A novel multi-frequency (polydyne) optical interferometry method is introduced and a prototype developed to evaluate its performance in a Michelson displacement interferometer configuration. The polydyne interferometer contains three main parts of 1) synchronous Radio-Frequency Frequency-Modulated (RF-FM) electrical signal generation, 2) electrical-to-optical signal patching by an Acousto-Optic Modulator (AOM), and 3) signal detection and processing unit. Each of these three parts are discussed briefly in a separate chapter as well as the basic concept of phase extraction from the interference of FM light beams.A novel synchronous RF-FM signal generation method is introduced that uses an atomic clock for timing all frequency components of the signal. The RF-FM signal generator uses a modulated, voltage-controlled time delay to correspondingly modulate the phase of a 10 MHz sinusoidal reference from the atomic clock. This modulated reference signal is, in turn, used to clock a Direct Digital Synthesizer (DDS) circuit resulting in an FM signal at its output. The modulating signal that is input to the voltage-controlled time delay circuit is generated by another DDS that is synchronously clocked by the same 10 MHz sine wave signal before modulation. Therefore, all the digital components are timed from a single sinewave oscillator that forms the basis of all timing. The resultant output electrical signal comprises a center, or carrier, frequency plus a series of phase-synchronized sidebands having exact integer harmonic frequency separation. The RF-FM electric signal is transferred into a He-Ne laser beam by diffraction of the beam through an Acousto-Optic Modulator (AOM). The first diffraction side-beam emerging from the AOM is selected by a slit to be used in a Michelson interferometer topology. Frequency spectra of the interfered FM light beams contains the harmonics of modulation frequency. The displacement measurement is derived from the phase measurement of selected modulation harmonic pairs. Individual modulation harmonic amplitudes are measured using Fourier transform applied to the signal from a single photodetector. Lock-in amplifiers were first used to perform Fourier transform on the detected signal. Displacement of the moving target was measured by harmonic pairs chosen from harmonics 1 to 5 of the modulation signal. Since the analog Lock-In amplifiers use low-pass filters to detect the signal of interest, they limit the bandwidth of measurement to one-tenth of measured signal frequency. This limit reduces the speed of measurement to a few μm/s in our system. Therefore, after validating the feasibility of displacement measurement using the changes in the amplitudes of harmonic pairs detected by Lock-in amplifiers, a Discrete Fourier Transform (DFT) algorithm was developed on a Field Programmable Gate Array (FPGA) microchip to increase the bandwidth and speed of measurement as well as to miniaturize the signal processing unit. The timing of the FPGA microchip was developed from a Phase Locked Loop (PLL) synchronous to the same 10 MHz sine wave from the atomic clock that is timing all the frequency components of the RF-FM signal. This synchronizes all the timings in the signal generation and detection units. The developed synchronous DFT provides measurements with speeds up to 10 mm/s, a limit that can be always improved using larger FPGA microchips and faster analog-to-digital convertors on the photodetector output. In the developed synchronous DFT algorithm, displacement-related-phase-change is derived from the amplitudes of harmonics 1 and 2 of the modulation signal. The measured displacements are compared with a commercial heterodyne interferometer being used as a reference for these studies. Displacements of the moving mirror of the interferometer over ranges up to 10 μm with speeds up to 10 mm/s all show differences of less than 50 nm between the polydyne interferometer and the reference interferometer measurements. A drift test is also used to evaluate long-term stability and repeatability of measurements with the developed polydyne interferometer.