The Talbot Effect as a Sequence of Quadratic Phase Corrections of the Object Fourier Transform

1983 ◽  
Vol 30 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Romuald Jóźwicki
Keyword(s):  
Fourier Transform ◽  
Talbot Effect ◽  
Quadratic Phase ◽  
Phase Corrections

scholarly journals Dynamically Focused Gaussian Beams for Seismic Imaging

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Robert L. Nowack
Keyword(s):  
Seismic Imaging ◽  
Initial Study ◽  
Gaussian Beams ◽  
Subsurface Scattering ◽  
Local Data ◽  
Quadratic Phase ◽  
Phase Corrections ◽  
Speed Up ◽  
Data Windows ◽  
Slant Stacking

An initial study is performed in which dynamically focused Gaussian beams are investigated for seismic imaging. Focused Gaussian beams away from the source and receiver plane allow the narrowest and planar portions of the beams to occur at the depth of a specific target structure. To match the seismic data, quadratic phase corrections are required for the local slant stacks of the surface data. To provide additional control of the imaging process, dynamic focusing is investigated where all subsurface points are specified to have the same planar beam fronts. This gives the effect of using nondiffracting beams, but actually results from the use of multiple focusing depths for each Gaussian beam. However, now different local slant stacks must be performed depending on the position of the subsurface scattering point. To speed up the process, slant stacking of the local data windows is varied to match the focusing depths along individual beams when tracked back into the medium. The approach is tested with a simple model of 5-point scatterers which are then imaged with the data, and then to the imaging of a single dynamically focused beam for one shot gather computed from the Sigsbee2A model.

Improvement of 3D surface reconstruction using fringe projection by Talbot effect and extended Fourier transform

2017 ◽  
Author(s):  
Mauricio Ortiz Gutiérrez ◽  
Rafael González Campos ◽  
Marco Antonio Salgado Verduzco ◽  
Mario Pérez Cortés ◽  
Arturo Olivares Pérez ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Surface Reconstruction ◽  
Fringe Projection ◽  
Talbot Effect ◽  
3D Surface Reconstruction ◽  
3D Surface

Producing absorption mode Fourier transform ion cyclotron resonance mass spectra with non-quadratic phase correction functions

2015 ◽  
Vol 29 (11) ◽  
pp. 1087-1093 ◽  
Author(s):  
David P. A. Kilgour ◽  
Konstantin O. Nagornov ◽  
Anton N. Kozhinov ◽  
Konstantin O. Zhurov ◽  
Yury O. Tsybin
Keyword(s):  
Fourier Transform ◽  
Cyclotron Resonance ◽  
Mass Spectra ◽  
Phase Correction ◽  
Ion Cyclotron Resonance ◽  
Quadratic Phase ◽  
Ion Cyclotron ◽  
Absorption Mode

scholarly journals A study of the gravitational wave pulsar signal with orbital and spindown effects

2006 ◽  
Vol 84 (6-7) ◽  
pp. 607-613
Author(s):  
S R Valluri ◽  
K M Rao ◽  
P Wiegert ◽  
F A Chishtie
Keyword(s):  
Fourier Transform ◽  
Gravitational Wave ◽  
Orbital Motion ◽  
Special Functions ◽  
The Moon ◽  
The Earth ◽  
Source Signal ◽  
Phase Corrections ◽  
The Fourier Transform ◽  
Monochromatic Source

In this work, we present an analytic and a preliminary numerical analysis of the gravitational wave signal from a pulsar that includes simple spindown effects. We estimate the phase corrections to a monochromatic source signal due to rotational and elliptical orbital motion of the Earth, and perturbations due to Jupiter and the Moon. We briefly discuss the Fourier transform of such a signal, expressed in terms of well-known special functions, and its applications. PACKS Nos.: 04.30.-w

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