Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


IMPACT FACTOR 2018: 0.881
5-year IMPACT FACTOR: 1.170

CiteScore 2018: 0.91

SCImago Journal Rank (SJR) 2018: 0.430
Source Normalized Impact per Paper (SNIP) 2018: 0.969

Mathematical Citation Quotient (MCQ) 2017: 0.49

Online
ISSN
1569-3945
See all formats and pricing
More options …
Volume 23, Issue 6

Issues

Regularization strategy for determining laser beam quality parameters

Teresa Regińska / Kazimierz Regiński
Published Online: 2015-05-21 | DOI: https://doi.org/10.1515/jiip-2014-0084

Abstract

A simplified model of a laser beam leads to an ill-posed Cauchy problem for the Helmholtz equation on an infinite strip. In the case of large wave numbers, the problem corresponds to an operator equation with an unbounded operator. The first problem considered concerns optimality of a spectral type regularization method for reconstructing the radiation field from measurements given only on a part of the boundary. The optimal order of convergence, previously known for particular cases, is proved for an arbitrary wave number and for nonzero Dirichlet and Neumann conditions under a priori and a posteriori choice of a regularization parameter. In the second part, the regularized solutions are employed to describe the geometrical properties of the beam and, in particular, to find approximate beam quality parameters such as the waist of the axial profile of the beam and its position. The mathematical considerations are preceded by a section where the main notions of laser beam optics are introduced and briefly explained.

Keywords: Cauchy problem for the Helmholtz equation; regularization; optimal convergence rate; discrepancy principle; axial profile of laser beam; smoothing and curve fitting

MSC: 35R25; 65D10; 65M30; 78A60

About the article

Received: 2014-11-27

Revised: 2015-02-18

Accepted: 2015-03-03

Published Online: 2015-05-21

Published in Print: 2015-12-01


Funding Source: Polish Ministry of Science and Higher Education

Award identifier / Grant number: N N515 524938


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 23, Issue 6, Pages 657–671, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2014-0084.

Export Citation

© 2015 by De Gruyter.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Emilia Pruszyńska-Karbownik, Kazimierz Regiński, and Maciej Bugajski
Optical and Quantum Electronics, 2016, Volume 48, Number 5

Comments (0)

Please log in or register to comment.
Log in