Biomedical Engineering Reference
In-Depth Information
Φ
A
L
1
=
L
2
L
1
Sine/cosine
demodulator
Laser
Sensing fiber
Φ
A
3 dB
Coupler
3 dB
Coupler
L
2
2
W
0
PZT
~
W
0
E
S
E
sum
E
R
FIGURE 4.12
Homodyne using phase-generated carrier (carrier generated by PZT).
Here an electrically controlled optical phase shifter has been introduced
into the reference fiber path. The detector output voltage is amplified and
passed through a low-pass filter to provide the control voltage to the optical
phase modulator. Figure 4.12 shows the optical power from the summing
device when the reference arm and the sensing arm outputs are in phase
quadrature. Assuming the output magnitudes are equal, the vector sum
is
℘2
times the amplitude. If a voltage is applied to the phase modulator in
a direction to increase the phase difference, the magnitude of the sum will
diminish. If this voltage is the amplified output of the photodetector, the ref-
erence and sense arm phase difference will be maintained at exactly 90°. AC
voltages appearing at the detector output that are above the cutoff frequency
of the low-pass filter will not reach the phase modulator. These voltages are
then representative of signal disturbances above the filter cutoff frequency.
If all unwanted drifts and instabilities occur below the filter cutoff and the
loop gain is high, the sensor is stabilized against drift and the two arms are
locked in quadrature phase.
Consider, for example, the scenario illustrated in Figure 4.13, in which a
vehicle follows a path along a chord subtended by a 90° angle at the cen-
ter of the 120-m-diameter circle describing the sensitivity limit. It will be
approaching the sensor for 42.4 m and receding for a like distance. If it is
traveling at 7.3 ft s
−1
, it will require 19 s to reach the closest point. If we take
the lowest-frequency response required as 1/19, we arrive at a cutoff fre-
quency of about 0.05 Hz. Drift mechanisms must be controlled to operate
below this frequency (e.g., by insulating the sensor from thermal and pres-
sure changes). If the sensor response extends from a very low frequency to
5000 Hz, it encompasses commercial power-line frequencies. Frequencies in
the range of 50-60 Hz can be rejected with notch filters.
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