Sub-λ/2 Displacement Sensor With Nanometric Precision Based on Optical Feedback Interferometry Used as a Non-Uniform Event-Based Sampling System

Abstract

In this paper, a method based on the inherent event-based sampling capability of the laser optical feedback interferometry (OFI) is proposed to recover sub-λ/2 displacement with a nanometric precision. The proposed method operates in open-loop configuration and relies on OFI's fringe detection, thereby improving its robustness and ease of use. The measured white noise power spectral density is less than 100 pm/ √ Hz with a corner noise frequency of approximately 80 Hz for a laser diode emitting wavelength λ0 of 785 nm placed at 30 cm of the target.

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

“…In the moderate feedback regime, based on ( 1 ) and ( 2 ), the information on is completely enclosed within phase . It was shown in [ 22 ] that SM interferometers can be perceived as an inherent non-uniform sampling system with its own embedded phase level-crossing detector. A phase domain level crossing every corresponding to the OOP discontinuities can thus be obtained ( Figure 2 ).…”

“…To solve this issue, the non-uniform sampling approach allows one to look at it from a different perspective [ 22 ]. Instead of considering and to be different, they can be supposed to be equal if a virtual square-like displacement is added on top of D , with its rising (decreasing) edges corresponding to the change in direction.…”

“…In accordance with Equation ( 2 ), it clearly shows that has a negligible influence on the obtained results. In addition, C estimation accuracy expectedly depends on the displacement amplitude since the performance of the reconstruction algorithm based on NUS greatly improves with the number of crossed quantization levels [ 22 ].…”

“…As a result, the proposed method to estimate C can be summarized by the block diagram shown in Figure 6 and the three following steps: (1) SM fringe detection, (2) displacement reconstruction based on non-uniform sampling approach [ 22 ] and (3) C estimation. During the first step, similarly to [ 22 ], from the SM signal, all the fringes should be detected to obtain all the time-phase pairs , where corresponds to the time instant when the SM signal experiences a phase discontinuity. Since these pairs must be recorded, these values are quantized with a time resolution of (where is the sampling frequency of the data acquisition system) to generate non-uniform samples, .…”

“…Subsequently, here we propose a new open-loop approach that allows estimating C while retaining the inherent simplicity of OFI as the required hardware consists only of amplifying and acquiring the SM signal. Here, as presented in [ 22 ], we propose perceiving SM interferometers as inherent non-uniform sampling systems with their own embedded phase level-crossing detectors. Non-uniform sampling (NUS) approaches are often used in applications for which the retrieved information is sparse.…”