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Bachelor's Thesis
Author of thesis: Vít Novák
Acad. year: 2025/2026
Supervisor: Mgr. Jan Stopka, Ph.D.
Reviewer: Mgr. Tomáš Radlička, Ph.D.
This thesis deals with the analysis of tolerance fields in electrostatic lenses used in particle optics and subsequently with the development of a fast approximate model for predicting the influence of manufacturing and assembly imperfections on the formation of electrostatic fields. Electrostatic lenses represent an important part of electron microscopes and other systems based on the principles of electron optics. Their properties and field-forming accuracy are strongly affected by deviations from the ideal manufacturing and assembly of individual components. These imperfections lead to the formation of parasitic fields, which significantly influence the trajectories of passing particles as well as the quality of the resulting image. The work primarily focuses on the analysis of defects such as misalignment, tilt, and ellipticity of individual lens electrodes and their influence on the multipole character of the generated field. Using 3D simulations, it was verified that specific defect types produce characteristic multipole components — for example, dipole fields caused by displacement and tilt, or quadrupole fields caused by ellipticity. Furthermore, an approximately linear dependence of field perturbations on small defect magnitudes was confirmed, which was subsequently utilized in the construction of a predictive algorithm for parasitic field reconstruction. The main contribution of this thesis is the development of a program for composing tolerance fields based on multipole expansion. Although the method requires a small initial set of elementary 3D simulations for model construction, it subsequently enables rapid approximation of parasitic fields for a given configuration without the need for a large number of computationally demanding numerical simulations. In contrast to conventional full 3D simulations, whose computation may require several hours, the proposed algorithm provides results within minutes while maintaining very good accuracy, especially for dipole components that play a crucial role in electron beam formation. The thesis therefore contributes to more efficient design and optimization of electrostatic optical systems.
Electrostatic lens, electrostatic field, electron microscope, manufacturing tolerances, boundary element method, multipole expansion, tolerance field
Date of defence
17.06.2026
Result of the defence
Defended (thesis was successfully defended)
Grading
B
Process of defence
Po otázkách oponenta bylo dále diskutováno: - srovnání metody konečných a okrajových prvků z hlediska výpočetní náročnosti - použitý software využívající numerickou metodu BEM - vliv polarity napětí na čočce na fokusačních vlastnostech čočky Student na otázky odpověděl.
Language of thesis
Czech
Faculty
Fakulta strojního inženýrství
Department
Institute of Physical Engineering
Study programme
Physical Engineering and Nanotechnology (B-FIN-P)
Composition of Committee
prof. Ing. Miroslav Kolíbal, Ph.D. (předseda) prof. RNDr. Tomáš Šikola, CSc. (místopředseda) prof. RNDr. Jiří Spousta, Ph.D. (člen) prof. RNDr. Petr Dub, CSc. (člen) prof. Ing. Jan Čechal, Ph.D. (člen) prof. Mgr. Miroslav Černý, Ph.D. (člen) doc. Mgr. Vlastimil Křápek, Ph.D. (člen) doc. Ing. Stanislav Průša, Ph.D. (člen) doc. Ing. Miroslav Bartošík, Ph.D. (člen) doc. Ing. Radek Kalousek, Ph.D. (člen) doc. Ing. Jakub Zlámal, Ph.D. (člen) prof. RNDr. Radim Chmelík, Ph.D. (člen)
Supervisor’s reportMgr. Jan Stopka, Ph.D.
Grade proposed by supervisor: A
Reviewer’s reportMgr. Tomáš Radlička, Ph.D.
Grade proposed by reviewer: C
Responsibility: Mgr. et Mgr. Hana Odstrčilová