Efficient methods for wave propagation in electron microscopy

TL;DR

This paper introduces two novel numerical methods, SASM and NLASM, that significantly improve the efficiency of wave-optical simulations in electron microscopy by reducing sampling requirements and computational costs.

Contribution

The paper presents two new approaches, SASM and NLASM, which enhance wave propagation simulation efficiency in electron microscopy by reducing sampling constraints and computational demands.

Findings

SASM reduces memory and computation by scaling the optical system.

NLASM suppresses lensing effects for efficient propagation.

Combined methods enable complex system simulations previously infeasible.

Abstract

Accurate wave-optical simulation in electron microscopy is severely constrained by the extreme sampling requirements imposed by short wavelengths and relatively large convergence angles. Conventional implementations of the angular spectrum method (ASM) rapidly become computationally intractable, often exceeding realistic memory and time limits. We present two numerical approaches -- the scaling angular spectrum method (SASM) and the no-lensing angular spectrum method (NLASM) -- that systematically reduce the sampling requirements while retaining the essential physics of wave propagation. SASM replaces the original optical system with a scaled equivalent in which lens-induced beam convergence or divergence is reduced, lowering memory usage and computational cost by approximately the square of the scaling factor. NLASM suppresses lensing effects altogether, enabling highly efficient propagation away from focal planes. Benchmarking against the Bluestein (chirp-z) transform reveals that the three methods are complementary and together enable wave-optical simulations of complex electron-optical systems previously considered infeasible. These results establish practical pathways toward routine wave-based modeling in electron microscope design.