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White light scanning interference (WLSI) microscopes provide an accuratesurface topography of engineered surfaces. However, the measurement accuracy issubstantially reduced in surfaces with low-reflectivity regions or highroughness, like a surface affected by corrosion. An alternative techniquecalled shape from focus (SFF) takes advantage of the surface texture to recoverthe 3D surface by using a focus metric through a vertical scan. In this work,we propose a technique called SFF-WLSI, which consists of recovering the 3Dsurface of an object by applying the Tenegrad Variance (TENV) focus metric toWLSI images. Extensive simulation results show that the proposed techniqueyields accurate measurements under different surface roughness and surfacereflectivity, outperforming the conventional WLSI and the SFF techniques. Wevalidated the simulation results on two real objects with a Mirau-typemicroscope. The first was a flat lapping specimen with Ra = 0.05 {\mu}m forwhich we measured an average value of Ra = 0.055 {\mu}m and standard deviation{\sigma} = 0.008 {\mu}m. The second was a metallic sphere with corrosion, whichwe reconstructed with WLSI versus the proposed SFF-WLSI technique, producing abetter 3D reconstruction with less undefined depth values.

Robust 3D Surface Recovery by Applying a Focus Criterion in White Light Scanning Interference Microscopy