FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

detect displacements of the movable mirror as small as
10-13 m. l%is configuration has the advantage that
little or no light is fed directly back into the laser.
This is in contrast to the Michelson configuration. A
more detailed description of how such feedback can lead
to laser instability and noise is contained in Section
4.2. It should be noted that there are two other beams
not shown explicitly in Fig. 4.2, that travel upward
from the second beam splitter, i.e. a reflected portion
of the upper horizontal beam and a transmitted portion
of the righthand vertical beam. These could be fed to
another optical detector to yield a second output signal
, which may be employed to advantage in certain applications.
4.1.1.4 The
Sagnac
Interferometer
Fig. 4.4
—
1
FIXED
t
MOVABLE
MIRROR
MIRROR
TRANSDUCER
The principle of the Fabry-Perot interferometer.
The
shown in Fig.
Sagnac interferometric configuration is sive mirrors. The reflectivity of these mirrors usually
is quite high, e.g. 95% or even higher. Assuming
4.3. With this arrangement, the two porthat
the reflectivity (reflection coefficient) is 95%,
at any instant 95% of the output light from the laser
source will be reflected back toward the laser and 5%
will be transmitted into the Interferometer cavity.
When this portion of the incident light reaches the
right-hand mirror, 95% of it will be reflected back
toward the left-hand mirror and 5% will be transmitted
through to the detector. This will combine with light
that has been reflected back and forth successively an
increasing number of times between the two mirrors.
Neglecting losses other than the 5% transmission (at
each interface), each successive output beam intensity
will be reduced from the previous one by the factor
II
II
(0.95)2 = 0.9025. Assuming that the laser has a coher-
) 1 11/ I A ence lenzth manv times the distance between the two
mirrors, the optical signal intensity incident on the
LASER
I
Fig. 4.3 The principle of the Sagnac interferometer.
tions of the laser’s output beam are sent in opposite
directions around the closed path formed by the beam
splitter and the two mirrors. They are then recombined
to be sent on to the photodetector and also back toward
the laser. If any of the mirrors is displaced perpendicular
to its reflecting surface, both path lengths
would be changed by the same amount and there should
be no detectable change in the interference process
at the photodetector. On the other hand, if the table
on which the interferometer is mounted were set into,
say clockwise, rotation about an axis perpendicular
to the plane of the beams, the beam traveling clockwiae,
i.e. In the direction of rotation, would be
delayed with respect to the counterclockwise traveling
beam. The clockwise beam has to “catch up” to the end
moving in the same direction. The counterclockwise beam
runs into the end moving in the opposite direction.
Thus, the Sagnac interferometer may be employed as a
sensitive rotation detector and, in principal, it is the
basis for the design of the ring laser gyroscope currently
in use in a number of inertial guidance systems.
4.1.
tion
4.4.
.5 The Fabry-Perot Interferometer
The fourth type of inter ferometric conf igurathe
Fabry-Perot interferometer, is shown In Fig.
It consists of two parallel, partially transmis-
4-2
detector may be found by forming the vector sum of the
electric fields of the various transmitted beams.
4.1.1.6 Interferometer Sensitivity
The sensitivity of various interferometers is
shown graphically in Fig. 4.5. Consider first, what
occurs in the first three type of interferometers that
were considered earlier. For the Michelson, Mach-Zehnder,
and Sagnac configurations, two separate optical
beams are combined at the sensitive interface of the
photodetector. As indicated in the upper left, the
wo electrical fields are represented by the vectors
~1 and 22 which are assumed to be of equal magnitude
and linearly polarized in the same direction. The optical
intensit is proportional to the square of their
vector sum, E z ( 8 ), which is at its maximum when the
temporal and spatial relative phase angle between the
two vectors is zero. If the length of one of the interferometer
paths changes the phase angle varies, and
E2( e ) and the intensity vary as indicated in the graph
in the upper right in Fig. 4.5. , i.e. , the intensity
drops to zero as 13 increases from O to n radians, varying
as cos e. For further increases in e, E2( e) oscillates
from zero to its maximum and back to zero again
each time 13 varies by 2T radians.
The corresponding diagrams for the Fabry-
Perot interferometer are shown in the lower portion of
Fig. 4.5. As pointed out earlier in this case, there
is a set of electrical field vectors, in principle infinite
in number, each successive one down from the
previous by a factor R2, where R is the amplitude reflection
coefficient. When the mirror separation is
some integral number of half wavelengths, all of these
vectors are in phase and the output intensity is at a
maximum. When the separation is increased slightly,
each successive vector is shifted with respect to the
previous one by the same angle. By continuing the vec -