Reduced measurement uncertainty of white-light interferometry on rough surfaces

Abstract

In white-light interferometry at rough surfaces ("Coherence radar") the measuring uncertainty is physically limited by the arbitrary phase of the individual speckle interferograms. As a consequence, the standard deviation of the measured shape data is inevitably given by the (optically unresolved) roughness of the surface. The statistical error in each measuring point depends on the brightness of the corresponding speckle; a dark speckle yields a more uncertain measurement than a bright one. If the brightness is below the noise threshold of the camera, the measurement fails completely and an outlier occurs. We present a new method to significantly reduce the measuring uncertainty and the number of outliers. We achieve this by generating several statistically independent speckle patterns, by use of different directions of the illumination. We evaluate the different measurements and select the best measurement or assign more weight to brighter speckles.

Height Fluctuations and Surface Gradients in Topographic Measurements

“…More precisely, reflectivity can influence white light interferograms by affecting the intensity, contrast, and visibility, and potentially introducing phase shifts in the interference fringes. Gross et al [13] demonstrated that the statistical error of each measurement location depends on the brightness of the associated speckle; a dark speckle gives a more uncertain measurement than a bright one. If the brightness is lower than the camera's noise threshold, the measurement fails completely, and an outlier appears that leads to a NaN value.…”