An improved method and apparatus have been devised for measuring cyclic errors in the readouts of laser heterodyne interferometers that are configured and operated as displacement gauges. The cyclic errors arise as a consequence of mixing of spurious optical and electrical signals in beam launchers that are subsystems of such interferometers. The conventional approach to measurement of cyclic error involves phase measurements and yields values precise to within about 10 pm over air optical paths at laser wavelengths in the visible and near infrared. The present approach, which involves amplitude measurements instead of phase measurements, yields values precise to about ≈0.1 pm — about 100 times the precision of the conventional approach.

Displacement Oscillations are introduced between two corner-cube retroreflectors that are commonto two displacement gauges. The magnitude of an amplitude modulation in the outputs of thegauges is measured.

In a displacement gauge of the type of interest here, the laser heterodyne interferometer is used to measure any change in distance along an optical axis between two corner-cube retroreflectors. One of the corner-cube retroreflectors is mounted on a piezoelectric transducer (see figure), which is used to introduce a low-frequency periodic displacement that can be measured by the gauges. The transducer is excited at a frequency of 9 Hz by a triangular waveform to generate a 9-Hz triangular-wave displacement having an amplitude of 25 μm.

The displacement gives rise to both amplitude and phase modulation of the heterodyne signals in the gauges. The modulation includes cyclic error components, and the magnitude of the cyclicerror component of the phase modulation is what one needs to measure in order to determine the magnitude of the cyclic displacement error. The precision attainable in the conventional (phase measurement) approach to measuring cyclic error is limited because the phase measurements are affected by phase noise contributed mainly by vibrations and air turbulence. However, the amplitude modulation associated with the cyclic phase error is not affected by vibrations and air turbulence.

Therefore, in the present approach, in order to achieve higher precision in measuring cyclic error, one measures the amplitude modulation instead of the phase modulation. The heterodyne error signal is fed to a relatively simple demodulator circuit, which removes the radio-frequency component of the heterodyne error signal, leaving only the 9- Hz amplitude modulation. The output of the demodulator is fed to a spectrum analyzer or an oscilloscope for measurement of the magnitude of the 9-Hz amplitude modulation.

This work was done by Daniel Ryan, Alexander Abramovici, Feng Zhao, Frank Dekens, Xin An, Alireza Azizi, Jacob Chapsky, and Peter Halverson of Caltech for NASA’s Jet Propulsion Laboratory. For more information, download the Technical Support Package (free white paper) at under the Physical Sciences category. NPO-45157

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Measuring Cyclic Error in Laser Heterodyne Interferometers

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This article first appeared in the February, 2010 issue of NASA Tech Briefs Magazine.

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