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Determination of analytical expansion from numerical field data
Tomás Radlicka1, Bohumila Lencová
1Institute of Scientific Instruments AS CR, Královopolská 147, 61264 Brno, Czech Republic. radlicka@isibrno.cz
Ultramicroscopy
|May 18, 2010
Summary
We present a new Green's theorem method for calculating axial fields in electrostatic lenses. This approach aids in determining aberration coefficients by providing precise high-order field derivatives.
Area of Science:
- Physics
- Applied Mathematics
Background:
- Accurate calculation of electron lens fields is crucial for understanding electron optics.
- High-order axial field derivatives are essential for computing aberration coefficients.
Purpose of the Study:
- To introduce a novel analytical method for calculating the field expansion near the axis of electrostatic lenses.
- To demonstrate the method's efficacy by comparing it with existing techniques in electron optics.
Main Methods:
- Application of Green's theorem to derive analytical field expansions.
- Utilizing finite-element method for computing the electrostatic field of a round unipotential lens.
- Comparison with Hermite polynomials and wavelet transformation methods.
Main Results:
- The Green's theorem approach provides accurate analytical expansions of the axial field.
- The method's results align well with established techniques, validating its applicability.
- Demonstrated capability to yield high-order axial field derivatives necessary for aberration calculations.
Conclusions:
- The proposed Green's theorem method offers a robust alternative for calculating axial fields in electron lenses.
- This technique is particularly valuable for precise computation of aberration coefficients.
- The method enhances the toolkit for advanced electron optics design and analysis.
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