Gradient-based sharpness function

Most autofocus methods are based on a sharpness function which delivers a real-valued estimate of an image quality. In this paper we study an L2-norm gradient-based sharpness function for two-dimensional images (2-D setting). Within this setting we are able to take into account the asymmetry of the optical device objective lens (astigmatism aberration). This study provides a useful extension of the analytical observations for one-dimensional images (1-D setting) that have been done before. The gradient-based autofocus method is implemented and demonstrated for the real-world application running in the FEI scanning transmission electron microscope prototype.