When to use the projection assumption and the weak-phase object approximation in phase contrast cryo-EM

The projection assumption (PA) and the weak-phase object approximation (WPOA) are commonly used to model image formation in cryo-electron microscopy. For simulating the next step in resolution improvement we show that it is important to revisit these two approximations as well as their limitations. Here we start off by inspecting both approximations separately to derive their respective conditions of applicability. The thick-phase grating approximation (TPGA) imposes less strict conditions on the interaction potential than PA or WPOA and gives comparable exit waves as a multislice calculation. We suggest the ranges of applicability for four models (PA, PA+WPOA, WPOA, and TPGA) given different interaction potentials using exit wave simulations. The conditions of applicability for the models are based on two measures, a worst-case (safest) and an average criterion. This allows us to present a practical guideline for when to use each image formation model depending on the spatial frequency, thickness and strength of the interaction potential of a macromolecular complex.