On strategy for determining displacement from perturbed phase of self
mixing interferometry when parameters are unknown
Abstract
While self-mixing interferometry(SMI) has proven to be suitable for
displacement measurement and other sensing applications, its
characteristic self-mixing signal shape is strongly governed by the
non-linear phase equation which forms relation between perturbed and
unperturbed phase of self-mixing laser. Therefore, while it is desirable
for robust estimation of displacement of moving target, the algorithms
to achieve this must have an objective strategy that can be achieved by
understanding the characteristic of extracting knowledge of the
perturbed phase from the unperturbed phase. Therefore, it has been
proved and shown that such a strategy must not involve sole methods
where the perturbed phase is a continuous function of the unperturbed
phase (e.g: Taylor series or fixed-point methods) or through successive
displacements (e.g: variations of Gauss-Seidel method). The subset of
this strategy is to perform spectral filtering of the perturbed phase
followed by perturbative or homotopic deformation. A less
computationally expensive approach of this strategy is adopted to
achieve displacement with a mean error of 62.2nm covering all feedback
regimes, when the coupling factor āCā is unknown.