Biomedical Engineering Reference
In-Depth Information
Acousto-optic
g
(
t
)
SSB
filter
h
(
x
)
Photo
detector
P
2
P
la
P
lb
L
1
L
2
P
3
L
3
(a)
Acousto-optic
cell
h
(
t
)
Photo
detector
array
SSB
filter
Light
source
g
(
t
)
P
2
P
1
L
0
L
1
L
2
P
3
(b)
FIGURE 3.15
(a) Space-integrating AO correlators. (b) Time-integrating AO correlators.
the necessary single-sideband modulation of the data” [30] by rejecting the
zeroth- and the undesired first-order modes.
The signal incident with
P
1b
is
g
(
x − vt
) =
g
(
t
− τ). Since τ is proportional
to
t
, which will be the output variable, this substitution is allowable.
Thus, incident on
P
1B
is a wavefront proportional to the complex-valued
signal
g
(
x
− τ). Stored on a mask at
P
1b
is the reference transmitted sig-
nal code
h
(
x
). The light distribution leaving
P
1b
is thus
h
(
x
) =
g
(
t
− τ). The
Fourier Transform of this signal is formed by L
3
at the output plane,
where we find
∫
(
−
j ux
2
τ
)
U u t
( , )
=
g x
(
−
τ
) ( )
h x e
d
x
(3.12)
2
When evaluated by an on-axis PD at P
3
, Equation 3.12 becomes
∫
U t
2
( )
=
h x g x
( ) (
−
τ
)
d =
x
h
⊗
g
(3.13)
or the correlation of
g
and
h
. The integration of Equation 3.13 is per-
formed over distance
x
. The output correlation variable is time, since the
time output from the simple on-axis PD is the correlation pattern. Hence,
the name space-integrating correlator is given to this architecture [31].
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