FPGA based laser feedback interferometry using heterodyne and phase shifting measurements of large and nanometer displacements in the optical path.

Using a broadband electro-optic phase modulator with a custom designed laser feedback interferometer enables the implementation of heterodyning or phase-shifting approaches for phase measurements. An FPGA based lock-in amplifier (Moku, Liquid Instruments) with a combined linear feedback controller can be used for rapid measurement and control of the optical path length (OPL). For large changes in the OPL, the interferometric response (i.e., the intensity) sweeps through a series of fringes and it is necessary to use phase unwrapping techniques. As the OPL varies, however, the rate of change of the sensitivity of the interferometer also varies. Provided the interferometer is primarily used to measure nanometer changes, the OPL can be maintained about a position of highest sensitivity using feedback control. By contrast, when the interferometer is used to measure nanometer variations in the OPL that are superimposed upon large changes in the OPL, it is critical to account for the rate of change of sensitivity. This effect is readily illustrated by measuring a series of discrete, equally sized nm steps of a piezoelectric device that is mounted on translator which introduces large changes in the OPL. Analysis of these combined changes requires methods that compensate for the variation in sensitivity.