A recursive resolution-enhancement using multiframe SRR based on meridian filter with Meridian-Tikhonov regularization

2011 ◽  
Author(s):  
Vorapoj Patanavijit
Keyword(s):  
Tikhonov Regularization ◽  
Resolution Enhancement

Off-axis electron holography applied to the study of interfaces

1992 ◽  
Vol 50 (1) ◽  
pp. 244-245
Author(s):  
J.K. Weiss ◽  
M. Gajdardziska-Josifovska ◽  
M. R. McCartney ◽  
David J. Smith
Keyword(s):  
Electric Fields ◽  
Resolution Enhancement ◽  
Interfacial Structure ◽  
Atomic Scale ◽  
Bulk Property ◽  
Electron Holography ◽  
Specimen Thickness ◽  
Composition And Structure ◽  
Chemical Segregation ◽  
Diffraction Effects

Interfacial structure is a controlling parameter in the behavior of many materials. Electron microscopy methods are widely used for characterizing such features as interface abruptness and chemical segregation at interfaces. The problem for high resolution microscopy is to establish optimum imaging conditions for extracting this information. We have found that off-axis electron holography can provide useful information for the study of interfaces that is not easily obtained by other techniques.Electron holography permits the recovery of both the amplitude and the phase of the image wave. Recent studies have applied the information obtained from electron holograms to characterizing magnetic and electric fields in materials and also to atomic-scale resolution enhancement. The phase of an electron wave passing through a specimen is shifted by an amount which is proportional to the product of the specimen thickness and the projected electrostatic potential (ignoring magnetic fields and diffraction effects). If atomic-scale variations are ignored, the potential in the specimen is described by the mean inner potential, a bulk property sensitive to both composition and structure. For the study of interfaces, the specimen thickness is assumed to be approximately constant across the interface, so that the phase of the image wave will give a picture of mean inner potential across the interface.

scholarly journals A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Solution Process ◽  
Tikhonov Regularization Method ◽  
Hermite Expansion ◽  
The Cauchy Problem ◽  
Ill Posed

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.

Sign in / Sign up

Export Citation Format

Share Document