Deep neural networks for efficient phase demodulation in wavelength shifting interferometry

TL;DR

This paper demonstrates that deep neural networks can outperform traditional phase demodulation algorithms in wavelength shifting interferometry by leveraging noise statistics and parameter constraints, achieving or exceeding the Cramér-Rao bound.

Contribution

The authors introduce a novel application of deep neural networks for phase demodulation that surpasses conventional limits by incorporating additional information during training.

Findings

DNNs outperform traditional algorithms in phase sensitivity.

DNNs can reach or exceed the Cramér-Rao bound with appropriate training.

Sensitivity approaches the single parameter CRB for well confined parameters.

Abstract

Analytical phase demodulation algorithms in optical interferometry typically fail to reach the theoretical sensitivity limit set by the Cram\'er-Rao bound (CRB). We show that deep neural networks (DNNs) can perform efficient phase demodulation by achieving or exceeding the CRB by significant margins when trained with new information that is not utilized by conventional algorithms, such as noise statistics and parameter constraints. As an example, we developed and applied DNNs to wavelength shifting interferometry. When trained with noise statistics, the DNNs outperform the conventional algorithm in terms of phase sensitivity and achieve the traditional three parameter CRB. Further, by incorporating parameter constraints into the training sets, they can exceed the traditional CRB. For well confined parameters, the phase sensitivity of the DNNs can even approach a fundamental limit we refer to as the single parameter CRB. Such sensitivity improvement can translate into significant increase in single-to-noise ratio without hardware modification, or be used to relax hardware requirements.