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A Linear Projection Approach for Resolving Community Structure

A heterodyne interferometer and an associated interferometric method are provided that significantly reduce polarization crosstalk and that permit the target to translate to a limited extent in a direction orthogonal to the direction of interest and to be tilted to a limited extent without adversely affecting the resulting measurement. The heterodyne interferometer includes a beamsplitter for splitting each of a first beam and a coherent second beam into at least two partial beams. Advantageously, the first beam and the partial first beams propagate in a first plane, while the second beam and the partial second beams propagate in a second plane that is offset from the first plane by at least two beam diameters so as not to spatially overlap with the first beam and the partial first beams, thereby preventing polarization crosstalk. The heterodyne interferometer also includes a reference arm and a measurement arm that each receive a partial first beam and a partial second beam. The measurement arm can include a pair of crossed porro prisms with at least one of the porro prisms being adapted to move in conjunction with the target. By utilizing the pair of crossed porro prisms, the target can translate to a limited extent in a direction orthogonal to the measurement path and can be tilted to a limited extent without adversely affecting the resulting measurements. The heterodyne interferometer can also include at least one and, more commonly, a pair of detectors for receiving partial beams that have traversed the reference arm and the measurement arm. Based upon the resulting interference fringes, the detector can provide a signal indicative of the target displacement.