An unconventional and highly effective technique has been devised to reduce cyclic errors that arise in the operation of a displacement-measuring heterodyne optical interferometer. The cyclic errors are attributable largely to undesired small exchanges of power between light beams that are nominally in mutually orthogonal polarization states (such exchanges are denoted generally as polarization leakage). Unlike some prior techniques for reducing cyclic errors, the present technique does not require additional optical or electronic signals, additional signal processing, or use of optical components other than those of the interferometer itself. Optionally, the present technique can be used in conjunction with the prior techniques to reduce errors further.
The figure schematically depicts a heterodyne optical interferometer that includes a target retroreflector and a fiducial retroreflector, the purpose of the interferometer being to measure displacements between these two retroreflectors. The beam from a single laser is split into two that are shifted in frequency by different amounts. Beam 1, having frequency n1, is designated the target beam; beam 2, having frequency n2, is designated the local or reference beam. The beams are collimated and then polarized orthogonally to each other: beam 1 is given s (out-of-plane) polarization, while beam 2 is given p (in-plane) polarization. The beams are combined at the injection polarizing beam splitter. A small fraction of the power of both beams is picked off at the reference beam splitter, combined at the reference polarizer, and mixed by the reference photodetector, which generates the reference heterodyne signal at the beat frequency n1-n2.
Most of the light propagates to the main polarizing beam splitter. Beam 2 (the p-polarized reference beam) passes through this beam splitter to the signal photodiode. Beam 1 (the s-polarized target beam) is reflected by this beam splitter onto the target path, where it makes a round trip between the target and fiducial retroreflectors and is then reflected into the signal photodiode, wherein beams 1 and 2 are mixed to obtain the target heterodyne signal at the beat frequency. Nominally, the phase of the target heterodyne signal relative to that of the reference signal varies linearly by 2Π radians per half wavelength of the target/retroreflector displacement. Hence, the variation of this phase is measured to determine the displacement.
In practice, the variation of phase with displacement deviates from perfect linearity because of a number of leakages, which give rise to the aforementioned cyclic errors. The main leakage is the passage of a small portion (≈0.1 percent) of s-polarized power from beam 1 directly through the main polarizing beam splitter to the signal photodetector.
In the present technique, one makes no attempt to reduce this main s-polarized leakage, because it cannot be stopped without also blocking the desired signal. Instead, one takes advantage of the fact that for complex reasons that involve the amplitude and phase relationships among the various polarization components, it is possible to compensate for the effects of the s-polarized leakage by deliberately introducing some additional p-polarized leakage from beam 2 onto the target path. First, one refines the alignments of all relevant optical components to minimize leakages other than the main one. Then, in a multistep procedure, one iteratively adjusts the polarizers and quarter-wave plates to introduce the correct amount of compensatory p-polarized leakage. The procedure can be alternatively characterized as one of seeking the optimum adjustment of the optical components. When optimum adjustment is achieved, the cyclic displacement-measurement error caused by the main and other leakages can be reduced by a large factor (≈10), without nulling the desired signal.
This work was done by Oliver Lay of Caltech for NASA's Jet Propulsion Laboratory.
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Adjusting Polarization to Reduce Error in an Interferometer
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