Fundamental structure of Fresnel diffraction: Longitudinal uniformity with respect to fractional Fourier order
Haldun M. Özaktaş
Arik, S. O.
Optical Society of America
103 - 105
Item Usage Stats
MetadataShow full item record
Fresnel integrals corresponding to different distances can be interpreted as scaled fractional Fourier transformations observed on spherical reference surfaces. Transverse samples can be taken on these surfaces with separation that increases with propagation distance. Here, we are concerned with the separation of the spherical reference surfaces along the longitudinal direction. We show that these surfaces should be equally spaced with respect to the fractional Fourier transform order, rather than being equally spaced with respect to the distance of propagation along the optical axis. The spacing should be of the order of the reciprocal of the space-bandwidth product of the signals. The space-dependent longitudinal and transverse spacings define a grid that reflects the structure of Fresnel diffraction.
Fractional Fourier transformations
Fractional Fourier transforms
Published Version (Please cite this version)http://dx.doi.org/10.1364/OL.37.000103
Showing items related by title, author, creator and subject.
Fractional Fourier transform pre-processing for neural networks and its application to object recognition Barshan, B.; Ayrulu, B. (Pergamon Press, 2002)This study investigates fractional Fourier transform pre-processing of input signals to neural networks. The fractional Fourier transform is a generalization of the ordinary Fourier transform with an order parameter a. ...
Dorsch, R. G.; Lohmann, A. W.; Bitran, Y.; Mendlovic, D.; Haldun M. Özaktaş (Optical Society of America, 1994-11-10)In the Wigner domain of a one-dimensional function, a certain chirp term represents a rotated line delta function. On the other hand, a fractional Fourier transform (FRT) can be associated with a rotation of the ...
Durak, L.; Özdemir, A. K.; Arıkan, Orhan; Song, I. (IEEE, 2005-09)The 2-D signal representations of variables rather than time and frequency have been proposed based on either Hermitian or unitary operators. As an alternative to the theoretical derivations based on operators, we propose ...