FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

Next consider the other extreme: the detection
of changes in length (or more exactly, phase) very
much smaller than a wavelength, such as 10-6 radians.
Any large amplitude drift (change) greatly increases
the difficulty of measuring small changes. The signal
to be considered will appear as a small amplitude perturbation
as was shown on the upper curve in Fig. 4.15.
The sensitivity to phase changes varies as the slope
of this curve. Thus, the lower curve, obtained by taking
the derivative of the photodetector output with
respect to$ is the phase sensitivity for amall amplitude
changes. The maximum sensitivity occurs for odd
multiples of T/2 while zero sensitivity occurs for even
multiples of n/2. This is shown in Fig. 4.15. Here the
photodiode current is plotted against the bias (phase)
angle. In order to demonstrate the sensitivity, a cw
(sinusoidal) signal of amplitude ~ 10” (electrical degrees)
is superimposed about a bias (quiescent or op-
+
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6
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----=-.—.—
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PHASE VARIATION
I
-20 0 20 40 60 80
BIAS ANGLE(”)
CURRENT OUT
II
Fig. 4.15 Sensitivity of fiberoptic
at O“ and 90° bias angle.
100 120 140
homodyne sensor
crating) point at O“ and at 90”. The amplitude of the
resulting output current is obtained by projecting the
phase oscillation (input signal) upward on to the solid
curve graphically and plotting the resulting output current
about a horizontal line as is normally done graphically
with any transfer function. At 90° the resulting
current is large and of the same frequency as the input
signal. At O“ bias however the amplitude of the photodetector
current is small and exhibits a frequency twice
the excitation frequency because oscillation is on both
sides of the maximum. Thus, consider such a signal initially
at the 90” bias point. Now for the magnitude of
input signal shown in Fig. 4.15, if the 90” relative
phase between the two arms of the interferometer drifts
toward the 0° point, the amplitude of the photodetector
current would decrease, and at leas than 10° biaa a
second harmonic would appear. The current amplitude
would become minimum at 0° bias at which point the fundamental
component will have become zero with only a
small second harmonic left. This process is referred to
as fading. The 90” bias condition is known as quadrature.
l%is mode of detection is called homodyne detection.
4.2.2 Homodyne Detection Applications
As pointed out in the discussion above, homodyne
detection requires quadrature operation and in addition
some means of compensating for large amplitude
4-8
drift. In addition laser noise reduction will be shown
to be necessary.
A schematic of the Mach-Zehnder fiberoptic
interferometer using phase-locked homodyne detection is
shown in Fig. 4.16. The light in the laser beam is
3dS COUPLER
REFERENCE ARM
SENSING ARM
/
OUTPUT HIGH PASS
-SIGNAL
SIGNAL“4+ F ILT ER $p
K(
LOW PASS
I
SIGNAL & NOISE
FILTER
3CU3COUPLER
Fig. 4.16
AMPLIFIER
& SUMMER
ePHOTODIODES
A Mach-Zehnder fiberoptic interferometer
employing phase-locked homodyne detection.
split by the 3-dB coupler into the two arms of the interferometer.
The arm on the right is taken to be the
signal arm and the arm on the left is taken to be the
reference arm. The latter contains the phase shifter
described below. The light through the two arms is recombined
by the lower 3-dB coupler that converts the
phase modulation to an intensity modulation. The two
optical outputs of the 3-dB coupler are each photodetected.
The electrical outputs of the two photodetectors
are fed into a differential amplifier. It in turn
feeds the compensator circuit. The compensator circuit
provides an output signal, the signal required for the
phase shifter, and a reset signal. A detailed discussion
is given in the next subsection.
There are many types of laser noise, such as
phase noise, amplitude noise, and noise due to multimode
and satellite mode operation. This is especially
important when the source is a diode laser that is
closely coupled to a fiber.
4.2.3 Phase Noise
The output noise of the interferometer in dBV
as a function of path length difference between the two
arms of the interferometer expressed in millimeters is
shown in Fig. 4.17. The system noise determines the
minimum detectable phaae shift. The minimum detectable
phase shift, measured in a 1 Hz bandwidth, is shown
plotted in radians using the ordinate scale on the
right in Fig. 4.17 (see Ref. 1 in Subsection 4.2.8).
Experimental data is given for 50 Hz, 500 Hz and 2 kHz.
The interferometer was operated in quadrature. On the
log acales used, a straight line plot of decreasing
noise at each frequency is obtained as the path length
is reduced. Notice that varying the path length from 1
mm to 1000 mm, that is, to 1 meter, results in a 60 dB
increase in output noise. The curves shown terminate
at a 1 mm path-length difference, but data points corresponding
to a 0.1 mm path difference are shown for
all 3 frequencies. As can be seen, little further reduction
in output noiae is achieved by decreasing the
path-length difference from 1 to 0.1 mm. Thus, if the
arms of the interferometer are matched to within 1 mm,
phase shifts of 10-6 radians can be detected at 2 kHz.
Attempts at reducing the path length difference to less
than 1 mm would be futile. This is due to the fact that
for an interferometer whose arms contain as much as a