ALPHABETA: a dedicated open-source tool for calculating TEM stage tilt angles.

This work describes the concepts, the mathematical framework and the implementation of the open source ALPHABETA software, a dedicated tool for calculating α and β tilt angles on any TEM double tilt stage. ALPHABETA provides an intuitive user interface to calibrate the orientation of the region of interest and to subsequently calculate the angle tilts to reach a zone axis, to perform a rotation around a given reflection, or to set up a 2-beam or weak beam condition. The orientation of the sample on the stage and the tilt range reachable domain can be visualised in a stereographic projection plot. The accuracy of the method to reach a set of zone axis was evaluated and some case studies are presented. The tool significantly reduces time for tilting work as major tilts can be performed in image mode and reachable zones are beforehand indicated in the software. Besides facilitating the tilting to different zone axes, the software can be used for miscellaneous applications such as making dark field tilt series without specialised hardware. LAY DESCRIPTION: ALPHABETA is an open-source program we developed to make the life of transmission electron microscope users easier. Work on the transmission electron microscope, or TEM, is done by correctly orienting a thin sample with respect to the electron beam. The orientation determines how images made from the sample will look. Studying a sample may require the user to orient it in multiple different ways. This orienting must be done by adjusting 'tilt' parameters of the stage on which the sample sits in the microscope. Correctly adjusting these tilt parameters to obtain the correct orientation is a job that requires practice and experience. Our program should facilitate this step of working with the microscope, because it calculates the tilt parameters to achieve a certain orientation. This paper describes the mathematics behind the software and provides some examples from the work of the authors. We also evaluate how accurate the calculation is. The examples included are orienting to different zone axes, which are special crystal orientations, and making a series of images that provide a 3D effect when played after each other of particles that can only be visualised in particular orientations.