Regularization techniques for 3D surface reconstruction from four quadrant backscattered electron detector images

In scanning electron microscopy (SEM), a four quadrants backscattered electron detector (FQBSD) provides signals that can be combined to obtain a tridimensional reconstruction of the surface. The main challenge of the reconstruction operation consists of integrating the gradient field obtained as the normalized signal difference from each pair of opposite quadrants. Owing to the presence of electronic noise that eventually turns into image noise, a least square integration approach has been widely adopted for surface reconstruction. In the present work, we demonstrate the possibility of adopting regularization techniques (Tichonov's and Dirichlet's) to the surface reconstruction from FQBSD images to reduce the distortions due to sensitivity variations amongst the detector quadrants or an imprecise alignment of the FQBSD with the gun axis. This allows for a substantial improvement in the 3D surface reconstruction quality in terms of resolution and reduction of artifacts. These procedures have been experimentally validated on AISI 316L stainless steel polished surfaces with hardness indentation and on laser-patterned aluminum and silicon samples showing promising results.