Applications of the second-order edge element method versus zero order in optical diffusion tomography

2022 ◽  
Vol 1 (1) ◽  
pp. 109-112
Author(s):  
Tomasz RYMARCZYK
Keyword(s):  
Zero Order ◽  
Second Order ◽  
Edge Element ◽  
Optical Diffusion Tomography ◽  
Element Method

Adaptive mesh generation for edge-element finite element method

2001 ◽  
Vol 89 (11) ◽  
pp. 6713-6715 ◽  
Author(s):  
Hajime Tsuboi ◽  
Szabolcs Gyimothy
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mesh Generation ◽  
Adaptive Mesh ◽  
Edge Element ◽  
Adaptive Mesh Generation ◽  
Element Method

The imaging properties of electron beams in arbitrary static electromagnetic fields

1952 ◽  
Vol 245 (894) ◽  
pp. 155-187 ◽  
Keyword(s):  
Variational Equation ◽  
Chromatic Aberration ◽  
Relativistic Correction ◽  
Zero Order ◽  
Second Order ◽  
Optical Systems ◽  
Characteristic Functions ◽  
Tensor Calculus ◽  
Paraxial Ray ◽  
Imaging Properties

Electron-optical systems with curved axes—such as mass spectrographs and certain beta-ray spectrometers—have long been in practical use, but there has been available no complete theory of the aberrations of such systems. It is the object of the present paper to construct such a theory and to demonstrate, by an example, its application to practical problems. An appropriate co-ordinate system is set up by means of a ray-axis together with its normal and binormal. The electric and magnetic fields are then investigated with the help of tensor calculus; the variational principle of electron optics is also put into tensor form. The integrand of the variational equation may be separated into a series of polynomials, one of which determines the paraxial imaging properties of the system and the rest of which determine the aberrations. The condition is established for which, upon an appropriate transformation, either of the paraxial ray equations contains only one off-axis co-ordinate. Subsequent investigations are restricted to systems, which are termed ‘orthogonal’, for which this condition is satisfied. It is shown that, in a certain sense, no orthogonal electron-optical system can be wholly divergent. The second-order aberration and the zero-order and paraxial chromatic aberrations are then investigated by the method of perturbation characteristic functions. All formulae are given in their relativistic forms but their non-relativistic forms are indicated; formulae are therefore given for the calculation of the zero-order and paraxial relativistic correction. It is indicated to what extent one forfeits control over the second-order aberration—and hence over the paraxial chromatic aberration also—by specifying that the paraxial behaviour of rays should be Gaussian. As an example, the imaging properties of a helical beam moving in the field of a pair of coaxial cylindrical electrodes are calculated. There is also an appendix which gives formulae for the effect upon aberrations of a change in the aperture position.

scholarly journals Analysis of diffraction gratings by using an edge element method

2005 ◽  
Vol 22 (2) ◽  
pp. 278 ◽  
Author(s):  
Kokou Dossou ◽  
Muthukumaran Packirisamy ◽  
Marie Fontaine
Keyword(s):  
Diffraction Gratings ◽  
Edge Element ◽  
Element Method
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