The Monte Carlo method as a tool for statistical characterisation of differential and additive phase shifting algorithms

Abstract

Abstract. Several metrological applications base their measurement principle in the phase sum or difference between two patterns, one original s(r,) and another modified t(r,+). Additive or differential phase shifting algorithms directly recover the sum 2+ or the difference  of phases without requiring prior calculation of the individual phases. These algorithms can be constructed, for example, from a suitable combination of known phase shifting algorithms. Little has been written on the design, analysis and error compensation of these new two-stage algorithms. Previously we have used computer simulation to study, in a linear approach or with a filter process in reciprocal space, the response of several families of them to the main error sources. In this work we present an error analysis that uses Monte Carlo simulation to achieve results in good agreement with those obtained with spatial and temporal methods.