be parameterized by the reflectance Rp0 of the substrate paper, the transmittance Ti of the ink layer, the parameter γ describing the ink penetration, and p¯ describing the Yule–Nielsen effect. We derive explicit expressions that relate the reflectance of the ink dots (Ri), the paper (Rp) and the halftone image (R) as functions of these parameters. We also describe the optical dot gain as a function of these parameters. We further demonstrate that ink penetration leads to a decrease in optical dot gain and that scattering in the paper results in the printed image’s being viewed as more saturated in color.

© 2001 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 (1936).
    [CrossRef]
  2. H. Neugebauer, “Die theoretischen Grundlagen des Mehrfarbenbuchdrucks,” Z. Tech. Phys. (Leipzig) 36, 75–89 (1937).
  3. J. Yule, W. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” in TAGA (Tech. Assoc. Graphic Arts) Proc., 65–76 (1951).
  4. I. Pobboravsky, M. Person, “Computation of dot areas required to match a colorimetrically specified color using the modified Neugebauer equations,” in TAGA (Tech. Assoc. Graphic Arts) Proc., 65–77 (1972).
  5. F. Ruckdeschel, O. Hauser, “Yule–Nielsen effect in printing: a physical analysis,” Appl. Opt. 17, 3376–3383 (1978).
    [CrossRef] [PubMed]
  6. S. Gustavson, “Dot gain in color halftones,” Ph.D. dissertation (Linköping University, Linköping, Sweden, 1997).
  7. S. Gustavson, “Color gamut of halftone reproduction,” J. Imaging Sci. Technol. 41, 283–290 (1997).
  8. G. Rogers, “Optical dot gain in a halftone print,” J. Imaging Sci. Technol. 41, 643–656 (1997).
  9. G. Rogers, “Effect of light scatter on halftone color,” J. Opt. Soc. Am. A 15, 1813–1821 (1998).
    [CrossRef]
  10. G. Rogers, “Neugebauer revisited: random dots in halftone screening,” Color Res. Appl. 23, 104–113 (1998).
    [CrossRef]
  11. G. Rogers, “Optical dot gain: lateral scattering probabilities,” J. Imaging Sci. Technol. 42, 341–345 (1998).
  12. J. Arney, “A probability description of the Yule–Nielsen effect I,” J. Imaging Sci. Technol. 41, 633–636 (1997).
  13. J. Arney, M. Katsube, “A probability description of the Yule–Nielsen effect II: the impact of halftone geometry,” J. Imaging Sci. Technol. 41, 637–642 (1997).
  14. J. Huntsman, “A new model of dot gain and its application to a multilayer color proof,” J. Imaging Sci. Technol. 13, 136–145 (1987).
  15. J. Arney, M. Alber, “Optical effects of ink spread and penetration on halftone printed by thermal ink jet,” J. Imaging Sci. Technol. 42, 331–334 (1998).
  16. L. Yang, B. Kruse, “Ink penetration and its effects on printing,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts V, R. Eschbach, G. G. Marcu, eds., Proc. SPIE3963, 365–375 (2000).
  17. J. Arney, P. Engeldrum, H. Zeng, “An expanded Murray–Davis model of tone reproduction in halftone imaging,” J. Imaging Sci. Technol. 39, 502–508 (1995).
  18. M. Andersson, “A study in how the ink set, solid ink density, and screening method influence the color gamut in four-color process printing,” M. Sc. thesis (Rochester Institute of Technology, Rochester, New York, 1997).

1998 (4)

G. Rogers, “Neugebauer revisited: random dots in halftone screening,” Color Res. Appl. 23, 104–113 (1998).
[CrossRef]

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

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

G. Rogers, “Effect of light scatter on halftone color,” J. Opt. Soc. Am. A 15, 1813–1821 (1998).
[CrossRef]

1997 (4)

S. Gustavson, “Color gamut of halftone reproduction,” J. Imaging Sci. Technol. 41, 283–290 (1997).

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

J. Arney, “A probability description of the Yule–Nielsen effect I,” J. Imaging Sci. Technol. 41, 633–636 (1997).

J. Arney, M. Katsube, “A probability description of the Yule–Nielsen effect II: the impact of halftone geometry,” J. Imaging Sci. Technol. 41, 637–642 (1997).

1995 (1)

J. Arney, P. Engeldrum, H. Zeng, “An expanded Murray–Davis model of tone reproduction in halftone imaging,” J. Imaging Sci. Technol. 39, 502–508 (1995).

1987 (1)

J. Huntsman, “A new model of dot gain and its application to a multilayer color proof,” J. Imaging Sci. Technol. 13, 136–145 (1987).

1978 (1)

1972 (1)

I. Pobboravsky, M. Person, “Computation of dot areas required to match a colorimetrically specified color using the modified Neugebauer equations,” in TAGA (Tech. Assoc. Graphic Arts) Proc., 65–77 (1972).

1951 (1)

J. Yule, W. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” in TAGA (Tech. Assoc. Graphic Arts) Proc., 65–76 (1951).

1937 (1)

H. Neugebauer, “Die theoretischen Grundlagen des Mehrfarbenbuchdrucks,” Z. Tech. Phys. (Leipzig) 36, 75–89 (1937).

1936 (1)

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

Alber, M.

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

Andersson, M.

M. Andersson, “A study in how the ink set, solid ink density, and screening method influence the color gamut in four-color process printing,” M. Sc. thesis (Rochester Institute of Technology, Rochester, New York, 1997).

Arney, J.

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

J. Arney, “A probability description of the Yule–Nielsen effect I,” J. Imaging Sci. Technol. 41, 633–636 (1997).

J. Arney, M. Katsube, “A probability description of the Yule–Nielsen effect II: the impact of halftone geometry,” J. Imaging Sci. Technol. 41, 637–642 (1997).

J. Arney, P. Engeldrum, H. Zeng, “An expanded Murray–Davis model of tone reproduction in halftone imaging,” J. Imaging Sci. Technol. 39, 502–508 (1995).

Engeldrum, P.

J. Arney, P. Engeldrum, H. Zeng, “An expanded Murray–Davis model of tone reproduction in halftone imaging,” J. Imaging Sci. Technol. 39, 502–508 (1995).

Gustavson, S.

S. Gustavson, “Color gamut of halftone reproduction,” J. Imaging Sci. Technol. 41, 283–290 (1997).

S. Gustavson, “Dot gain in color halftones,” Ph.D. dissertation (Linköping University, Linköping, Sweden, 1997).

Hauser, O.

Huntsman, J.

J. Huntsman, “A new model of dot gain and its application to a multilayer color proof,” J. Imaging Sci. Technol. 13, 136–145 (1987).

Katsube, M.

J. Arney, M. Katsube, “A probability description of the Yule–Nielsen effect II: the impact of halftone geometry,” J. Imaging Sci. Technol. 41, 637–642 (1997).

Kruse, B.

L. Yang, B. Kruse, “Ink penetration and its effects on printing,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts V, R. Eschbach, G. G. Marcu, eds., Proc. SPIE3963, 365–375 (2000).

Murray, A.

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

Neugebauer, H.

H. Neugebauer, “Die theoretischen Grundlagen des Mehrfarbenbuchdrucks,” Z. Tech. Phys. (Leipzig) 36, 75–89 (1937).

Nielsen, W.

J. Yule, W. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” in TAGA (Tech. Assoc. Graphic Arts) Proc., 65–76 (1951).

Person, M.

I. Pobboravsky, M. Person, “Computation of dot areas required to match a colorimetrically specified color using the modified Neugebauer equations,” in TAGA (Tech. Assoc. Graphic Arts) Proc., 65–77 (1972).

Pobboravsky, I.

I. Pobboravsky, M. Person, “Computation of dot areas required to match a colorimetrically specified color using the modified Neugebauer equations,” in TAGA (Tech. Assoc. Graphic Arts) Proc., 65–77 (1972).

Rogers, G.

G. Rogers, “Effect of light scatter on halftone color,” J. Opt. Soc. Am. A 15, 1813–1821 (1998).
[CrossRef]

G. Rogers, “Neugebauer revisited: random dots in halftone screening,” Color Res. Appl. 23, 104–113 (1998).
[CrossRef]

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.

Yang, L.

L. Yang, B. Kruse, “Ink penetration and its effects on printing,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts V, R. Eschbach, G. G. Marcu, eds., Proc. SPIE3963, 365–375 (2000).

Yule, J.

J. Yule, W. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” in TAGA (Tech. Assoc. Graphic Arts) Proc., 65–76 (1951).

Zeng, H.

J. Arney, P. Engeldrum, H. Zeng, “An expanded Murray–Davis model of tone reproduction in halftone imaging,” J. Imaging Sci. Technol. 39, 502–508 (1995).

Appl. Opt. (1)

Color Res. Appl. (1)

G. Rogers, “Neugebauer revisited: random dots in halftone screening,” Color Res. Appl. 23, 104–113 (1998).
[CrossRef]

J. Franklin Inst. (1)

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

J. Imaging Sci. Technol. (8)

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

J. Arney, “A probability description of the Yule–Nielsen effect I,” J. Imaging Sci. Technol. 41, 633–636 (1997).

J. Arney, M. Katsube, “A probability description of the Yule–Nielsen effect II: the impact of halftone geometry,” J. Imaging Sci. Technol. 41, 637–642 (1997).

J. Huntsman, “A new model of dot gain and its application to a multilayer color proof,” J. Imaging Sci. Technol. 13, 136–145 (1987).

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

S. Gustavson, “Color gamut of halftone reproduction,” J. Imaging Sci. Technol. 41, 283–290 (1997).

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

J. Arney, P. Engeldrum, H. Zeng, “An expanded Murray–Davis model of tone reproduction in halftone imaging,” J. Imaging Sci. Technol. 39, 502–508 (1995).

J. Opt. Soc. Am. A (1)

TAGA (Tech. Assoc. Graphic Arts) Proc. (2)

J. Yule, W. Nielsen, “The penetration of light into paper and its effect on halftone reproduction,” in TAGA (Tech. Assoc. Graphic Arts) Proc., 65–76 (1951).

I. Pobboravsky, M. Person, “Computation of dot areas required to match a colorimetrically specified color using the modified Neugebauer equations,” in TAGA (Tech. Assoc. Graphic Arts) Proc., 65–77 (1972).

Z. Tech. Phys. (Leipzig) (1)

H. Neugebauer, “Die theoretischen Grundlagen des Mehrfarbenbuchdrucks,” Z. Tech. Phys. (Leipzig) 36, 75–89 (1937).

Other (3)

S. Gustavson, “Dot gain in color halftones,” Ph.D. dissertation (Linköping University, Linköping, Sweden, 1997).

L. Yang, B. Kruse, “Ink penetration and its effects on printing,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts V, R. Eschbach, G. G. Marcu, eds., Proc. SPIE3963, 365–375 (2000).

M. Andersson, “A study in how the ink set, solid ink density, and screening method influence the color gamut in four-color process printing,” M. Sc. thesis (Rochester Institute of Technology, Rochester, New York, 1997).

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Figures (5)

Fig. 1
Fig. 1

Overview of the halftone image. The surface is subdivided into two groups: points under ink dots (Σ1) and points between dots (Σ2).

Fig. 2
Fig. 2

Systematic diagrams of ink penetration. (a) Without ink layer on the substrate surface; (b) with ink layer on substrate.

Fig. 3
Fig. 3

(a) Computed reflectance and (b) optical dot gain with p¯=Rp0=0.87, Ti=0.2.

Fig. 4
Fig. 4

(a) Computed reflectance and (b) optical dot gain with p¯ given in Eq. (35), where Rp0=0.87, m=0.7. Solid curves, no ink penetration, Ti=T0=0.2, γ=1; dotted curves, with consideration of ink penetration, Ti=1.3T0,γ=0.8.

Fig. 5
Fig. 5

Schematic diagram of W0-W versus f variation. W0-W (solid curve) is computed by present model, and W0-WMD by Murray–Davis model.

Equations (48)

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R=Ri f+Rp(1-f ).
W=Wi f+Wp(1-f )(W=X, Y, Z)
R=[Ri1/nf+Rp1/n(1-f )]n.
d2J12=p(r1,r2)TiI0dσ1dσ2.
dJ12=I0TiΣ1p(r1, r2)dσ1dσ2.
J12=I0TiΣ1Σ2p(r1, r2)dσ1dσ2.
Σ1Σ2p(r1, r2)dσ1dσ2
d2J21=p(r2, r1)TiI0dσ1dσ2.
p(r1, r2)=p(r2, r1).
J12=J21.
p¯=1f(1-f )Σ1Σ2p(r1,r2)dσ1dσ2,
J21=J12=I0Ti p¯f(1-f ).
P11+P12=α
P21+P22=β,
J110=I0 fP11,
J120=I0 fP12,
J210=I0(1-f )P21,
J220=I0(1-f )P22.
Jp0=I0[P12 f+P22(1-f )].
Rp0=Jp0(1-f )I0=P12f(1-f )+P22.
Ji0=I0[P11 f+P21(1-f )],
Ri0=P11+P21[(1-f )/f].
P21=p¯f,
P12=p¯(1-f ).
P12 f=P21(1-f ).
Ri0=α,
Rp0=β.
Rp=J12+J22(1-f )I0=P22+P12f1-f Ti,
Ri=J11+J21fI0=P11Ti2+P211-ff Ti.
Rp=Rp0-p¯f(1-Ti),
Ri=Ti[γRp0Ti+p¯(1-f )(1-Ti)],
γ=Ri0/Rp0.
R=Ri f+Rp(1-f ),
R=RMD-ΔR,
RMD=Ri0Ti2f+Rp0(1-f )
ΔR=(1-Ti)2p¯f(1-f ).
Δf=ΔRRp0(1-γTi2)=(1-Ti)2p¯f(1-f )Rp0(1-γTi2).
p¯f(1-f )+p¯(1-2 f )=0,
p¯=dp¯df.
p¯=Rp0[1-fm(1-f )1-m],
W=Wi f+Wp(1-f ),
W=R(λ)S(λ)w¯(λ)dλ,
Wi=Ri(λ)S(λ)w¯(λ)dλ,
Wp=Rp(λ)S(λ)w¯(λ)dλ.
W=WMD-ΔW,
WMD=RMD(λ)S(λ)w¯(λ)dλ
ΔW=ΔR(λ)S(λ)w¯(λ)dλ
W0-WW0-WMD.

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