Abstract

The phase retrieval problem has gained considerable attention since the wave phase is lost or impractical to measure in several applications in Electromagnetic Engineering. Quite a few approaches have been proposed recently for the extraction of phase from amplitude-only data; however few of them investigate the uniqueness of the problem prior to the solution. In this communication, the problem of the uniqueness of the phase retrieval problem from far field amplitude-only data is examined in detail. It is shown that uniqueness is guaranteed if two experiments can be performed that differ by a quadratic term in the phase. Conversely, experiments creating only linear phase differences in the data do not guarantee uniqueness. This result is demonstrated by considering the problems of a scattering target illuminated in two experiments differing by a quadratic phase shift, corresponding to two different values of defocusing of the incident wave.

Original languageEnglish (US)
Article number5678629
Pages (from-to)1053-1057
Number of pages5
JournalIEEE Transactions on Antennas and Propagation
Volume59
Issue number3
DOIs
StatePublished - Mar 1 2011

Fingerprint

uniqueness
retrieval
far fields
Experiments
Phase shift
defocusing
Scattering
phase shift
communication
Communication
engineering
electromagnetism
scattering

Keywords

  • Amplitude-only
  • far field
  • phase retrieval
  • uniqueness

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Electrical and Electronic Engineering

Cite this

On the uniqueness of the phase retrieval problem from far field amplitude-only data. / Inan, Kivanc; Diaz, Rodolfo.

In: IEEE Transactions on Antennas and Propagation, Vol. 59, No. 3, 5678629, 01.03.2011, p. 1053-1057.

Research output: Contribution to journalArticle

@article{63c13e3f877e434e85c6eea63bf1948c,
title = "On the uniqueness of the phase retrieval problem from far field amplitude-only data",
abstract = "The phase retrieval problem has gained considerable attention since the wave phase is lost or impractical to measure in several applications in Electromagnetic Engineering. Quite a few approaches have been proposed recently for the extraction of phase from amplitude-only data; however few of them investigate the uniqueness of the problem prior to the solution. In this communication, the problem of the uniqueness of the phase retrieval problem from far field amplitude-only data is examined in detail. It is shown that uniqueness is guaranteed if two experiments can be performed that differ by a quadratic term in the phase. Conversely, experiments creating only linear phase differences in the data do not guarantee uniqueness. This result is demonstrated by considering the problems of a scattering target illuminated in two experiments differing by a quadratic phase shift, corresponding to two different values of defocusing of the incident wave.",
keywords = "Amplitude-only, far field, phase retrieval, uniqueness",
author = "Kivanc Inan and Rodolfo Diaz",
year = "2011",
month = "3",
day = "1",
doi = "10.1109/TAP.2010.2103000",
language = "English (US)",
volume = "59",
pages = "1053--1057",
journal = "IEEE Transactions on Antennas and Propagation",
issn = "0018-926X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "3",

}

TY - JOUR

T1 - On the uniqueness of the phase retrieval problem from far field amplitude-only data

AU - Inan, Kivanc

AU - Diaz, Rodolfo

PY - 2011/3/1

Y1 - 2011/3/1

N2 - The phase retrieval problem has gained considerable attention since the wave phase is lost or impractical to measure in several applications in Electromagnetic Engineering. Quite a few approaches have been proposed recently for the extraction of phase from amplitude-only data; however few of them investigate the uniqueness of the problem prior to the solution. In this communication, the problem of the uniqueness of the phase retrieval problem from far field amplitude-only data is examined in detail. It is shown that uniqueness is guaranteed if two experiments can be performed that differ by a quadratic term in the phase. Conversely, experiments creating only linear phase differences in the data do not guarantee uniqueness. This result is demonstrated by considering the problems of a scattering target illuminated in two experiments differing by a quadratic phase shift, corresponding to two different values of defocusing of the incident wave.

AB - The phase retrieval problem has gained considerable attention since the wave phase is lost or impractical to measure in several applications in Electromagnetic Engineering. Quite a few approaches have been proposed recently for the extraction of phase from amplitude-only data; however few of them investigate the uniqueness of the problem prior to the solution. In this communication, the problem of the uniqueness of the phase retrieval problem from far field amplitude-only data is examined in detail. It is shown that uniqueness is guaranteed if two experiments can be performed that differ by a quadratic term in the phase. Conversely, experiments creating only linear phase differences in the data do not guarantee uniqueness. This result is demonstrated by considering the problems of a scattering target illuminated in two experiments differing by a quadratic phase shift, corresponding to two different values of defocusing of the incident wave.

KW - Amplitude-only

KW - far field

KW - phase retrieval

KW - uniqueness

UR - http://www.scopus.com/inward/record.url?scp=79952141758&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952141758&partnerID=8YFLogxK

U2 - 10.1109/TAP.2010.2103000

DO - 10.1109/TAP.2010.2103000

M3 - Article

VL - 59

SP - 1053

EP - 1057

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

IS - 3

M1 - 5678629

ER -