Fast and accurate computation of normalized Bargmann transform

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.

Accepted by Journal of the Optical Society of America A (JOSA A)

References in corpus (4)

• Fast Discrete Linear Canonical Transform Based on CM-CC-CM Decomposition and FFT
• Two-dimensional nonseparable discrete linear canonical transform based on CM-CC-CM-CC decomposition
• Reversible Joint Hilbert and Linear Canonical Transform Without Distortion
• Discrete Gyrator Transforms: Computational Algorithms and Applications