Non-Uniform Sampling Theory applied to FM Channel Optical Feedback Interferometry for Displacement Sensors

In this paper, the optical feedback interferometry (OFI) signals obtained from the frequency modulated (FM) channel are processed by a non-uniform sampling (NUS) method to retrieve target displacements. The FM OFI channel signal is converted into its corresponding amplitude modulated (AM) signal using a free-space Michelson interferometer as an edge filter with a sensitivity of 1.3 (GHz)(-1). The laser diode (LD) is operated in moderate optical feedback regime and its wavelength is modulated with a sinusoidal dithering signal applied on the LD driving-current. This dithering signal allows the recovery of sub half-wavelength displacements. Contrary to phase unwrapping methods, the proposed method based on NUS relies only on OFI's fringe detection to recover the target's displacement and thus is not affected by the non-linear response of the employed edge filter. In addition, compared to lock-in techniques, the dynamic range is not limited by the tuning range of the LD. Using a laser diode emitting at 1550 nm, the noise equivalent displacement for a 1 kHz bandwidth is approximately 8.4 nm and 0.9 nm for the AM- and the FM-channel, respectively.