Optimizing the phase shift and the cut-on periodicity of phase plates for TEM

Images acquired with a phase plate often exhibit fringing and/or contrast reversal artifacts. The two basic parameters controlling the performance of the phase plate are phase shift and cut-on periodicity. We investigate theoretically and numerically the effect of these parameters on the image quality. The analysis covers not just the typical negative phase shift phase plates but also positive phase shift ones. The theoretical study derives formulas for calculating the optimal phase plate phase shift and for the maximum achievable contrast with a given specimen. Two figures of merit - fidelity and contrast - were defined and used to quantify the numerical results. Larger cut-on periodicities provide better performance with higher contrast and less artifacts in the images. Both, the theoretical results and the simulations indicate that positive phase shift phase plates generate higher contrast with better linearity and are free from contrast reversal artifacts. However, with such phase plates the amplitude and the phase contrast components are opposed to each other and the simulations show stronger fringing outside of objects. Based on these results it is difficult to predict if and to what extent the positive phase shift phase plates will be advantageous in practice. Two methods for reduction of fringing artifacts were compared-tapered phase plate and low-frequency amplification software filter. Overall the software solution produced better results and is much easier to implement than modifying the hardware of the phase plate to realize the taper.