On central focusing for contrast optimization in direct electron ptychography of thick samples

Ptychography provides high dose efficiency images that can reveal light elements next to heavy atoms. However, despite ptychography having an otherwise single signed contrast transfer function, contrast reversals can occur when the projected potential becomes strong for both direct and iterative inversion ptychography methods. It has recently been shown that these reversals can often be counteracted in direct ptychography methods by adapting the focus. Here we provide an explanation of why the best contrast is often found with the probe focused to the middle of the sample. The phase contribution due to defocus at each sample slice above and below the central plane in this configuration effectively cancels out, which can prevent contrast reversals when dynamical scattering effects are not overly strong. In addition we show that the convergence angle can be an important consideration for removal of contrast reversals in relatively thin samples.