Fundamental structure of Fresnel diffraction: Natural sampling grid and the fractional Fourier transform
Ozaktas, H., M.
Please cite this item using this persistent URLhttp://hdl.handle.net/11693/21879
Fresnel integrals corresponding to different distances can be interpreted as scaled fractional Fourier transformations observed on spherical reference surfaces. We show that by judiciously choosing sample points on these curved reference surfaces, it is possible to represent the diffracted signals in a nonredundant manner. The change in sample spacing with distance reflects the structure of Fresnel diffraction. This sampling grid also provides a simple and robust basis for accurate and efficient computation, which naturally handles the challenges of sampling chirplike kernels. © 2011 Optical Society of America.
- Research Paper 
Showing items related by title, author, creator and subject.
Fundamental structure of Fresnel diffraction: Longitudinal uniformity with respect to fractional Fourier order Ozaktas, H., M.; Arik, S.O.; Coşkun, T. (2012)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 ...
Fast and accurate linear canonical transform algorithms [Hizli ve Hassas Doʇrusal Kanonik Dönüşüm Algoritmalari] Özaktaş H.M.; Koç, A. (Institute of Electrical and Electronics Engineers Inc., 2015)Linear canonical transforms are encountered in many areas of science and engineering. Important transformations such as the fractional Fourier transform and the ordinary Fourier transform are special cases of this transform ...
Durak L.; Arikan, O. (2003)Shift and rotation invariance properties of linear time-frequency representations are investigated. It is shown that among all linear time-frequency representations, only the short-time Fourier transform (STFT) family with ...