Image Processing Reference
In-Depth Information
The above integral has a different closed-form solution for different values of the
parameter p. The Springett
-
Melnyk PIDC equations for different values of p are
given below.
If p
¼
1, then
V
(
X
)
V
r
V
i
V
r
e
h
0
V
(
X
)
V
i
þ
V
c
ln
þ
C
X
¼
0
(
10
:
17
)
If p
6¼
1, then
"
#
p
1
p
1
V
c
V
c
V
(
X
)
V
r
V
c
V
i
V
r
e
h
0
C
X
¼
V
(
X
)
V
i
þ
þ
0
(
10
:
18
)
1
p
where V
i
is the initial voltage. It is not possible to obtain an explicit general form for
V(X) in terms of p. However, for the special case of p
¼
2, it is possible to obtain an
explicit form. This case is sometimes referred to as the quadratic Melnyk (QM) PIDC
model and is given by
q
b
2
V
(
X
) ¼
V
r
þ b þ
þ
V
2
c
(
10
:
19
)
V
2
c
e
h
0
1
where
b ¼
2
[
V
i
V
r
V
i
V
r
C
X
]
It is customary to de
ne a coef
cient of exposure as S. Hence,
e
h
0
C
¼
e
h
0
L
e
S
¼
(
10
:
20
)
The initial slope of the PIDC, that is, dV
=
0 is called the sensitivity of the
photoconductor. It is calculated from Equation 10.14 by using V
¼
V
i
at X
¼
dX at X
¼
0:
X
¼
0
¼
d
V
d
X
S
p
(
10
:
21
)
V
c
V
i
V
c
1
þ
Generally, in photoconductors of practical interest, Vi.
c
<
V
i
. This implies that the
initial slope of the PIDC is practically independent on the initial voltage Vi,
i
, thus all
PIDCs start with the same slope regardless of the initial voltage:
X
¼
0
d
V
d
X
S
p
(
10
:
22
)
V
V
i
1
þ
This de
ciency in the PIDC model is overcome by modifying the exposure param-
eter S, so that the model captures the functional form of a PIDC throughout the
operating region. The new parameter introduced is S
¼
LS
0
, where S
0
¼
e
h
0
=e
and
the ratio L
=
L
0
can be considered equal to 1 for our purpose. It is important to
note, however, that the ratio L
=
L
0
is signi
cant when photoconductors of varying
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