Image Processing Reference
In-Depth Information
CX + paper
1.2
1
0.8
0.6
0.4
0.2
0
400
500
600
700
Wavelength (nm)
FIGURE 10.30
Substrate reectance, R
s
(
l
).
because for half-toned images, light may enter the toner, get re
ected by the paper,
and then exit through air instead of toner. The abstraction of the process using the
three terms,
t
0
(m
i
;
that
is,
t
(m
i
;
l
), R
s
(
l
), and
l
),
is very effective since the
t
0
(m
i
;
transmittance factors
), are independent of the characteristics
of the paper type. In fact, the effect of changing the media type is captured only by
R
s
(
t
(m
i
;
l
) and
l
). This is somewhat similar to the idea considered in Ref. [31] but gives a more
elegant and complete representation. The substrate re
l
ectance can be found through
measurements, and a typical curve is shown in Figure 10.30.
We still need to calculate the transmittance as a function of the masses (TMAs)
of the four toners denoted as m
C
, m
M
, m
Y
, and m
K
. This is done using an empirical
model derived by
fitting the model to experimental data and is presented in Equa-
tions 10.58 through 10.61. The transmittance through air, through toner, and
finally
to paper surface,
t
(m
i
;
l
), is first written as
"
#
X
3
t(
m
C
, m
M
, m
Y
, m
K
;
l) ¼ exp
M
i
(l)s
i
(
m*
) s
4
(
m
K
)
(
10
:
58
)
i
¼
1
where
i
¼
1, 3 for C, M, Y and i
¼
4 for K
M
i
(
1, 2, 3) is the toner absorption spectra (also called the toner master
curve), which is assumed to be a function of the toner material
s
i
denotes the mathematical mass for separation (i), which is a function of the
TMAs (m
i
) and is given by
l
)(i
¼
(
"
!
g
i
#
)
exp b
i
X
7
C
ji
m
j
s
i
(
m*
) ¼ a
i
1
for
i
¼
1,2,3
(
10
:
59
)
j
¼
1
þ b
4
2
m
K
r
t
m
K
r
t
s
4
(
m
K
) ¼ a
4
(
10
:
60
)
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