Fiber-Optic Sensors - Applied Optics Fundamentals and Device Applications - page 192

Input
coupler

Laser

Medium

Sensor
coil

PZT phase
shifter

SIG
proc

Output
coupler

Output

Photo-
diodes

Induced optical phase shift
∆ =

( )

1δ h
n δ P

1δ h
L δ P

+ knL ∆ P

FIGURE 4.25
Interferometric sensor concept.

As a practical matter, if the unperturbed sensing fiber and the reference
fiber are exactly the same length, the combined outputs will be a maximum,
and either shortening or lengthening the sensor fiber will produce a reduced
output. It is therefore not possible to discern from the output whether the
quantity being measured is initially increasing or decreasing. Also, the rate
of change in the magnitude of the sum of two sinusoids with respect to phase
offset is very small when the phase separation is small.
Both of these difficulties can be overcome by inserting a fixed quarter
wavelength (90°) phase difference between the sensing and reference fiber
paths. In this case, the peak of one waveform occurs at the zero of the other,
so that the sum is one half of the maximum occurring when the phase differ-
ence is zero. The slope at the zero crossing is maximum and the sums change
rapidly. The transfer matrix of the directional coupler is such that when the
path lengths differ by 90°, the two outputs to the photodetectors are of equal
magnitude.
The detector outputs are applied to a difference amplifier whose output
is then zero in the undisturbed state. When the phase difference is zero, the
sum of the amplitudes is maximum at one photodetector and zero at the