A NEW HETERODYNE INTERFREOMETER WITH ZERO PERIODIC ERROR AND TUNABLE BEAT FREQUENCY Hyo Soo Kim 1 , Tony L. Schmitz, 1 John F. Beckwith 2,* , and Matthew C. Rueff 1 1 Department of Mechanical and Aerospace Engineering University of Florida, Gainesville, FL, USA 2 Electronics Engineering Technologies Division Lawrence Livermore National Laboratory, Livermore, CA 94550, USA * Retired INTRODUCTION Since its introduction in the mid-1960s, displacement measuring interferometry has offered high accuracy, range, and resolution for non-contact displacement measurement applications, including position feedback for lithographic stepper stages, precision cutting machines, and coordinate measuring machines, as well as transducer calibration, for example. A common configuration choice in these situations is the heterodyne (or two frequency) Michelson- type interferometer with single, double, or multiple passes of the optical paths. These systems infer changes in displacement of a selected optical path by monitoring the optically induced variation in the photodetector current, which is generated from the optical interference signal. Periodic error remains an intrinsic error source that prevents traditional configurations from achieving sub-nanometer level accuracy. The purpose of this research is to validate the absence of periodic error in a new interferometer design that does not rely on polarization coding, where the two (heterodyne) optical frequencies are carried on coincident, linearly polarized, mutually orthogonal laser beams and separated/recombined using polarization dependent optics. Rather, the two frequencies are carried on spatially separate beams in a polarization independent optical configuration that also enables the user to select the beat (or split) frequency. By eliminating the potential for mixing between the two heterodyne frequencies, the periodic error source is removed. PERIODIC ERROR BACKGROUND Imperfect separation of the two light frequencies into the moving and fixed paths in polarization coded heterodyne interferometers has been shown to produce first and second order periodic errors, or errors of one and two cycles per wavelength of optical path change, respectively. In a perfect system, a single frequency would travel to the fixed target, while a second, single frequency traveled to the moving target. Interference of the combined signals would yield a perfectly sinusoidal trace with phase that varied, relative to a reference phase signal, in response to motion of the moving target. However, the inherent frequency leakage in actual implementations produces an interference signal which is not purely sinusoidal (i.e., contains unintended spectral content) and leads to a periodic error in the measured displacement. Quenelle [1] performed an early investigation of periodic error in heterodyne interferometers. Subsequent areas of research have included efforts to measure periodic error using frequency domain analysis [2], analytical modeling techniques [3], Jones calculus modeling [4], and reduction of periodic error [5-7]. Schmitz and Beckwith [8] summarized the potential periodic error contributors using a Frequency-Path model, which identified all possible paths for each light frequency from the source to detector and predicted the number of interference terms that may be expected at the detector output. For the single pass, polarization-coded heterodyne interferometer, it was demonstrated that 10 distinct interference terms exist in a fully leaking interferometer (i.e., each frequency is present in both the moving and fixed paths). These interference terms may be grouped by optical path change dependency into only four categories: 1) optical power which contributes a constant intensity to the photodetector current independent of optical path changes; 2) AC reference terms with phase that varies by one full cycle over the synthetic wavelength; 3) DC interference, which are Doppler shifted up from zero frequency during