Monte Carlo based techniques of two-stage phase shifting algorithms

The recovering of phase information from irradiance values is a recurring subject for long time in Optical Metrology. Many of its techniques require a measurement associated to the phase sum or the phase difference between two fringe patterns. These can be directly recovered with two-stage phase shifting algorithms combining, in a non-linear way for example, known phase shifting algorithms. In previous works we have studied the response of several families of two-stage phase shifting algorithms to the main error sources using numerical simulation, a linear approach, and a Fourier description of the evaluation process. Here we present an error analysis using the Monte Carlo simulation method to characterize the probabilistic properties of the systematic and random sensitivities in non-linear two-stage phase shifting algorithms.

Research Highlights
► Two-stage evaluations play a fundamental role in several metrology applications.
► Monte Carlo method allows effective measurements of the influence in the recovered phase of the main systematic and random errors when two-stage phase shifting algorithms are employed.
► Monte Carlo method performs the rapid and efficient characterization of the behaviour of two-stage phase shifting algorithms regardless of the non-linear dependence of the irradiance values or the error models used.