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Fast and accurate computation of normalized Bargmann transform.

Authors
  • Pei, Soo-Chang
  • Huang, Shih-Gu
Type
Published Article
Journal
Journal of the Optical Society of America A
Publisher
The Optical Society
Publication Date
Jan 01, 2017
Volume
34
Issue
1
Pages
18–26
Identifiers
DOI: 10.1364/JOSAA.34.000018
PMID: 28059230
Source
Medline
License
Unknown

Abstract

The linear canonical transform (LCT) was extended to complex-valued parameters, called complex LCT, to describe the complex amplitude propagation through lossy or lossless optical systems. Bargmann transform is a special case of the complex LCT. In this paper, we normalize the Bargmann transform such that it can be bounded near infinity. We derive the relationships of the normalized Bargmann transform to Gabor transform, Hermite-Gaussian functions, gyrator transform, and 2D nonseparable LCT. Several kinds of fast and accurate computational methods of the normalized Bargmann transform and its inverse are proposed based on these relationships.

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