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The Fractional Fourier Transform: with Applications in Optics and Signal Processing
TLDR
The fractional Fourier transform (FFT) as discussed by the authors has been used in a variety of applications, such as matching filtering, detection, and pattern recognition, as well as signal recovery.Abstract:
Preface. Acknowledgments. Introduction. Signals, Systems, and Transformations. Wigner Distributions and Linear Canonical Transforms. The Fractional Fourier Transform. Time-Order and Space-Order Representations. The Discrete Fractional Fourier Transform. Optical Signals and Systems. Phase-Space Optics. The Fractional Fourier Transform in Optics. Applications of the Fractional Fourier Transform to Filtering, Estimation, and Signal Recovery. Applications of the Fractional Fourier Transform to Matched Filtering, Detection, and Pattern Recognition. Bibliography on the Fractional Fourier Transform. Other Cited Works. Credits. Index.read more
Citations
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Journal ArticleDOI
Fractional Fourier transform of off-axial elliptical cosh-Gaussian beams
Xinyue Du,Daomu Zhao +1 more
TL;DR: In this paper, the analytical expression for an off-axial elliptical cosh-Gaussian beam passing through a FRFT system is derived in terms of tensor method.
Journal ArticleDOI
General formulation of digital in-line holography from correlation with a chirplet function
TL;DR: In this article, a mathematical model that describes the recording-reconstruction process as a linear shift-invariant system with a pseudo-point spread function even when the images are out of the optimal plane in the sense of signal processing is proposed.
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The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy.
TL;DR: The fractional Fourier transform is introduced as a tool for numerical simulations of X-ray wavefront propagation and the imaging resolution of a CRL-based imaging system is estimated, and the FrFT approach is shown to be significantly more precise than comparable approaches using geometrical optics.
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Propagation characteristics of the kurtosis parameters of flat-topped beams passing through fractional Fourier transformation systems with a spherically aberrated lens
TL;DR: In this article, the propagation characteristics of the kurtosis parameters of flat-topped beams passing through fractional Fourier transformation systems with spherically aberrated lenses are studied in detail.
Journal ArticleDOI
Digital in-line holography in a droplet with cavitation air bubbles
Sébastien Coëtmellec,Darawan Pejchang,D. Allano,Gérard Gréhan,Denis Lebrun,M. Brunel,Augustus J. E. M. Janssen +6 more
TL;DR: In this article, the modelisation of an air bubble as inclusion in a droplet is treated from scalar theory point of view (Fresnel's theory), and the elaborated model is compared with Lorenz-Mie scattering theory and with an experimental results.