# Ubiquity of Fourier transformation in optical sciences.

@article{Mansuripur2020UbiquityOF, title={Ubiquity of Fourier transformation in optical sciences.}, author={Masud Mansuripur}, journal={Applied optics}, year={2020}, volume={59 22}, pages={ G47-G63 } }

Fourier transformation is an important conceptual as well as computational tool in the arsenal of every practitioner of physical and mathematical sciences. I discuss some of its applications in optical science and engineering to provide a broad perspective on the intimate relation between the physical and mathematical concepts that are elegantly interwoven within the theory of Fourier transforms.

## 2 Citations

Ubiquity of Fourier transformation in optical sciences

- PhysicsOptical Engineering + Applications
- 2021

The applications of Fourier transformation described in the present paper include the central limit theorem of probability and statistics, the Shannon-Nyquist sampling theorem, and computing the electromagnetic field radiated by an oscillating magnetic dipole.

An extremely simplified optics laboratory for teaching the fundamentals of Fourier analysis

- PhysicsEuropean Journal of Physics
- 2020

In this paper, we describe easy and cheap optics experiences for teaching undergraduate students the fundamental properties of Fourier transforms on an experimental basis. By exploiting the eye as…

## References

SHOWING 1-10 OF 31 REFERENCES

Eigenfunctions of the Fourier Transform

- Mathematics, Physics
- 2008

An eigenfunction of the Fourier transform operator is a function whose shape is identical to that of its Fourier transform. The Gaussian curve, appropriately scaled, is an example. It is well known…

The Fourier Transform and Its Applications

- Mathematics
- 1965

1 Introduction 2 Groundwork 3 Convolution 4 Notation for Some Useful Functions 5 The Impulse Symbol 6 The Basic Theorems 7 Obtaining Transforms 8 The Two Domains 9 Waveforms, Spectra, Filters and…

Classical Optics and its Applications

- Physics
- 2002

Covering a broad range of fundamental topics in classical optics and electro-magnetism, this book is ideal for graduate-level courses in optics, providing supplementary reading materials for teachers…

Time-Harmonic Electromagnetic Fields

- Mathematics
- 1961

Foreword to the Revised Edition. Preface. Fundamental Concepts. Introduction to Waves. Some Theorems and Concepts. Plane Wave Functions. Cylindrical Wave Functions. Spherical Wave Functions.…

Roadmap on superoscillations

- PhysicsJournal of Optics
- 2019

Superoscillations are band-limited functions with the counterintuitive property that they can vary arbitrarily faster than their fastest Fourier component, over arbitrarily long intervals. Modern…

Optical Coherence and Quantum Optics

- Physics
- 1995

Preface 1. Elements of probability theory 2. Random (or stochastic) processes 3. Some useful mathematical techniques 4. Second-order coherence theory of scalar wavefields 5. Radiation from sources of…

Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles

- Physics
- 2011

This tutorial gives an overview of the use of the Wigner function as a tool for modeling optical field propagation. Particular emphasis is placed on the spatial propagation of stationary fields, as…

Introduction to Quantum Optics

- Physics
- 1995

The theory of quantum propagator and time–dependent integrals of motion in quantum optics is reviewed as well as the properties of Wigner function, Q– function, and coherent state representation.…

Quantum mechanics as a statistical theory

- Physics
- 1949

An attempt is made to interpret quantum mechanics as a statistical theory, or more exactly as a form of non-deterministic statistical dynamics. The paper falls into three parts. In the first, the…

Waves and Fields in Inhomogeneous Media

- Mathematics
- 1990

Preface. Acknowledgements. 1: Preliminary background. 2: Planarly layered media. 3: Cylindrically and spherically layered media. 4: Transients. 5: Variational methods. 6: Mode matching method. 7:…