Toward an Estimation of the Optical Feedback Factor C on the Fly for Displacement Sensing

Abstract

In this paper, a method based on the inherent event-based sampling capability of laser optical feedback interferometry (OFI) is proposed to assess the optical feedback factor C when the laser operates in the moderate and strong feedback regimes. Most of the phase unwrapping open-loop OFI algorithms rely on the estimation of C to retrieve the displacement with nanometric precision. Here, the proposed method operates in open-loop configuration and relies only on OFI’s fringe detection, thereby improving its robustness and ease of use. The proposed method is able to estimate C with a precision of <5%. The obtained performances are compared to three different approaches previously published and the impacts of phase noise and sampling frequency are reported. We also show that this method can assess C on the fly even when C is varying due to speckle. To the best of the authors’ knowledge, these are the first reported results of time-varying C estimation. In addition, through C estimation over time, it could pave the way not only to higher performance phase unwrapping algorithms but also to a better control of the optical feedback level via the use of an adaptive lens and thus to better displacement retrieval performances.

Integration of Zero Crossing Method in a Nonuniform Sampling System Using Optical Feedback Interferometry

“…Few specific cases are also discussed here. When the ZC method is applied to an experimental OFI signal corresponding to 0.25 µm amplitude at 10 Hz with α = 5 and C = 1.78 (estimated by using the method reported in [26] with a precision of < 5%), an improvement of 92% in RMS error ©2023 IEEE. Personal use of this material is permitted.…”

“…Note that C is needed in the derived expressions. Here, the C estimation method proposed in [26] is used, as shown in Fig. 3.…”

“…It was demonstrated in [26] that C can be retrieved by estimating this phase level difference ∆Φ. Thus, the simple NUS based approach described in [4] interpolates just these discontinuity points to recover the phase signal ϕ 0 (t).…”

Fringe Detection and Displacement Sensing for Variable Optical Feedback-Based Self-Mixing Interferometry by Using Deep Neural Networks

“…The C parameter depends upon the amount of feedback, surface reflectivity, coupling efficiency, and the distance to the target [16]. The shape of OFI signals and value of modulation index m depend on C [25].…”

“…Speckle causes measurement errors [13] and spectral broadening [14]. For displacement sensing, fringe detection (FD) is an integral part of many SMI-based measurement algorithms (e.g., using phase unwrapping [15] or non-uniform sampling [16]) and is easily achieved if the optical feedback remains constant. However, variable optical feedback (VOF) conditions make it very difficult to achieve correct FD, especially in the presence of noise.…”