  White light scanning interference (WLSI) microscopes provide an accurate
surface topography of engineered surfaces. However, the measurement accuracy is
substantially reduced in surfaces with low-reflectivity regions or high
roughness, like a surface affected by corrosion. An alternative technique
called shape from focus (SFF) takes advantage of the surface texture to recover
the 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 3D
surface of an object by applying the Tenegrad Variance (TENV) focus metric to
WLSI images. Extensive simulation results show that the proposed technique
yields accurate measurements under different surface roughness and surface
reflectivity, outperforming the conventional WLSI and the SFF techniques. We
validated the simulation results on two real objects with a Mirau-type
microscope. The first was a flat lapping specimen with Ra = 0.05 {\mu}m for
which 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, which
we reconstructed with WLSI versus the proposed SFF-WLSI technique, producing a
better 3D reconstruction with less undefined depth values.
