Neural Network-Based Estimation of Optical Feedback Factor in Self-Mixing Interferometry Systems Across Various Feedback Regimes

Self-mixing interferometry (SMI) system is a promising and low-cost approach for displacement measurements. The resolution and precision of displacement estimation depend on key parameters of the SMI system and, in particular, on the optical feedback factor (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i>). This paper presents a new method for estimating this <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> factor based on an artificial neural network that analyzes certain specific fringe shape features of SMI signals. Specifically, only six features of the SMI signal are taken into account as input to a compact neural network with one hidden neuron layer (14 neurons) by the estimation process, which reduces the computational cost and simplifies its deployment. This study evaluates the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i>-estimation capability of the method in various simulated and experimental scenarios, including variations in displacement amplitude and frequency, random displacements, noise levels and speckle effects. These analyses show that the method works correctly for a moderate feedback regime (1 < <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> < 4.6) with an average relative estimation error inferior to 5% and even 2% for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> ≥ 1.5. For the strong feedback regime (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> > 4.6), this error is less than 2% (for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> < 8). Comparisons with other methods show similar or better accuracy but with the advantage of being able to handle all displacement waveforms (sinusoidal or arbitrary) at low computational cost, which facilitates integration into a real-time embedded system.