Ince-Gaussian two-dimensional fractional Fourier transform for optical wave propagation

2005 ◽  
Author(s):  
Miguel Bandres ◽  
Julio C. Gutierrez-Vega
Keyword(s):  
Wave Propagation ◽  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Two Dimensional ◽  
Optical Wave ◽  
Optical Wave Propagation

scholarly journals The Solvability of a Class of Convolution Equations Associated with 2D FRFT

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1928
Author(s):  
Zhen-Wei Li ◽  
Wen-Biao Gao ◽  
Bing-Zhao Li
Keyword(s):  
Fourier Transform ◽  
Convolution Operator ◽  
Fractional Fourier Transform ◽  
Hankel Transform ◽  
Polar Coordinates ◽  
Two Dimensional ◽  
Spatial Shift ◽  
Fractional Hankel Transform ◽  
The Relationship ◽  
Convolution Equations

In this paper, the solvability of a class of convolution equations is discussed by using two-dimensional (2D) fractional Fourier transform (FRFT) in polar coordinates. Firstly, we generalize the 2D FRFT to the polar coordinates setting. The relationship between 2D FRFT and fractional Hankel transform (FRHT) is derived. Secondly, the spatial shift and multiplication theorems for 2D FRFT are proposed by using this relationship. Thirdly, in order to analyze the solvability of the convolution equations, a novel convolution operator for 2D FRFT is proposed, and the corresponding convolution theorem is investigated. Finally, based on the proposed theorems, the solvability of the convolution equations is studied.

Visualization of Optical Wave Propagation in Femtosecond Photoemission Electron Microscopy

2013 ◽  
Vol 19 (S2) ◽  
pp. 306-307 ◽  
Author(s):  
R. Koenenkamp ◽  
R.C. Word ◽  
J.P.S. Fitzgerald
Keyword(s):  
Electron Microscopy ◽  
Wave Propagation ◽  
Optical Wave ◽  
Photoemission Electron Microscopy ◽  
Optical Wave Propagation ◽  
Photoemission Electron

Extended abstract of a paper presented at Microscopy and Microanalysis 2013 in Indianapolis, Indiana, USA, August 4 – August 8, 2013.

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