Adaptive Volterra processor for fringe order identification in white-light interferometric systems

Abstract

Comparatively high success rates with the application of linear adaptive least mean square (LMS) algorithms to identify the zero order fringe in the presence of additive Gaussian noise only have been reported in spatially-scanned white-light interferometric (WLI) systems. However, when the corrupting noise causing the problems with fringe identification is signal-dependent and/or exhibits transient behaviour mainly attributable to mechanical vibrations (shocks) in such systems, nonlinear filtering accompanied by a suitable adaptation algorithm should lead to better overall performance. The paper presents a study conducted to appraise the use of Volterra processors in conjunction with adaptive LMS, against the linear filtering counterpart previously published, when the analogue-to-digital (A/D) converters employed in the interferometric system introduce quadratic and/or cubic nonlinearity distortion. The paper also attempts to resolve the linear/nonlinear modelling dilemma of a suspected kind of nonlinearity due to chromatic aberration effects which manifests two important characteristics in the fringe pattern, namely, skewness and nonGaussianity. It is shown that the Volterra processor produces less satisfactory results than a linear filter with optimal choice of the step size parameter. Thus contradicting the hypothesis which regards the effects of chromatic aberrations as nonlinear.