Abstract

In recent years there has been a renewed interest in modeling the halftone microstructure to better control the colors produced in a halftone image. Diffusion of light within the paper has a significant effect on the halftone color; this effect is known as optical dot gain or the Yule–Neilsen effect. Because of diffusion, a photon may exit the paper from a different region of the halftone microstructure than that into which it entered the paper. To account rigorously for this effect requires knowledge of the paper’s point-spread function or, equivalently, the paper’s modulation transfer function (MTF). A new technique for measuring the MTF of paper—the series-expansion bar-target technique—is introduced. The method uses a bar target, but the analysis more closely resembles that of the edge-gradient technique. In the series-expansion method, bar-target image data are expanded into a Fourier series, and the paper’s MTF is given by the series-expansion coefficients. It differs from the typical bar-target analysis in that the typical method plots the amplitude of the fundamental frequency component for several targets of varying frequency, whereas the series-expansion method plots the amplitude of the fundamental and its harmonics for a single target. Two possible techniques for measuring the MTF with the bar-target series-expansion method are considered. In the first, the image of the bar target is projected onto the paper, and in the second, the bar target is placed directly on the paper, in close contact.

© 1998 Optical Society of America

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References

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  1. H. R. Kang, Color Technology for Electronic Imaging Devices (SPIE, Bellingham, Wash., 1997).
  2. S. Gustavson, “Color gamut of halftone reproduction,” J. Imaging Sci. Technol. 41, 283–290 (1997).
  3. G. L. Rogers, “Optical dot gain in a halftone print,” J. Imaging Sci. Technol. 42, 643–656 (1997).
  4. G. L. Rogers, “Effect of light scatter on halftone color,” J. Opt. Soc. Am. A 15, 1813–1821 (1998).
    [CrossRef]
  5. J. S. Arney, C. D. Arney, M. Katsube, “An MTF analysis of papers,” J. Imaging Sci. Technol. 40, 19–25 (1996).
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  7. J. C. Dainty, R. Shaw, Image Science (Academic, New York, 1974).
  8. S. Inoue, N. Tsumura, Y. Miyake, “Measuring MTF of paper by sinusoidal test pattern projection,” J. Imaging Sci. Technol. 41, 657–661 (1997).
  9. G. D. Boreman, S. Yang, “Modulation transfer function measurement using three- and four-bar targets,” Appl. Opt. 34, 8050–8052 (1995).
    [CrossRef] [PubMed]
  10. D. N. Sitter, J. S. Goddard, R. K. Ferrell, “Method for the measurement of the modulation transfer function of sampled imaging systems from bar-target patterns,” Appl. Opt. 34, 746–751 (1995).
    [CrossRef] [PubMed]
  11. J. W. Coltman, “The specification of imaging properties by response to a sine wave input,” J. Opt. Soc. Am. 44, 468–471 (1954).
    [CrossRef]
  12. J. Pospisil, V. Bumba, “Measurement of the modulation transfer function of negative black-and-white photographic materials by means of the method with rectangular parallel wave grating,” Optik Stuttgart 34, 136–145 (1971).
  13. R. Barakat, “Determination of the optical transfer function directly from the edge spread function,” J. Opt. Soc. Am. 55, 1217–1221 (1965).
    [CrossRef]
  14. J. A. C. Yule, D. J. Howe, J. H. Altman, “Effect of the spread-function of paper on halftone reproduction,” Tappi 50, 337 (1967).
  15. J. Primot, M. Chambon, “Modulation transfer function assessment for sampled imaging systems: effect of intensity variations in thin-line targets,” Appl. Opt. 36, 7307–7314 (1997).
    [CrossRef]

1998 (1)

1997 (4)

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

G. L. Rogers, “Optical dot gain in a halftone print,” J. Imaging Sci. Technol. 42, 643–656 (1997).

S. Inoue, N. Tsumura, Y. Miyake, “Measuring MTF of paper by sinusoidal test pattern projection,” J. Imaging Sci. Technol. 41, 657–661 (1997).

J. Primot, M. Chambon, “Modulation transfer function assessment for sampled imaging systems: effect of intensity variations in thin-line targets,” Appl. Opt. 36, 7307–7314 (1997).
[CrossRef]

1996 (1)

J. S. Arney, C. D. Arney, M. Katsube, “An MTF analysis of papers,” J. Imaging Sci. Technol. 40, 19–25 (1996).

1995 (3)

1971 (1)

J. Pospisil, V. Bumba, “Measurement of the modulation transfer function of negative black-and-white photographic materials by means of the method with rectangular parallel wave grating,” Optik Stuttgart 34, 136–145 (1971).

1967 (1)

J. A. C. Yule, D. J. Howe, J. H. Altman, “Effect of the spread-function of paper on halftone reproduction,” Tappi 50, 337 (1967).

1965 (1)

1954 (1)

Altman, J. H.

J. A. C. Yule, D. J. Howe, J. H. Altman, “Effect of the spread-function of paper on halftone reproduction,” Tappi 50, 337 (1967).

Arney, C. D.

J. S. Arney, C. D. Arney, M. Katsube, “An MTF analysis of papers,” J. Imaging Sci. Technol. 40, 19–25 (1996).

Arney, J. S.

J. S. Arney, C. D. Arney, M. Katsube, “An MTF analysis of papers,” J. Imaging Sci. Technol. 40, 19–25 (1996).

Barakat, R.

Boreman, G. D.

Bumba, V.

J. Pospisil, V. Bumba, “Measurement of the modulation transfer function of negative black-and-white photographic materials by means of the method with rectangular parallel wave grating,” Optik Stuttgart 34, 136–145 (1971).

Chambon, M.

Coltman, J. W.

Dainty, J. C.

J. C. Dainty, R. Shaw, Image Science (Academic, New York, 1974).

Engeldrum, P. G.

P. G. Engeldrum, B. Pridham, “Application of turbid medium theory to paper spread function measurements,” Tech. Assoc. Graphic Arts Proc. 47, 339–347 (1995).

Ferrell, R. K.

Goddard, J. S.

Gustavson, S.

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

Howe, D. J.

J. A. C. Yule, D. J. Howe, J. H. Altman, “Effect of the spread-function of paper on halftone reproduction,” Tappi 50, 337 (1967).

Inoue, S.

S. Inoue, N. Tsumura, Y. Miyake, “Measuring MTF of paper by sinusoidal test pattern projection,” J. Imaging Sci. Technol. 41, 657–661 (1997).

Kang, H. R.

H. R. Kang, Color Technology for Electronic Imaging Devices (SPIE, Bellingham, Wash., 1997).

Katsube, M.

J. S. Arney, C. D. Arney, M. Katsube, “An MTF analysis of papers,” J. Imaging Sci. Technol. 40, 19–25 (1996).

Miyake, Y.

S. Inoue, N. Tsumura, Y. Miyake, “Measuring MTF of paper by sinusoidal test pattern projection,” J. Imaging Sci. Technol. 41, 657–661 (1997).

Pospisil, J.

J. Pospisil, V. Bumba, “Measurement of the modulation transfer function of negative black-and-white photographic materials by means of the method with rectangular parallel wave grating,” Optik Stuttgart 34, 136–145 (1971).

Pridham, B.

P. G. Engeldrum, B. Pridham, “Application of turbid medium theory to paper spread function measurements,” Tech. Assoc. Graphic Arts Proc. 47, 339–347 (1995).

Primot, J.

Rogers, G. L.

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

G. L. Rogers, “Optical dot gain in a halftone print,” J. Imaging Sci. Technol. 42, 643–656 (1997).

Shaw, R.

J. C. Dainty, R. Shaw, Image Science (Academic, New York, 1974).

Sitter, D. N.

Tsumura, N.

S. Inoue, N. Tsumura, Y. Miyake, “Measuring MTF of paper by sinusoidal test pattern projection,” J. Imaging Sci. Technol. 41, 657–661 (1997).

Yang, S.

Yule, J. A. C.

J. A. C. Yule, D. J. Howe, J. H. Altman, “Effect of the spread-function of paper on halftone reproduction,” Tappi 50, 337 (1967).

Appl. Opt. (3)

J. Imaging Sci. Technol. (4)

S. Inoue, N. Tsumura, Y. Miyake, “Measuring MTF of paper by sinusoidal test pattern projection,” J. Imaging Sci. Technol. 41, 657–661 (1997).

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

G. L. Rogers, “Optical dot gain in a halftone print,” J. Imaging Sci. Technol. 42, 643–656 (1997).

J. S. Arney, C. D. Arney, M. Katsube, “An MTF analysis of papers,” J. Imaging Sci. Technol. 40, 19–25 (1996).

J. Opt. Soc. Am. (2)

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

Optik Stuttgart (1)

J. Pospisil, V. Bumba, “Measurement of the modulation transfer function of negative black-and-white photographic materials by means of the method with rectangular parallel wave grating,” Optik Stuttgart 34, 136–145 (1971).

Tappi (1)

J. A. C. Yule, D. J. Howe, J. H. Altman, “Effect of the spread-function of paper on halftone reproduction,” Tappi 50, 337 (1967).

Tech. Assoc. Graphic Arts Proc. (1)

P. G. Engeldrum, B. Pridham, “Application of turbid medium theory to paper spread function measurements,” Tech. Assoc. Graphic Arts Proc. 47, 339–347 (1995).

Other (2)

J. C. Dainty, R. Shaw, Image Science (Academic, New York, 1974).

H. R. Kang, Color Technology for Electronic Imaging Devices (SPIE, Bellingham, Wash., 1997).

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Figures (3)

Fig. 1
Fig. 1

(a) Target function τ(x); (b) reflectance R(x) for projection method; and (c) reflectance R(x) for contact method, where, for both, an exponential line-spread function is used with a/〈x〉 = 50, and α = 1, β = 0.

Fig. 2
Fig. 2

Simulated reflectance data R(x) for the contact method and the transformed reflectance R′(x) with α = 1, β = 0. Band-limited noise has been added to data generated using an exponential line-spread function with a/〈x〉 = 50.

Fig. 3
Fig. 3

(a) MTF as determined from the simulated data in Fig. 2 (filled diamonds) and (b) MTF obtained as the Fourier transform of the exponential line-spread function with a/〈x〉 = 50 (curve).

Equations (37)

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I x = I 0 τ x + I s ,
τ x = n   τ n x ,
τ n x = 1 ,   na x < n + 1 2 a 0 ,   x n + 1 2 a   or   x < na ,
R x = R p I 0 + I s -   I x L x - x d x ,
τ x = 1 2 + 2 π n   odd 1 n sin ω n x ,
ω n = 2 π n a ,
-   L x - x sin ω n x d x .
sin ω n x -   L x cos ω n x d x ,
R x = α + β 2 + 2 π α - β n   odd L ˜ ω n n sin ω n x ,
α = R p ,   β = R p I s I 0 + I s .
L ˜ ω n = i ω n 2 0 a   R x exp - i ω n x d x × α - β - 1 ,     n   odd .
L a / 2 = L - a / 2 = 0 .
R x = α - β n na n + 1 / 2 a   L x - x d x + β .
e x = - x   L x d x ,
a b   L x - x d x = e x - a - e x - b .
R x = α - β n e x - na - e x - n + 1 / 2 a + β .
e x = 0 ,   if   x - a / 2 ;     e x = 1 ,     if   x a / 2 ,
R x = α - β e x - e x - a / 2 + e x - a + β .
L ˜ ω n = 1 + i ω n - a a   e x exp - i ω n x d x .
L ˜ ω n = - d e x d x exp - i ω n x d x ,
R x = R p τ x -   L x - x τ x d x ,
R x = R p n   R n x - na ,
R n x - na = e x - na - e x - n + 1 2 a , na x < n + 1 2 a 0 , x < na   or   x n + 1 2 a .
R n x = R 2 n x , 0 x < 1 2   a 1 - R 2 n + 1 x - 1 2   a , 1 2   a x < a 0 , x < 0   or   x a ,
R x = R p n   R n x - na .
R x = α e x - e x - a / 2 + e x - a .
x k = k Δ ,
Δ = a N p .
R k R x k .
R k = R nN p + k , nN p k < n + 1 2 N p 1 - R n + 1 2 N p + k , n + 1 2 N p k < n + 1 N p ,
r n = Δ M a k = 0 N - 1   R k exp i ω n x k .
r n = 1 N k = 0 N - 1   R k exp i 2 π nk N p .
L ˜ ω n = π n | r n | α - β - 1 .
f c = N P 2 a .
N p 2 a > 1 x ,
N p > 2 a x ,
a     2 x .

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