FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

5.4.9 Fiberoptic Rotation-Rate Sensors
A simple configuration of a multiturn fiberoptic
rotation-rate aensor (see Ref. 7, Subsection
5.4.20) is shown in Fig. 5.50. Light from a laser or
some other suitable light source ia divided into two
beams by a 50-50 (3 dB) beamsplitter and then coupled
into the two ends of a multiturn (multlloop) singlemode
fiber coil. The light emerging from the two fiber
ends is combined by the beamsplitter and detected in a
photodetector. In the abaence of rotation, the two
emerging beams interfere either destructively or constructively
depending on the type of beamsplitter used.
For a 50-50 (3 dB) lossless beamsplitter the emerging
beams, as shown in Fig. 5.50, interfere destructively.
Fig. 5.50
d
DETECTOR
L –L~cw=~NQ
Cw
c
n
e,g. N=1000:A=100cm2: Q=f)E
=AL~16gcm
-5A
=2X1O
A$=8mANQs10-4 RAD
Aoc
NTURNS
Computation of the phaae change for a multiturn
fiberoptic interferometric rotationrate
sensor.
However, the emerging beams that return back to the
light source interfere constructively, i.e., at the peak
of a fringe. In the presence of a rotation rate $2, a
AL will be generated given by:
Typically, for a fiber attenuation rate of 1 dB/km, the
optimum length is several km.
5.4.10 Photon Shot-Noise Limit
Earlier a proof was given of a comparison of
the basic limits to the rotation measurement using the
three techniques outlined in Fig. 5.46. In this section
we will derive an approximate formula for the limit in
a fiberoptic rotation-rate sensor.
Fig. 5.51 shows a plot of intensity I or detector
output current iD versus nonreciprocal phase
shift A+ . In this case, the peak intensity, due to constructive
interference, is shown centered on A$ = O for
a zero rotation rate. In the presence of a rotation,
A+ shifts from zero and therefore a change in detection
current iD occurs. The greatest change in iD for a
given small change in A$ clearly occurs at the point on
the fringe with the maximum slope, i.e., where A$ = +
~12. Therefore, by applying a fixed nonreciprocal bia~
of T/2, the operating point can be maintained where the
sensitivity to rotation is a maximum. In this way, an
applied rotation causes a A$ which in turn generates a
change in the light intensity at the detector that is
proportional to the rotation. A problem arises when the
1
&I D
,)
;1
,1 i
,1
,1
INTENSITY NOISE
-w OY?$7
)
A+
8(A+)
- PHOTON
/ SHOT NOISE
N O I S E - -
8( AIP)s-= — iD/~ - iD/IT
T
7r
*LS .—
SIN iDm m
*OC ~=87AN
BUT A@=* —Q AOC
AL = Lcw - Lccw = (4Atf/c)n = (LDIc)Q (5.48)
where A, N, L, D have been defined earlier. This AL
will therefore cause a fringe shift Az given by:
or a phase shift of:
AZ = (LD/ioC)n (5.49)
A$ = (21TWaoC) (5.50)
For A = ~D2/4 = 100 cm2 and N = L/rD = 1000 (i.e., D
‘11.3 cm and Lx 355 meters) and if i. = 0.63 ~m and
n= 1.5, we get a phase shift of 3.0 rad for a rotation
rate of 1 rad/sec. Therefore, to detect the full earth
rotation, we must measure a phase shift of 9.1 x 10-5
radians and for typical navigation applicat ons (10-3
~) the phase ahift reduces to about 10 -{ radians.
For a given size sensor, i.e., a fixed coil
diameter D, the sensitivity may be enhanced by increasing
the length of the fiber L by adding more turns. Unfortunately
L cannot be increased indefinitely because
of the finite attenuation of optical power in the fiber.
Fig. 5.51
The optical intensity (power) or photodetector
output current as a function of
phase change and photon shot-noise computation
in a fiberoptic rotation-rate sensor.
intensity of the light source varies since this cannot
be distinguished from a change in intensity due to a
rotation. Therefore, the uncertainty in the measurement
of a given rotation rate, i.e., a given A$, must
be influenced by the intensity noise in the light. M-
though there are many ways of compensating for intensity
variations of the light source, it is not, however,
possible to reduce the effect of photon shot noise (see
Ref. 12, Subsection 5.4.20) because it is a random proceas.
Therefore under ideal conditions the uncertainty
in the measurement of A$ ia limited only by the photon
ahot noise (see Ref. 12, Subsection 5.4.20). This uncertainty
6(A$) is therefore given by:
6(A$) = (photon shot noise)/(fringe alope) (5.51)
5-18