Journals > > Topics > Feature issue on Imaging Electron Optics
Feature issue on Imaging Electron Optics|4 Article(s)
Imaging Electron Optics of a Combined Electromagnetic Concentric Spherical System. Part D: Asymptotic Solutions of Paraxial Equation
Zhou Liwei
The asymptotic solutions of the paraxial equation for a combined electromagnetic concentric spherical system have been explored. Expressions of each kind of coefficients of two special solutions given by the asymptotic method for solving the paraxial equation have been deduced. By verifying the exact solution of two special solutions of the combined electromagnetic concentric spherical system, this paper proves that the approach based on asymptotic solutions given by Monastyrski ［Journal of Technical Physics, 1978, 48(6): 1117-1122］to solve the two special solutions of paraxial equation in electron optics is basically correct and feasible, and only a few aspects need to be improved. The asymptotic solutions of the paraxial equation for a combined electromagnetic concentric spherical system have been explored. Expressions of each kind of coefficients of two special solutions given by the asymptotic method for solving the paraxial equation have been deduced. By verifying the exact solution of two special solutions of the combined electromagnetic concentric spherical system, this paper proves that the approach based on asymptotic solutions given by Monastyrski ［Journal of Technical Physics, 1978, 48(6): 1117-1122］to solve the two special solutions of paraxial equation in electron optics is basically correct and feasible, and only a few aspects need to be improved.
Acta Optica Sinica
- Publication Date: Jan. 01, 2019
- Vol. 39, Issue 4, 411004 (2019)
Imaging Electron Optics of a Combined Electromagnetic Concentric Spherical System. Part C: Approximate Solutions of Paraxial Equation
Zhou Liwei
The approximate expressions of special solutions of the paraxial equation and its paraxial lateral aberrations have been explored by an ideal model of a combined electromagnetic concentric spherical system in this paper. The approximate expressions of two special solutions of the paraxial equation in a combined electromagnetic concentric spherical system have been derived, and on this basis, some special types of paraxial lateral aberrations such as paraxial spherical-chromatic aberration, paraxial magnification chromatic aberration, and paraxial anisotropic chromatic aberration have been deduced. The results show that the paraxial lateral aberration deduced from the approximation of two special solutions is exactly the same as through the exact solution, which proves the feasibility of the approximation to solve the paraxial lateral aberration. The approximate expressions of special solutions of the paraxial equation and its paraxial lateral aberrations have been explored by an ideal model of a combined electromagnetic concentric spherical system in this paper. The approximate expressions of two special solutions of the paraxial equation in a combined electromagnetic concentric spherical system have been derived, and on this basis, some special types of paraxial lateral aberrations such as paraxial spherical-chromatic aberration, paraxial magnification chromatic aberration, and paraxial anisotropic chromatic aberration have been deduced. The results show that the paraxial lateral aberration deduced from the approximation of two special solutions is exactly the same as through the exact solution, which proves the feasibility of the approximation to solve the paraxial lateral aberration.
Acta Optica Sinica
- Publication Date: Jan. 01, 2019
- Vol. 39, Issue 4, 411003 (2019)
Imaging Electron Optics of a Combined Electromagnetic Concentric Spherical System. Part B: Paraxial Aberrations
Zhou Liwei
Starting from the two special solutions of the paraxial equation of the combined electromagnetic concentric spherical system, the paraxial longitudinal and lateral aberrations of the combined electromagnetic concentric spherical system have been explored by expanding the representation of the image rotation angle at the ideal imaging position. The main contribution of this paper is to obtain the analytical expression of the two special solutions of paraxial equation at ideal image plane, and it has proved that the paraxial spherical-chromatic aberration of second order that determines the limited spatial resolution of imaging can still be characterized in terms of the Recknagel-Artimovich formula. Expressions of the paraxial lateral aberration composed of paraxial spherical-chromatic aberration, paraxial magnification chromatic aberration, and paraxial anisotropic chromatic aberration have been deduced. Starting from the two special solutions of the paraxial equation of the combined electromagnetic concentric spherical system, the paraxial longitudinal and lateral aberrations of the combined electromagnetic concentric spherical system have been explored by expanding the representation of the image rotation angle at the ideal imaging position. The main contribution of this paper is to obtain the analytical expression of the two special solutions of paraxial equation at ideal image plane, and it has proved that the paraxial spherical-chromatic aberration of second order that determines the limited spatial resolution of imaging can still be characterized in terms of the Recknagel-Artimovich formula. Expressions of the paraxial lateral aberration composed of paraxial spherical-chromatic aberration, paraxial magnification chromatic aberration, and paraxial anisotropic chromatic aberration have been deduced.
Acta Optica Sinica
- Publication Date: Jan. 01, 2019
- Vol. 39, Issue 4, 411002 (2019)
Imaging Electron Optics of a Combined Electromagnetic Concentric Spherical System. Part A: Paraxial Optics
Zhou Liwei
The ray solutions of paraxial equation for imaging electron optics have been explored by an ideal model of combined electromagnetic concentric spherical system in the present paper. The exact analytical expressions of rotational angle as well as two special solutions of paraxial equation in this system have been firstly derived, and the paraxial imaging properties have also been investigated. The results have been generalized to the bi-electrode electrostatic concentric spherical system, the homogeneous and parallel combined electromagnetic system, and the electrostatic proximity system. The ray solutions of paraxial equation for imaging electron optics have been explored by an ideal model of combined electromagnetic concentric spherical system in the present paper. The exact analytical expressions of rotational angle as well as two special solutions of paraxial equation in this system have been firstly derived, and the paraxial imaging properties have also been investigated. The results have been generalized to the bi-electrode electrostatic concentric spherical system, the homogeneous and parallel combined electromagnetic system, and the electrostatic proximity system.
Acta Optica Sinica
- Publication Date: Jan. 01, 2019
- Vol. 39, Issue 4, 411001 (2019)
Topics
© Copyright 2018-2021 | Chinese Laser Press. All Rights Reserved 沪ICP备15018463号-20