Data-dependent systems methodology for noise-insensitive phase unwrapping in laser interferometric surface characterization

Abstract

Phase unwrapping recovers the actual surface topography from a calculated phase map, which is often degraded by a combination of surface defects and measurement noise. Prevalent unwrapping techniques are unable to differentiate between the surface and noise-created discontinuities, resulting in an improper surface recovery. In our approach the stochastic nature of the phase map is used by the data-dependent systems (DDS) methodology to separate the surface from noisy measurements. The DDS methodology identifies an adequate autoregressive moving-average model representing the measured phase values. An adaptive thresholding scheme carries out the phase discontinuity removal from the model residuals, employing statistical outlier detection. We then recover the surface by using the model and clean residuals. The proposed technique is found useful for unwrapping especially noisy and degraded phase maps.