On nature of determining displacement from sole knowledge of self interferometric perturbed phase

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 direction which can be achieved by understanding the characteristic of extracting knowledge of perturbed phase from unperturbed phase. Therefore, this paper tends to deduce results from the self mixing interferometry(SMI) phase equation,by showing the impossibility of analytically deriving perturbed phase as continuous function of unperturbed phase either through finite or infinite substitutions. Therefore we never get exact displacement just by sole knowledge of perturbed phase. Moreover, it has theoretically shown that the action of practically deriving unperturbed phase from perturbed phase becomes a filltering process in spectral domain followed by perturbative or homotopical deformation.