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

Abstract

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.

All Analog Processing of Speckle Affected Self-Mixing Interferometric Signals

“…For example, a Hilbert transform based method calculates the instantaneous phase of the speckle affected SMI signal, which has the interesting property of being unaffected by amplitude modulation of the SMI signal [18]. However, the method suffers from directional ambiguity and uses traditional derivative based threshold approach to ascertain displacement direction [18].…”

“…One approach is to avoid the Date of publication : 15 th of Sptember 2017 occurrence of speckle within SMI either by using cooperative target surface, or by adding electro-mechanical/optical/laser [15][16][17] components to the SMI sensor. The second approach uses additional DSP algorithms for signal recovery such as Hilbert transform [18], envelope extraction [19] and wavelet transform methods [20,21]. The later approach is thus preferable as it maintains the inherent simplicity of SMI sensor design.…”

Robust Detection of Non-Regular Interferometric Fringes From a Self-Mixing Displacement Sensor Using Bi-Wavelet Transform

“…4). Similar to [22], [25], an add-on routine should be then used to determine the displacement direction in order to reconstruct the displacement with a precision of λ/2 ( Fig. 4 (a)).…”

“…Techniques based on envelope tracking and adaptive threshold scheme [21] were shown to improve the robustness of displacement reconstruction but in some cases, fringes might not be detected. A Hilbert transform-based algorithm [22] was then proposed to extract the instantaneous SM phase. Nevertheless, it cannot inherently determine the target direction and sub-wavelength displacements could be wrongly interpreted.…”

In-situ measurement of non-steady flows using optical feedback interferometry

“…Mainly used for velocity [2], absolute distance [3], vibration and displacement of solid targets [4]- [6], this technique has been recently extended to flow measurements [7].…”