Third-order Geometrical Aberrations Research Articles

TEMGYM Advanced: Software for electron lens aberrations and parallelised electron ray tracing

Characterisation of the electron beams trajectory in an electron microscope is possible in a few select commercial software packages, but these tools and their source code are not available in a free and accessible manner. This paper introduces the free and open-source software TEMGYM Advanced, which implements ray tracing methods that calculate the path of electrons through a magnetic or electrostatic lens and allow evaluation of the first-order properties and third-order geometric aberrations. Validation of the aberration coefficient calculations is performed by implementing two independent methods – the aberration integral and differential algebra (DA) methods and by comparing the results of each. This paper also demonstrates parallelised electron ray tracing through a series of magnetic components, which enables near real-time generation of a physically accurate beam-spot including aberrations and brings closer the realisation of a digital twin of an electron microscope. TEMGYM Advanced represents a valuable resource for the electron microscopy community, providing an accessible and open source means of characterising electron lenses. This software utilises the Python programming language to complement the growing ecosystem of free and open-source software within the electron microscopy community, and to facilitate the application of machine learning to an electron microscope digital twin for instrument automation. The software is available under GNU Public License number Three (GPL 3).

TEMGYM Advanced – NanoMi lens characterisation

A complete analysis including finite element method (FEM) calculation, focal length properties, and thirdorder geometric aberrations of the open-source electrostatic lens from the NanoMi project is presented. The analysis is carried out by the software TEMGYM Advanced, a free package developed to carry out ray-tracing and lens characterisation in Python. Previously TEMGYM Advanced has shown how to analyse the aberrations of analytical lens fields; this paper expands upon this work to demonstrate how to apply a suitable fitting method to discrete lens fields obtained via FEM methods so that the aberrations of real lens designs can be calculated. Each software platform used in this paper is freely available in the community and creates a free and viable alternative to commercial lens design packages.

The aberration theory of a combined electron focusing–deflection system with a rotating deflection field following the rotation of the electrons

A new type of combined magnetic focusing–electrostatic deflection systems whose orientation of deflection field is rotated synchronously with the beam electrons is proposed. This rotation deflection field can be formed by twistification of tube wall electrode (TWE) deflectors. Formulae are derived for the first-order optical properties, third-order geometrical aberrations and first-order chromatic aberrations of this system. A program was written in FORTRAN for numerical computation. An example is given; the computation results show that compared to the conventional systems, the proposed new system has lower deflection aberration coefficients.

Outline of an ultracorrector compensating for all primary chromatic and geometrical aberrations of charged-particle lenses

A novel ultracorrector is outlined which compensates for the primary and secondary first-order chromatic aberrations and all third-order geometrical aberrations of electron optical systems with a straight axis. Owing to the imposed symmetry conditions on the fields and the paraxial fundamental rays, the corrector does not introduce aberrations with 2-fold symmetry. The chromatic aberrations are corrected by means of crossed electric magnetic quadrupoles while the third-order geometrical aberrations are eliminated by octopoles. By placing these elements at distinct positions within the corrector, it is possible to successively eliminate the third-order aberrations in such a way that each subsequent correction does not affect the aberrations corrected in the preceding correction steps.

Outline of an Ultracorrector Compensating for all Primary Chromatic and Geometrical Aberrations of Charged-Particle Lenses

A novel ultracorrector is outlined which compensates for the primary and secondary first-order chromatic aberrations and all third-order geometrical aberrations of electron optical systems with a straight axis. Owing to the imposed symmetry conditions on the fields and the paraxial fundamental rays, the corrector does not introduce aberrations with 2-fold symmetry. The chromatic aberrations are corrected by means of crossed electric magnetic quadrupoles while the third-order geometrical aberrations are eliminated by octopoles. By placing these elements at distinct positions within the corrector, it is possible to successively eliminate the third-order aberrations in such a way that each subsequent correction does not affect the aberrations corrected in the preceding correction steps.

Transverse second- and third-order geometrical aberrations of optical systems with pseudoaxion-type aspheric surfaces

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text R. E. Il'inski , "Transverse second- and third-order geometrical aberrations of optical systems with pseudoaxion-type aspheric surfaces," J. Opt. Technol. 66, 658- (1999) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

A method for evaluating optical properties of electrostatic systems

Equations for evaluating paraxial properties, first-order chromatic, and third-order geometrical aberrations of electrostatic optics systems composed of round lenses and cosine-distributed deflectors are derived. Some comments on electrode design are made.

Third-Order Aberrations of `Doubly Symmetric' Systems

The third-order geometric aberrations of non-rotationally symmetric imaging systems are classified, and their characteristics given diagrammatically for the case of a circular exit aperture. The systems are `doubly symmetric', that is, they retain symmetry about each of two mutually perpendicular planes. Eleven new aberrations occur, three of which are third-order distortions, three give curved image surfaces, three are analogous to coma, and two to spherical aberration.