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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