Sub-Aperture Interferometers

NASA’s Jet Propulsion Laboratory, Pasadena, California

Sub-aperture interferometers — also called wavefront-split interferometers — have been developed for simultaneously measuring displacements of multiple targets. The terms “sub-aperture” and “wavefront-split” signify that the original measurement light beam in an interferometer is split into multiple sub-beams derived from non-overlapping portions of the original measurement- beam aperture. Each measurement sub-beam is aimed at a retroreflector mounted on one of the targets. The splitting of the measurement beam is accomplished by use of truncated mirrors and masks, as shown in the example below.

In this Wavefront-Split Interferometer, the truncated retroreflector on the first target and the retroreflector on the second target form a measurementoptical cavity. The roles played by the measurement and reference beams in a typical prior interferometer are here played by two measurement sub-beamsderived from the same measurement beam without use of extra optics.

Sub-aperture interferometers incorporate some of the innovations described in two previous NASA Tech Briefs articles: “Common-Path Heterodyne Interferometers” (NPO-20786), Vol. 25, No. 7 (July 2001), page 12a. and “Interferometer for Measuring Displacement to Within 20 pm” (NPO- 21221), Vol. 27, No. 7 (July 2003), page 8a. Wavefront splitting is one of those innovations. To recapitulate from the second-mentioned article: Heretofore, the most popular method of displacement-measuring interferometry has involved two beams, the polarizations of which are meant to be kept orthogonal upstream of the final interference location, where the difference between the phases of the two beams is measured. Polarization leakage (deviations from the desired perfect orthogonality) contaminates the phase measurement with cyclic nonlinear errors. The advantage afforded by wavefront splitting arises from the fact that one does not utilize polarization in the separation and combination of the interfering beams; the cyclic nonlinear errors are much smaller because the polarization-leakage contribution is eliminated.

One example of a sub-aperture interferometer, denoted a sub-aperture vertex-to-vertex interferometer, is one of several prototype common-path heterodyne interferometers designed and built at NASA’s Jet Propulsion Laboratory. This interferometer (see figure) makes use of two collimated laser beams — one at a frequency of f₀, the other at the slightly different frequency of f₀ + Δf. The f₀ beam is denoted

the measurement beam. It passes through beam splitter 1 on its way toward two targets. The retroreflector on the first target is truncated; it is a flat mirror that reflects a portion of the measurement beam and contains two holes through which portions of the measurement beam continue toward the second target and through which they return after reflection from the retroreflector on the second target. A mask establishes guard bands between the measurement subbeams to reduce diffraction. The measurement sub-beams returning from the targets are reflected from beam splitter 1 to beam splitter 2, where the f₀ + Δf beam becomes superimposed upon them. Then by use of mirrors (one of which is truncated) and lenses, the f₀ sub-beam from target 1 and part of the f₀ + Δf beam are sent to photodiode 1 while the f₀ sub-beam from target 2 and another part of the f₀ + Δf beam are sent to photodiode 2. The lowest-frequency components of the heterodyne outputs of the two photodetectors are signals of frequency Δf. The difference between the phases of these heterodyne signals is proportional to the difference between the lengths of the optical paths to the two target retroreflectors. Any displacement of either target along the optical path results in a proportional change in this phase difference. Hence, measurement of the phase difference and of any change in the phase difference yields information on the displacement.

This work was done by Feng Zhao of Caltech for NASA’s Jet Propulsion Laboratory. For more information, contact This email address is being protected from spambots. You need JavaScript enabled to view it.. NPO-30779