Biomedical Engineering Reference
In-Depth Information
piezoelectric cylinder. Dimensional (diameter) changes in the cylinder pro-
duce axial strains in the fiber, changing the path length and total phase shift.
These devices have the desirable properties of requiring very little power
for low-bandwidth (slow) phase changes and of operating in a voltage rather
than a current mode. The latter produce magnetic disturbances that could
lead to instabilities in a sensitive fiber magnetometer.
4.14.2 Fiber Sensor System Noise
Both inputs to the phase detector will have a very high signal-to-noise ratio
(SNR); since the sensor is a phase sensor, it is operated with the carrier power
well above the threshold level where a loop can phase lock. Because of ample
signal power at both inputs of the phase detector, the phase stability of the
laser and the self-noise of the photodiode and loop amplifiers will be the
SNR-limiting factors in the sensor.
The laser phase noise is applied to both inputs of the phase detector with
slightly different time delays. If the phase fluctuation power spectral density
is known, the effects of this phase noise on the detector output can be pre-
dicted as follows. The phase detector output β(
t
) is proportional to the phase
difference between the two signal paths:
β
( )
t
=
A
cos
(
ω
t
+
a
)
+
A
cos
(
ω
t
+
a
).
(4.1)
c
1
c
2
We are interested in the noise component of the detector output
E
(
t
). The
photodiode produces an output proportional to the intensity of β(
t
), which is
the sum of two phasors:
(
a
−
a
)
⎡
⎢
⎤
⎥
2
2
2
1
2
| ( )|
β
t
=
4
A
cos
2
where
a
1
and
a
2
are the phases of the input signals. Both phases have a com-
mon noise component φ
n
(
t
) but delayed differently in time:
a t
( )
=
δ
( )
t
+
ϕ
( )
t
and
a t
( )
=
δ
( )
t
+
ϕ
1
n
2
n
(If τ = 0, the source phase noises will completely cancel.) The allowable delay
difference between the two paths is obtained by studying the autocorrela-
tion function of φ
n
(
t
); high correlation coefficients result in a high degree of
phase noise cancellation.
The time autocorrelation function
R
φ(
t
) is (assuming an ergodic process)
T
1
2
∫
R t
ϕ
( )
=
lim
→∞
φ
( )
t n t
ϕ
(
−
τ
)
(4.2)
T
n
T
−
T
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