Numerical calculation of electron optical aberrations
Related Experiment Video
Updated: Sep 28, 2026

Single-Digit Nanometer Electron-Beam Lithography with an Aberration-Corrected Scanning Transmission Electron Microscope
Published on: September 14, 2018
1Institut für Angewandte Physik der Universität Tübingen, Auf der Morgenstelle 12, 72076 Tübingen, Germany.
Abstract:
A numerical method for the accurate calculation of aberration figures in systems with a straight optical axis is concisely outlined. The method involves computing a fundamental set of paraxial rays, and then directly ray-tracing a judiciously chosen set of deviations from these paraxial rays, that enable the direct plotting of aberration figures. This method avoids using complicated aberration integrals, and can directly handle the effects of high-order aberrations and asymmetry errors. A fast general predictor-corrector method for the numerical ray-tracing is also presented.
Related Concept Videos
Numerical Calculations
The solution to a problem is obtained using different methods. While manually solving algebraic symbols is one of the most common methods, the graphical method is often preferred. Computers...
Influence of Earth's Curvature and Atmospheric Refraction on Leveling
Imaging Biological Samples with Optical Microscopy
In optical microscopy, the specimen to be viewed is placed on a glass slide and clipped on the stage...

