Page 160 - Computational Colour Science Using MATLAB

CHARACTERIZATION OF HALF-TONE PRINTERS 147
Equation (9.6)] has been shown to be most accurate (Bala, 2003). In the n-
modified Neugebauer model all the reflectances are raised to the power 1/n as in
Equation (9.5).
In order to implement the Neugebauer approach the digital counts are first
converted into the dot coverage areas using a tone-reproduction curve, as
described in the previous section. A method to compute the actual areas of the
primary and secondary colours is then required. For the three-colour example,
the proportional areas of the eight colour regions can be computed using
Demichel’s equation (Green, 2002c),
A w ¼ð1 cÞð1 mÞð1 cÞ,
A c ¼ cð1 mÞð1 yÞ,
A m ¼ mð1 cÞð1 yÞ,
A y ¼ yð1 cÞð1 mÞ,
ð9:7Þ
A b ¼ cmð1 yÞ,
A g ¼ cyð1 mÞ,
A r ¼ myð1 cÞ,
A k ¼ cmy,
where c, m and y are the proportional dot areas of the three primary colours
obtained from the tone-reproduction curves. Demichel’s equation has been
shown (Viggiano, 1990) to work reasonably well for rotated half-tone screen
configurations where the screens for cyan, magenta and yellow are placed at
different angles that are carefully selected to avoid moire ´ artifacts.
It is important to note, however, that Equations (9.7) make certain
assumptions concerning the amount of overlap between the primary colours.
If we consider the case where c ¼ 0.4, y ¼ 0.4 and m ¼ 0, then Demichels’s
equation will predict A ¼ 0.36, A ¼ 0.24, A ¼ 0.24 and A ¼ 0.16. However, it
w c y g
would be possible for the cyan and magenta dots to be printed without overlap
(A ¼ 0.20, A ¼ 0.40, A ¼ 0.40 and A ¼ 0.00), with total overlap (A ¼ 0.60,
w
w
y
c
g
A ¼ 0.00, A ¼ 0.00 and A ¼ 0.40) or with any intermediate amount of overlap.
y
g
c
The primaries normally are printed at different screen angles and the relationship
between these two angles is one of several factors that could affect the degree of
overlap. The dot-on-dot half-tone configuration, for example, places the primary
dots at the same screen angle and phase so that they maximally overlap. In
practice it has been shown that a weighted combination of the Demichel model
and the dot-on-dot model can give good performance (Bala, 2003).
9.4.3 The Kubelka–Munk model

The Neugebauer models assume that the reflectance (for spectral Neugebauer
approaches) or tristimulus values (for tristimulus Neugebauer approaches) are