Axial imaging necessitates loss of lateral shift invariance

2001 ◽  
Author(s):  
George Barbastathis ◽  
Andy Stein ◽  
Arnab Sinha
Keyword(s):  
Lateral Shift ◽  
Shift Invariance

Axial imaging necessitates loss of lateral shift invariance: proof with the Wigner analysis

2009 ◽  
Vol 48 (30) ◽  
pp. 5881 ◽  
Author(s):  
Se Baek Oh ◽  
George Barbastathis
Keyword(s):  
Lateral Shift ◽  
Shift Invariance

Axial imaging necessitates loss of lateral shift invariance

2002 ◽  
Vol 41 (29) ◽  
pp. 6055 ◽  
Author(s):  
Andy Stein ◽  
George Barbastathis
Keyword(s):  
Lateral Shift ◽  
Shift Invariance

scholarly journals Preliminaryin vivoatherosclerotic carotid plaque characterization using the accumulated axial strain and relative lateral shift strain indices

2008 ◽  
Vol 53 (22) ◽  
pp. 6377-6394 ◽  
Author(s):  
Hairong Shi ◽  
Carol C Mitchell ◽  
Matthew McCormick ◽  
Mark A Kliewer ◽  
Robert J Dempsey ◽  
...  
Keyword(s):  
Carotid Plaque ◽  
Axial Strain ◽  
Lateral Shift ◽  
Plaque Characterization

scholarly journals Unbounded Wiener–Hopf Operators and Isomorphic Singular Integral Operators

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Domenico P. L. Castrigiano
Keyword(s):  
Singular Integral ◽  
Polar Decomposition ◽  
Integral Operators ◽  
Canonical Representation ◽  
Friedrichs Extension ◽  
Finite Dimensional ◽  
Transformation Type ◽  
Rational Symbols ◽  
Shift Invariance ◽  
Densely Defined

AbstractSome basics of a theory of unbounded Wiener–Hopf operators (WH) are developed. The alternative is shown that the domain of a WH is either zero or dense. The symbols for non-trivial WH are determined explicitly by an integrability property. WH are characterized by shift invariance. We study in detail WH with rational symbols showing that they are densely defined, closed and have finite dimensional kernels and deficiency spaces. The latter spaces as well as the domains, ranges, spectral and Fredholm points are explicitly determined. Another topic concerns semibounded WH. There is a canonical representation of a semibounded WH using a product of a closable operator and its adjoint. The Friedrichs extension is obtained replacing the operator by its closure. The polar decomposition gives rise to a Hilbert space isomorphism relating a semibounded WH to a singular integral operator of Hilbert transformation type. This remarkable relationship, which allows to transfer results and methods reciprocally, is new also in the thoroughly studied case of bounded WH.

Splitting in lateral shift induced by strong coupling in Kretschmann configuration involving molecular J-aggregates

2019 ◽  
Vol 33 (30) ◽  
pp. 1950370
Author(s):  
Kunwei Pang ◽  
Haihong Li ◽  
Gang Song ◽  
Pengfei Zhang
Keyword(s):  
Strong Coupling ◽  
Metal Film ◽  
Previous Experiment ◽  
Lateral Shift ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Incident Wavelength ◽  
Rabi Splitting ◽  
Kretschmann Configuration ◽  
J Aggregates

Molecular J-aggregates are widely used as emitters to achieve the quantum effects, such as the strong coupling phenomenon. We investigate the lateral shift splitting/Goos–Hänchen (GH) shift splitting induced by strong coupling in Kretschmann configuration involving molecular J-aggregates by using classical methods. The optical response of molecular J-aggregates is modeled by a single Lorentzian oscillator, and Fresnel equations and the stationary phase method are employed to solve our proposed structure. Our results show that the lateral shift versus the incident wavelength shows Rabi splitting-like line shape and the reflection spectrum exhibits the strong coupling phenomenon. Based on the results of the previous experiment work, we well explain the relation between Rabi splitting and the thickness of the metal film and provide a new method to choose the parameters of the structure for experiment.

FINITE IMPULSE RESPONSE DOUBLE DENSITY FILTER BANKS AND FRAMELETS

2013 ◽  
Vol 11 (01) ◽  
pp. 1350010
Author(s):  
ASHOKA JAYAWARDENA ◽  
PAUL KWAN
Keyword(s):  
Wavelet Transform ◽  
Impulse Response ◽  
Filter Bank ◽  
Filter Banks ◽  
Finite Impulse Response ◽  
Wavelet Filters ◽  
Density Filter ◽  
Shift Invariance ◽  
Factorization Methods ◽  
Invariant Properties

In this paper, we focus on the design of oversampled filter banks and the resulting framelets. The framelets obtained exhibit improved shift invariant properties over decimated wavelet transform. Shift invariance has applications in many areas, particularly denoising, coding and compression. Our contribution here is on filter bank completion. In addition, we propose novel factorization methods to design wavelet filters from given scaling filters.

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