Additional Material, Journal of Imaging Science - Society for Imaging ...

Mourad: Improved calibration of optical characteristics of paper by an adapted paper-MTF model
Figure 9. Calculated optical dot gain curves at medium area coverage
against the screen ruling with respect to two typically used halftone
screens. The plots were predicted using the data of the APCO paper.
Figure 11. Comparison of our LSF-predictions with normalized measurement
points of a different but apparently similar paper type published by
Arney et al. 5 The dots depict Arney’s measurements. The dashes and the
solid line plot the obtained predictions for the ColorCopy and the APCO
paper, respectively.
particular the impact of the optical dot-gain’s variations
around the commonly used ruling of 60 lpcm 150 lpi.
In this region, any slight shift of the screen ruling obviously
induces a non-negligible error arising solely from the optical
dot gain.
Figure 10. Calculated optical dot gain curves for two different types of
office paper plotted against screen ruling. The conventional circular dot
screen was used. The dashes and the solid line plot the obtained predictions
for the ColorCopy paper and the APCO paper, respectively.
frequencies (so-called ruling). The type and magnitude of
the optical dot gain curves shown are close to analyses presented,
e.g., by Gustavson 8 or by Yang [Ref. 41 p. 201], which
apply a simple Gaussian-like function to approach the shape
of the paper PSF.
Clearly, for calculating the halftone reflectances, the
simplifying assumption underlying Eq. (9) no longer holds
true and the coefficients become spatially dependent. Hence
we numerically evaluate the spatial formula, Eq. (3), by using
the standard inverse two-dimensional fast Fourier transform
(iFFT). 24 Thereby we sample the coefficients of concern
at spatial high resolution frequency grids , with a
sampling frequency exceeding the Nyquist rate of the halftone
structures, i.e., the coefficients are filled out at each
x i ,y j according to the simulated binary image Ix i ,y j with
the calibrated values of section Calibration Results.
Another application example is given in Figure 9, which
illustrates the influence of different types of halftone screens
on the magnitude of the optical dot gain at medium area
coverage of a s =50%. With the proposed simulation, it is
also convenient to explore the effect of changing the type of
paper on the optical dot gain. For the case of the conventional
circular dot halftone screen, Figure 10 shows the optical
dot gain prediction for the APCO paper compared with
results obtained with a similarly calibrated parameter set for
the ColorCopy office paper. 42 These graphs demonstrate in
MODEL COMPARISON AND DISCUSSION
To explore the performance of our microscopic predictions,
we consider results of edge-trace measurements published by
Arney et al. 5 For this purpose, we compare our prediction
results with their published data of a measured line spread
function (LSF) and the corresponding MTF of an office copy
paper of a similar type to those analyzed in our laboratory.
Figure 11 depicts a direct comparison of Arney’s measurements
and our prediction of a microscopic line edge observation
derived by using Eq. (3). The comparison of the
MTF, the normalized modulus of the digital Fourier transform
of the same data is illustrated in Figure 12. Both figures
demonstrate good agreement between our predictions and
the microdensitometric measurements. Note that the model
parameters were calibrated using spectral measurements of
solid patches only.
A further comparison arises from Arney’s discussion of
the influence of Kubelka-Munk’s absorption coefficient K on
Oittinen and Engeldrum’s model. Oittinen, 2 as well as
Engeldrum and Pridham, 1 suggested a simplified relationship
between the Kubelka-Munk theory and the MTF of
paper. According to their approach, the MTF of paper approximates
the vertical derivative of the classical KM
function. 3 It depends on the thickness of the sample D, the
scattering coefficient S, and the absorption coefficient K.
However, with edge-trace measurements Arney et al. showed
that K has only a small influence on the width of the MTF of
the paper compared to S and D. 4 Figure 13 illustrates this
finding and compares the results of our model with those
obtained by Oittinen and Engeldrum’s model. In particular,
the figure plots the scalar measure k p proposed by Arney,
which is equal to the inverse of the frequency at which the
normalized MTF loses its half magnitude. The plot demon-
290 J. Imaging Sci. Technol. 514/Jul.-Aug. 2007