Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Complex signal representation, Mandel’s theorem, and spiral phase quadrature transform

Not Accessible

Your library or personal account may give you access

Abstract

Complex (or analytic) signal representation as introduced by Gabor plays an important role in optical signal processing and in coherence theory of optical fields. Several definitions for extending the notion of complex signal representation to two dimensions have appeared in the literature. These defini tions differ in their choice of the quadrature transform for a two-dimensional signal. We study the problem of determining the complex representation for two-dimensional real signals (or images) using a least-square minimization framework first used by Mandel [J. Opt. Soc. Am. 57, 613 (1967)JOSAAH0030-3941]. In particular, we seek a suitable quadrature transform such that the resultant complex image has the least fluctuating envelope in an ensemble-averaged sense. It is observed that the spiral phase quadrature transform for two-dimensional signals is a solution of this analysis.

© 2008 Optical Society of America

Full Article  |  PDF Article
More Like This
Carrier-frequency estimation for digital holograms of phase objects

Nishant Goyal and Kedar Khare
Appl. Opt. 63(7) B42-B48 (2024)

Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform

Kieran G. Larkin, Donald J. Bone, and Michael A. Oldfield
J. Opt. Soc. Am. A 18(8) 1862-1870 (2001)

Phase imaging using spiral-phase diversity

Manoj Kumar Sharma, Charu Gaur, Paramasivam Senthilkumaran, and Kedar Khare
Appl. Opt. 54(13) 3979-3985 (2015)

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (35)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved