Journal ArticleDOI
Extended fractional Fourier transforms
TLDR
In this paper, the concept of an extended fractional Fourier transform (FRT) is proposed and the physical meaning of any optical Fresnel diffraction through a lens is explained.Abstract:
The concept of an extended fractional Fourier transform (FRT) is suggested. Previous FRT’s and complex FRT’s are only its subclasses. Then, through this concept and its method, we explain the physical meaning of any optical Fresnel diffraction through a lens: It is just an extended FRT; a lens-cascaded system can equivalently be simplified to a simple analyzer of the FRT; the two-independent-parameter FRT of an object illuminated with a plane wave can be readily implemented by a lens of arbitrary focal length; when cascading, the function of each lens unit and the relationship between the adjacent ones are clear and simple; and more parameters and fewer restrictions on cascading make the optical design easy.read more
Citations
More filters
Journal ArticleDOI
Optical encryption by double-random phase encoding in the fractional Fourier domain.
TL;DR: An optical architecture that encodes a primary image to stationary white noise by using two statistically independent random phase codes that has an enhanced security value compared with earlier methods is proposed.
Journal ArticleDOI
Double image encryption based on random phase encoding in the fractional Fourier domain
TL;DR: A novel image encryption method is proposed by utilizing random phase encoding in the fractional Fourier domain to encrypt two images into one encrypted image with stationary white distribution that can be recovered without cross-talk.
Journal ArticleDOI
Digital Computation of Linear Canonical Transforms
TL;DR: The algorithms compute LCTs with a performance similar to that of the fast Fourier transform algorithm in computing the Fouriertransform, both in terms of speed and accuracy.
Journal ArticleDOI
Convolution theorems for the linear canonical transform and their applications
Bing Deng,Ran Tao,Yue Wang +2 more
TL;DR: The sampling and reconstruction formulas are deduced, together with the construction methodology for the multiplicative filter in the time domain based on fast Fourier transform (FFT), which has much lower computational load than the construction method in the linear canonical domain.
Journal ArticleDOI
Fully phase encryption using fractional Fourier transform
TL;DR: A fully phase encryption system, using fractional Fourier transform to encrypt and decrypt a 2-D phase image obtained from an amplitude image, and experimental results in support of the proposed idea are presented.
References
More filters
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
Lens-System Diffraction Integral Written in Terms of Matrix Optics
TL;DR: In this paper, a diffraction integral is derived which relates the electromagnetic fields on the input plane of a lens system to those on its output plane, which indicates a connection between ray optics and diffraction theory.
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.
Journal ArticleDOI
On Namias's fractional Fourier transforms
A. C. McBRIDE,F. H. Kerr +1 more
TL;DR: In this paper, it is stated que "for lever toute ambiguite, on montre qu'il est necessaire de modifier les operateurs fractionnaires de Namia On demontre des theoremes pour les operateur modifies and on developpe un calcul operationnel".
Related Papers (5)
Optical image encryption based on input plane and Fourier plane random encoding.
Philippe Réfrégier,Bahram Javidi +1 more