During data acquisition, the path difference is
controlled very accurately using a signal from the
reference laser, which is housed in a thermally stabilized environment
to
prevent drifting of the laser lines (
). The laser beam is linearly
polarized
and is then
directed to the beam splitter and into the arms of the interferometer.
As the
laser beam enters each arm of the interferometer it is passed through
quarter-wave plates to induce circular
polarization. The quarter-wave plates in
the two arms are oriented such that the polarization vector rotates in a
clockwise direction in one arm, and a counterclockwise direction in the
other.
As a result, when the beams are recombined, a rotating, linearly
polarized signal of
constant intensity is produced. The azimuth of the resulting
electromagnetic vector depends on the net path difference, within one
wavelength.
The angle of polarization, which contains information on the path
difference, is measured using the following procedure. The rotating,
linear polarized
reference laser beam is directed away from the interferometer to
another beam splitter, positioned before two polarizing filters and
photodiodes.
The polaroid filters are rotated such that the signals incident on the
photodiodes have polarization angles differing by 
, so that
the signals output from the photodiodes are phase displaced by 
to
each other and each
measure the strength of a different component of the incident
electromagnetic vector. The signals measured by the photodiodes are
where 
is the path difference and 
is the wavelength of the
reference laser.
If the path difference is modulated about a mean path difference of 
then
where 
is 
times the modulation frequency and 
is
the amplitude of modulation in terms of 
. The
signals measured by the photodiodes are then
If the modulation is such that 
1 then
simple trigonometric relations can be used to reduce these expressions
further to the two quadrature signals
If these two signals are summed after phase delaying 
by 
at frequency
, the result is then
This is the phase modulated reference to which the command position is
compared to generate the error signal which in turn drives the servo
system. However, in practice the phase of 
is not measured directly. The low frequency component of the error
signal (
Hz)
is sent to the loudspeaker motor while the high frequency component
(
Hz) is sent to the piezo stacks.
The 
and 
signals are displayed as a Lissajou on an oscilloscope
on the Section 3.1.4. If the Lissajou figure on
this
oscilloscope is skewed then the net difference
in polarization angles is markedly different from 
and
the polaroid filters in front of one of the photodiodes should be
adjusted - consult CFHT support personnel.