Speckle-insensitive fringe detection method based on Hilbert transform for self-mixing interferometry.

A robust phase measurement method to detect self-mixing signals from rough surface targets is addressed. Using the Hilbert transform to create the analytic signal of the monitored optical output power, an accurate instantaneous phase can be extracted without being affected by amplitude variations induced by the speckle phenomenon. In case of fringe fading, a running average filter removes the local bias offset improving the calculations. This also allows one to observe the phase at dynamic feedback levels within the same calculation, avoiding the need of adding external optical, mechanical or electronic components. This method provides confidence for the fringe detection required in subsequent steps to reach subwavelength precision of a reconstructed displacement or for velocimetry applications.