Page 159 - Computational Colour Science Using MATLAB

146 CHARACTERIZATION OF PRINTERS

Figure 9.2 Light that strikes the unprinted area of the substrate may be absorbed by the ink
because of scattering of light within the substrate

Some alternative methods for determining dot areas that minimize the error in
CIELAB colour-difference units are also available (Bala, 1999).

9.4.2 Device-independent representation

For half-tone printers, device-independent representation is normally obtained
by finding a mapping between the proportional dot coverages for the inks and
the spectral reflectance of the print, from which it is then trivial to compute XYZ
values. Alternative methods may use neural networks to find a mapping either
from dot coverages to reflectance or even directly to CIE XYZ values. The most
common method for predicting reflectance involves the Neugebauer model which
takes into account the various overlapping binary mixtures. For example, if
cyan, magenta and yellow inks are considered, then the resulting reflectance will
be a function of the reflectances of the unprinted substrate P , the three solid
w
colours (P , P , P ) and the four overlap colour combinations of cyan+magenta
c m y
(blue P ), cyan+yellow (green P ), yellow+magenta (red P ) and black P . If the
b g r k
fractional areas of these eight areas are represented by A , A , etc. then we can
c m
write
P ¼ A w P w þ A c P c þ A m P m þ A y P y þ A b P b þ A g P g þ A y P y þ A k P k . ð9:6Þ
It is evident that the Neugebauer model is a straightforward extension of the
Murray–Davies equation [Equation (9.1)] which assumes that the reflectance of a
spatial area is the additive combination of the reflectances of the primary colours
and their overlapping areas. In the original Neugebauer equations the approach
was used to predict the broadband reflectance in the short-, medium- and long-
wavelength portions of the spectrum and, indeed, modern versions of
Neugebauer sometimes operate using XYZ tristimulus values. However the n-
modified spectral Neugebauer approach [illustrated for a CMY system by