FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

This is a minimum where the fringe slope is a maximum.
In other words:
15(A$) z n(2eiDB) qiD .
iT(nph~DT )1’2/nph~DT
(5.52)
where e iS the electron charge; B is the bandwidth of
the detection system; nph is the number of photonsfsec
falling on the detector; ~ is the quantum efficiency of
the detector; and T is the averaging time = l/2B. Since
Eq. (5.50) iS:
A+ = 2nLD/loc
the uncertainty in the measurement of ~, i.e., 6$2, becomes:
62 = Aoc&(A41)/21rLD
Fig. 5.53
JtL
o ‘ $7 A#J—
I/
iii-
-7r 0 r 4#J—
Two DC methods for measurement of phase
change, LO, in a fiberoptic rotation-rate
sensor.
which : s the same expression given earlier.
5.4.11
= (C/LD)(lo/2)/(nphtlT)l’2 = (5.53)
cio/2LD(iD/2eB)112
Ideal Performance
The ideal performance of a fiberoptic “gyro”
may be summarized as shown in Fig. 5.52. The random
drift : s limited by photon shot noise and there should
not be any aource of bias or drift in the absence of
rotation. For a given rotation, the stability of the
scale factor, i.e., 2nLD/aoc, which related !2 to Ah
must be limited by the stability of L, D and ~o.
A much better method is to use an a.c. modulation
scheme employing nonreciprocal phase dither (see
Ref. 11, Subsection 5.4.20) as shown in Fig. 5.54. The
requirements for optimum operation are that the amplitude
of the phase modulation should be + r/2 and the
rate of the modulation should be high enou~h so that the
detector noise is dominated by photon shot noise. Fig.
5.55 is a sketch of a typical noise spectrum of a laser
showing the large “l/f” noise component at low frequencies.
The start of the ahot-noise-limited region depends
on the particular light source and can be any
where from a few kHz to a few hundred kHz. Using such
●
RANDOM DRIFT IS LIMITED BY PHOTON SHOT NOISE
.MODULATION METHODS
●
●
Fig. 5.52
5.4.12
NO BIAS OR DRIFT WHEN!! =0
SCALE FACTOR STABILITY IS LIMITED BY STABILITY OFL,D
ANDAO
Ideal performance features of a fiberoptic
rotation-rate sensor (L = coil length, D =
diameter, and i. = source wavelength).
Measurement of Nonreciprocal Phase Shift
In order to reach the ideal performance disthe
previous section, a number of problems
cussed in
must be overcome. The measurement of nonreciprocal
phase shift A@ with an uncertainty that is limited only
by the photon shot noise will now be described.
A simple way of measuring A$ is illustrated
in Fig. 5.53, where a T/2 bias is applied so as to operate
at the point of maximum slope. In thia way an increase
in intensity correaponda to a negative A$ and
vice veraa. Among the disadvantages of this method is
the stability of the bias and the need to compensate for
laser intensity fluctuations. A better method might be
to employ a differential scheme in which two detectors
are placed astride a fringe as ahown in the lower diagram
of Fig. 5.53. l%is scheme has twice the sensitivity
of the first, and better discrimination againat
intensity variations. However, it still suffers from
the instability of the operating points and requires
high common mode rejection.
Fig. 5.54
I
I
‘D
\,& .+
REQUIREMENTS:
-w ; o : w
● AMPLITuDE*r/2
e~NONRECIPROCAL
PHASE MODULATION
cRATE – HIGH ENOUGH TO GIVE SHOT-NOISE LIMIT
AC measurement of phase change, A$, in a
fiberoptic rotation-rate sensor.
It
INTENSITY
NOISE
PHOTON 1 ——-—-——
SHOT —
NOISE
o f—
Fig. 5.55
Atypical intensity-noise spectrum of a
laser showing inverae frequency (l/f) and
phase noise.
5-19