Combination of Phase Stepping and Fringe Tracking to Evaluate Strain from Noisy DSPI Data

Phase-stepping Digital Speckle Pattern Interferometry (DSPI) is known to suffer from speckle phase noise. In most cases this is the dominant source of measurement uncertainty, even more so, when a series of phase patterns is added up to increase the measurement range [1]. In order to obtain quantitative strain values from DSPI displacement data numerical differentiation is applied which decreases the signal to noise ratio further. Many techniques to filter the original unwrapped phase data have been reported in the literature, including low pass filtering, Gaussian convolution, image moments, power series expansions, or Fourier techniques. All these methods work satisfactorily when a smoothly varying, continuous strain field may be assumed. In presence of interfaces or object boundaries where a sudden change of strain values occur, such an assumption might not be valid. Filtering along a line of evaluation would obscure the very effect of strain transfer or peak strain values of interest. This is due to the fact that in transition zones the fringe density is changing rapidly, and strain values cannot be filtered out by low-pass techniques. Hence, both smoothing the data over a sub-window as well as filtering the data along a line of interest inevitably blurs object boundaries and transition zones. Smoothing along the line of interest is only possible if a mathematical model assumption of the displacement or strain values is made a priori. This model can either be motivated from a physical law or an analytical solution, or be a purely phenomenological model such as a polynomial ansatz. However, without a prioriknowledge, a justification of the model is difficult.