Journal ArticleDOI
Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm
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TLDR
A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fouriertransform (FFT) algorithm is presented and scaling factors for the FRT and Fresnel diffraction when calculated through the FFT are discussed.Abstract:
A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT’s in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from −1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT are discussed.read more
Citations
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Journal ArticleDOI
Optical image encryption by random shifting in fractional Fourier domains
TL;DR: A new technique based on a random shifting, or jigsaw, algorithm is proposed, which does not require the use of phase keys for decrypting data and shows comparable or superior robustness to blind decryption.
Journal ArticleDOI
Phase-shifting color digital holography.
TL;DR: Compared the images reconstructed by two algorithms using a single Fourier transformation and a convolution with each other by both experiments and numerical simulations have proved not to cause serious deterioration of the reconstructed images.
Journal ArticleDOI
Fast algorithms for free-space diffraction patterns calculation
TL;DR: A fast algorithm based on the Fractional Fourier transform allow accurate evaluation of the Fresnel integral from object to Fraunhofer domain in a single step.
Journal ArticleDOI
Novel optical image encryption scheme based on fractional Mellin transform
TL;DR: Numerical simulations demonstrate that the proposed novel nonlinear image encryption scheme is robust with noise immunity, sensitive to the keys, and outperforms the conventional linear encryption methods to counteract some attacks.
Journal ArticleDOI
Optical image encryption using fractional Fourier transform and chaos
Narendra Singh,Aloka Sinha +1 more
TL;DR: In this article, a new method for image encryption using fractional Fourier transform and chaos theory is proposed, where the input image is combined with the first random phase mask at the object plane and is then transformed using the FFT transform.
References
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Journal ArticleDOI
An algorithm for the machine calculation of complex Fourier series
J.W. Cooley,John W. Tukey +1 more
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
Journal ArticleDOI
The Fractional Order Fourier Transform and its Application to Quantum Mechanics
TL;DR: In this article, a generalized operational calculus is developed, paralleling the familiar one for the ordinary transform, which provides a convenient technique for solving certain classes of ordinary and partial differential equations which arise in quantum mechanics from classical quadratic hamiltonians.
Journal ArticleDOI
Digital computation of the fractional Fourier transform
TL;DR: An algorithm for efficient and accurate computation of the fractional Fourier transform for signals with time-bandwidth product N, which computes the fractionsal transform in O(NlogN) time.
Journal ArticleDOI
Image rotation, Wigner rotation, and the fractional Fourier transform
TL;DR: In this article, the degree p = 1 is assigned to the ordinary Fourier transform and the degree P = 1/2 to the fractional transform, where p is the degree of the optical fiber.
Journal ArticleDOI
Fractional Fourier transforms and their optical implementation. II
TL;DR: In this paper, the linear transform kernel for fractional Fourier transform is derived and the spatial resolution and the space-bandwidth product for propagation in graded-index media are discussed.
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