Full-Field High-Strain Gradient Evaluation from Wrapped ESPI Data Using Phasors

Electronic Speckle Pattern Interferometry (ESPI) is a sensitive optical method commonly used for making full-field measurements of surface displacements. It would be very desirable to be able to extend the technique also to determine surface strains. This would provide a full-field, non-contact strain measurement method that avoids the substantial installation burden of strain gauges. A mathematical approach is described where the ESPI data from an in-plane interferometer are numerically differentiated to determine surface strains. This is a challenging process because numerical differentiation is very sensitive to the presence of noise and ESPI data are inherently noisy. In addition, the phase information from ESPI data are wrapped modulo-2π. The resulting phase discontinuities make it difficult to use local averaging to smooth the data. A technique is described here where phasors are used to avoid the need for phase unwrapping. The effect of noise is reduced by a localized multiple smoothing technique that is effective in preserving spatial resolution, even near very high strain concentrations. Example measurements are shown and the effectiveness of the proposed method is illustrated.