2.2 Generation of Error Signals

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.

Please send comments and suggestions to: veillet@cfht.hawaii.edu