FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

100 meters of fiber, length changes on the order of 0.1
mm can be expected as a result of changes in temperature,
presaure, tension, and other environmental conditions.
Thus, the fluctuation in laser optical output amplitude
is eliminated. The subtraction is actually accomplished
electrically in the differential amplifier following
the photodetector as was shown in Fig. 4.7.
Experimental verification of common mode rejection
is shown in Fig. 4.18 (see Ref. 2 in Subsection
6-
a
II
~ 10.0 ~
k
OUTPUT FROM ONE PORT
F
m
u
(n
u 1.0 -
I
L
w
d
a
01 -
!3 OUTPUT OF BOTH PORTS
u
USING COMMON-MODE REJECTION /
h
a
I
I
01 1 10 100 1000
PATH LENGTH DIFFERENCE (mm)
Fig. 4.17 Variation of homodyne interferometer output
noise as a function of sensing arm path
length difference for several output frequencies.
After A. Dandridge, et al., Appl. Phys. Lett. ~, 77
(1981)
4.2.4 Amplitude Noise
Common mode rejection refers to a method for
the elimination of laser amplitude noise. Expressions
for the optical intensity at the two output ports of
the lower 3-dB coupler that was shown in Fig. 4.16 are:
and
11 = (1/2)(1 + ~sin~st) (4.19)
12 = (1/2)(1 - ~sinust) (4.20)
where I is the output optical intensity (power) of the
laser minus the various insertion and fiber absorption
losses. Aa is the amplitude of the phase shift produced
by a signal of angular frequency us. Conservation
of energy dictates the plus and minus signs in Eqs.
(4.19) and (4.20) respectively. Summing Eqs. (4.19)
and (4.20) yields I as required. Multiplying Eqs. (4.19)
and (4.20) by 1 + AI/I where AI/I is an amplitude fluctuation
whose ma nitude is the same order of magnitude
as As, e.g. 10 -5 or 10-6, yields:
and
211 = I + AI + IAssinost (4.21)
212 = I + AI - IAssin@st (4.22)
where higher order terms in the infinitesimals AI/I and
As are neglected. Subtracting Eq. (4.22) fromEq. (4.21)
results in the expression:
11 - 12 = IA a
sinost (4.23)
4-9
Fig. 4.18 Minimum detectable phase shift versus fre -
quency in a fiberoptic homodyne interferometric
sensor using common-mode rejection
of laser amplitude noise.
After Dandridge and Tveten, Appl. Phys. Lett. ~, 2337
(1981).
4.2.8). The minimum detectable phase shift, expressed in
microradians, is plotted versus frequency. The squares
represent the output from a single port of the interferometer.
The solid line is the average of these points.
The circles are the data obtained when the output from
both of the ports of the interferometer are detected
and the different signals taken. By comparing these
results it is seen that an order of magnitude decrease
in the minimum detectable phase shift is achieved at
low frequency. At frequencies above 1 kHz a minimum detectable
phase shift of 0.1 urad (10-7 radians) is accomplished.
This is representative of the kind of sensitivity
that canbe achieved when common mode rejection
is employed and the arms of the interferometer are
matched to within 1 mm as was the case in this experiment.
Laser noise due to satellite modes and multimode
operation was also eliminated.
4.2.5 Satellite Modea and Multimode Operation
The influence of various amounts of optical
feedback on the modal output of a Hitachic HLP 1400
diode laser is shown by the output spectrum of the
laser plotted for varioua conditions of optical feedback
as shown in Fig. 4.19 (see Ref. 3 in Subsection
4.2.8). Spectrum (a) is for the free running laser with
a spectral width of 5 MHz. The spectra (b), (c), and
(d) illustrate the effect of increasing amounts of feedback
(from 0.04% to 1.5%). Notice that for spectra (b)
and (c) the horizontal scale remains the same (i.e.,
from -0.2 to +0.2 A) but for spectrum (d) the scale has
changed, going from -6.0 to +6.0 A. The second and
third curves correspond to 0.04% and 0.06% feedback.
Here satellite modes appear and increaae as the amount
of feedback increases. Such satellite modes arise as
the result of coupling two resonant cavities: one the
laser itself and the other the resonant cavity formed
by the length of fiber from the laser to the primary
reflection. Effects due to optical feedbacks of up to
0.06% are eliminated when the interferometer lengths
are matched to within lmm.