1. Optimal representation and processing of optical signals in quadratic-phase systems
- Author
-
Haldun M. Ozaktas, Sercan O. Arik, and Haldun M. Özaktaş
- Subjects
Computation ,02 engineering and technology ,Quadratic phase systems ,01 natural sciences ,Efficient computation ,Fractional Fourier transforms ,Linear canonical transform ,Fundamental structures ,Nonuniform sampling ,010309 optics ,symbols.namesake ,Optics ,Number of samples ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,Chirp ,Fourier optics ,Electrical and Electronic Engineering ,Physical and Theoretical Chemistry ,Representation (mathematics) ,Sampling ,Physics ,business.industry ,Quadratic-phase systems ,Sampling (statistics) ,020206 networking & telecommunications ,Mines ,Digital signal processing ,Sample (graphics) ,Atomic and Molecular Physics, and Optics ,Fractional Fourier transform ,ABCD systems ,Electronic, Optical and Magnetic Materials ,Fourier transforms ,Fourier transform ,symbols ,ABCD system ,Mathematical transformations ,business - Abstract
Optical fields propagating through quadratic-phase systems (QPSs) can be modeled as magnified fractional Fourier transforms (FRTs) of the input field, provided we observe them on suitably defined spherical reference surfaces. Non-redundant representation of the fields with the minimum number of samples becomes possible by appropriate choice of sample points on these surfaces. Longitudinally, these surfaces should not be spaced equally with the distance of propagation, but with respect to the FRT order. The non-uniform sampling grid that emerges mirrors the fundamental structure of propagation through QPSs. By providing a means to effectively handle the sampling of chirp functions, it allows for accurate and efficient computation of optical fields propagating in QPSs. © 2015 Elsevier B.V. All rights reserved.
- Published
- 2016