Fractional Fourier transforms and their optical implementation: I
Open accessAbstract
Fourier transforms of fractional order a are defined in a manner such that the common Fourier transform is a special case with order a = 1. An optical interpretation is provided in terms of quadratic graded index media and discussed from both wave and ray viewpoints. Several mathematical properties are derived.
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Our method of derivation closely resembles the continuous definition originally given in [6] and [7].
“Our method of derivation closely resembles the continuous definition originally given in [6] and [7].”
From The discrete fractional Fourier transform (2000) · cites this paper as [6]
The continuous FRT is defined through spectral expansion in [6] and [7].
“In these papers, the continuous FRT is defined through spectral expansion.”
From The discrete fractional Fourier transform (2000) · cites this paper as [6]
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Self-citation
- Authors
- Mendlovic, D., & Ozaktas, H. M.
- Venue
- Journal of the Optical Society of America A
- Publisher
- Optica Publishing Group
- Published
- 1993-09-01
- Volume
- 10
- Issue
- 9
- Pages
- 1875
- ISSN
- 1084-7529 (ISSN-L)
- 1520-8532
- OpenAlex
- W2099006587
- Semantic Scholar
- f98b614bf56edb4b9e1384e81cbd2bb27e253dd2
- Cited by
- 848
- References
- 18
- Citations by year
- 2026: 9 · 2025: 14 · 2024: 20 · 2023: 12 · 2022: 22 · 2021: 32 · 2020: 25 · 2019: 18 · 2018: 27 · 2017: 25 · 2016: 24 · 2015: 28 · 2014: 27 · 2013: 22 · 2012: 28
- FWCI
- 46.09
- Type
- journal article
- Language
- en
- Open access
- green
- hdl.handle.net
- Locations
- Journal of the Optical Society of America A (publishedVersion)
- Bilkent University Institutional Repository (Bilkent University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Mathematics › Modeling and Simulation › Fractional Differential Equations Solutions
- Physical Sciences › Engineering › Biomedical Engineering › Advanced optical system design
- Keywords
- fractional Fourier transform, optical implementation, graded-index media, geometrical optics, physical optics
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