FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

● ANGULAR MOMENTUM CRYOSCOPES
MECHANICAL - ROTATING WHEELIBALL
NUCLEAR - SPINNING NUCLEI
● SAGNAC EFFECT “GYROSCOPES”
E.M. WAVES
MAITER WAVES
● DISTANT-STARS TRACKERS
Fig. 5.41
SIMPLE STAR TRACKERS
LONG-BASELINE STELL4R INTERFEROMETRY
Various rotation-rate sensor devices.
5.4.3 Interest in Optical Rotation Sensors
The main advantages of optical “gyroscopes”
over mechanical ones are briefly outlined in Fig. 5.42.
However, it is the promise of the projected low cost of
the optical devices that is driving their development.
where A is the area enclosed by the path, i.e., A = ~R2
and c ia the velocity of light in a vacuum.
The rigorous derivation of this formula is
based on the propagation of light in a rotating frame
(see Ref. 5, Subsection 5.4.20) i.e., an accelerating
frame of reference, where the general theory of relativity
must be used to perform the calculation. However,
a simple way of explaining the formula in Eq.
(5.30) iS given in Fig. 5.43. Again, consider the disc
D ----------- % 1
i’R,,@j
,’ .
2
‘1 ,,, ,’
‘., ,/’
‘.
..- --
,,
------
Lcw=2mR+R~tcw= Ccwtcw
{
Lccw=27rR-R~tccw= Cc,-wtccw
>tcw= ~c::RRQ
~At=tcw–tccw= ‘wR
IN A VACUUM CCW=CCCW=C
2*R
: tccw = Cccw + RQ
[2R~ - (Ccw - Cccw)]
Ccw ccc.
Fig- 5.42
● NO MOVING PARTS
● No wARM-UPTIME
● NO G-SENSITIVITY
. LARGE DYNAMIC RANGE
● DIGITAL READOUT
● LOW COST
● SMALL SIZE
● USES LIGHT
Potential advantages of optical rotationrate
sensors (gyroscopes).
In this section we will give a brief and
ple derivation of the Sagnac effect in vacuum and
in a medium; discuss techniques of implementing
simalso
the
Sagnac effect for the measurement of rotation together
with the fundamental limits on sensitivity in each case.
The basic principle of fiberoptic rotation aensors will
then be considered with emphasis on techniques, problem
areas, and recently achieved performance.
5.4.4 Sagnac Effect in a Vacuum
AH the optical rotation sensors under development
are based on the Sagnac effect (ace Ref. 5,
Subsection 5.4.20) which generatea an optical path difference
AL that is proportional to a rotation rate fl.
For example, if we have a diac of radius R that is
rotating with angular velocity Q, as shown in Fig. 5.43,
the optical path difference AL experienced by light
propagating along opposite directions along the perimeter
is given by:
~ At = ‘TR ~ O = %() ; ~ AL= LCW– LCCW. ~C)
Fig. 5.43 A demonstration of the Sagnac relationships
for the vacuum case.
of radius R rotating with an angular velocity !l about
an axis perpendicular to the plane of the disc. At a
given point on the perimeter, designated by 1 in Fig.
5.43, identical photons are sent in clockwise and counterclockwise
directions along the perimeter. If Q = o,
the photons, which travel at the speed of light in a
vacuum, will arrive at the starting point 1 after covering
an identical distance 2?TR in a time t = 2nR/c. Now
in the presence of a disc rotation $2, the ccw photon
will arrive at the starting point on the disc, which is
now located at position 2, after covering a distance
Lccw which iS shorter than the perimeter 2TR given by:
L Ccw
= 2TR - l?iltccw = cccwtccw (5.31)
where Ri2 is the tangential velocity of the disc and
tccw is the time taken to cover the distance Lccw. I n
addition, Lccw is also given by the product of the
velocity of light Cccw in the ccw direction and tccw.
For propagation in a vacuum Cccw = C. Similarly, the
photons propagating in the cw direction experience a
larger perimeter Lcw given by:
Using Eqs. (5.31)
tccw as given In
between clockwise
comes:
LCw = 2TR + R!ltcw = ccwtcw (5.32)
At = tcw - tccw
and (5.32) we can solve for tcw and
Fig. 5.43 so that the difference At
and counterclockwise propagation be-
. (21TR)(2Rf0/C2 =
(5.33)
AL = (4A/c)$l (5.30)
4TR2nlc2 =
(4A/c2)sl
5-15