Image Processing Reference
In-Depth Information
In Equation 10.69, the substrate re
ectance is obtained from the re
ectance
measurement for the patch of C
¼
M
¼
Y
¼
K
¼
0 of the real printer R(0;
l
) using
Equation 10.70 that is modeled based on Equation 10.69:
R
(
0, g;
l)
C
1
C
2
R
s
(l) ¼
(
10
:
70
)
In order to determine the toner master curve for a particular printer for a single
separation, for example, the cyan channel, a single patch C
¼
255, M
¼
0, Y
¼
0, and
K
¼
0 is printed and the spectral re
ectance measurements are taken. Keep the other
three channels
fixed at 0 so that their toners will not be deposited and will not affect
the transmittance term,
t
l
). The reason for choosing 100% area coverage for
cyan is to avoid the effects of halftoning on the spectral measurements. Equation
10.69 can then be written as
(m
i
;
2
R
(
m
C
;
l) ¼
C
1
þ
C
2
t
(
m
C
;
l)
R
s
(l)
(
10
:
71
)
R
(
m
C
;
l)
C
1
C
2
R
s
(l)
2
t
(
m
C
;
l) ¼
(
10
:
72
)
For the patch C
¼
255, M
¼
0, Y
¼
0, and K
¼
0, m
1
¼
m
C
and m
2
¼
m
3
¼
0in
Equations 10.58 through 10.61, Equations 10.59 and 10.60 can be simpli
ed to
exp b
C
m
g
C
s
C
(
m*
) ¼ a
C
1
s
M
(
m*
) ¼
0
(
10
:
73
)
s
Y
(
m*
) ¼
0
s
K
(
m*
) ¼
0
From Equations 10.58 and 10.73, we have
exp b
C
m
g
C
t(
m
C
;
l) ¼ exp
M
C
(l)a
C
1
(
10
:
74
)
Taking the natural logarithm of both sides of Equation 10.74, we obtain
exp b
C
m
g
C
ln t(
m
C
;
l) ¼
M
C
(l)a
C
1
(
10
:
75
)
Taking the natural logarithm of both sides of Equation 10.72 and simplifying,
we obtain
h
i
Rm
C
;
l
ð
Þ
C
1
ln
ln
R
s
(l)
C
2
ln t(
m
C
;
l) ¼
(
10
:
76
)
2
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