The Gouy phase shift reinterpreted via the geometric Fourier transform

2018 ◽  
Author(s):  
Olga Baladron-Zorita ◽  
Zongzhao Wang ◽  
Christian Hellmann ◽  
Frank Wyrowski
Keyword(s):  
Fourier Transform ◽  
Phase Shift ◽  
Gouy Phase

Fourier transform infrared phase shift cavity ring down spectrometer

2013 ◽  
Author(s):  
Elizabeth Schundler ◽  
David J. Mansur ◽  
Robert Vaillancourt ◽  
Ryan Benedict-Gill ◽  
Scott P. Newbry ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Phase Shift ◽  
Fourier Transform Infrared ◽  
Cavity Ring Down

Gouy phase shift of lens-generated quasi-nondiffractive beam

2017 ◽  
Vol 396 ◽  
pp. 78-82
Author(s):  
Chunjie Zhai ◽  
Zhaolou Cao
Keyword(s):  
Phase Shift ◽  
Gouy Phase

The Gouy phase shift of the highly focused radially polarized beam

2007 ◽  
Vol 371 (3) ◽  
pp. 259-261 ◽  
Author(s):  
Hao Chen ◽  
Qiwen Zhan ◽  
Yanli Zhang ◽  
Yong-Ping Li
Keyword(s):  
Phase Shift ◽  
Radially Polarized Beam ◽  
Polarized Beam ◽  
Gouy Phase ◽  
Radially Polarized

The Hartley transform in seismic imaging

Geophysics ◽  
2001 ◽  
Vol 66 (4) ◽  
pp. 1251-1257 ◽  
Author(s):  
Henning Kühl ◽  
Maurico D. Sacchi ◽  
Jürgen Fertig
Keyword(s):  
Fourier Transform ◽  
Phase Shift ◽  
Shift Operator ◽  
Three Dimensions ◽  
Lateral Velocity ◽  
Data Set ◽  
Prestack Migration ◽  
Hartley Transform ◽  
Alternative Means ◽  
The Fourier Transform

Phase‐shift migration techniques that attempt to account for lateral velocity variations make substantial use of the fast Fourier transform (FFT). Generally, the Hermitian symmetry of the complex‐valued Fourier transform causes computational redundancies in terms of the number of operations and memory requirements. In practice a combination of the FFT with the well‐known real‐to‐complex Fourier transform is often used to avoid such complications. As an alternative means to the Fourier transform, we introduce the inherently real‐valued, non‐symmetric Hartley transform into phase‐shift migration techniques. By this we automatically avoid the Hermitian symmetry resulting in an optimized algorithm that is comparable in efficiency to algorithms based on the real‐to‐complex FFT. We derive the phase‐shift operator in the Hartley domain for migration in two and three dimensions and formulate phase shift plus interpolation, split‐step migration, and split‐step double‐square‐root prestack migration in terms of the Hartley transform as examples. We test the Hartley phase‐shift operator for poststack and prestack migration using the SEG/EAGE salt model and the Marmousi data set, respectively.

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