miun.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
A Two-Phase Parameter Estimation Method for Radiative Transfer Problems in Paper Industry Applications
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.ORCID iD: 0000-0002-0529-1009
2008 (English)In: Inverse Problems in Science and Engineering, ISSN 1741-5977, Vol. 16, no 7, 927-951 p.Article in journal (Refereed) Published
Abstract [en]

A two-phase method for estimation of the scattering and absorption coefficients and the asymmetry factor (sigma_s, sigma_a and g) in the radiative transfer problem is presented. The first phase parameterizes sigma_s and sigma_a through g via a simplified model and performs - at a relatively low cost - a scalaroptimization over g. It is shown that this gives such a good starting point that the second phase can be accurately performed by a simple Gauss-Newton method. It is also shown that a part of the first phase can be used on its own when only sigma_s and sigma_a are wanted, and it is noted that this gives higheraccuracy than the commonly used Kubelka-Munk method when using standardized paper industry reflectance factor measurements.The parameter estimation problem is shown to be non-trivial and ill-conditioned, and its character is analyzed. It is discussed that standard optimization methods are so sensitive to the choice ofstarting point for this problem that it is hard to find a starting point that gives convergence at all. The new two-phase method is illustrated by application to relevant paper industry problems, and efficiency and sensitivity measures are given.

Place, publisher, year, edition, pages
2008. Vol. 16, no 7, 927-951 p.
Keyword [en]
Radiative transfer, Integro-ordinary differential equations, Inverse problems, Paper industry applications
National Category
Mathematics Other Engineering and Technologies
Identifiers
URN: urn:nbn:se:miun:diva-6447DOI: 10.1080/17415970802080066ISI: 000259645600007Scopus ID: 2-s2.0-52949137438Local ID: 4930OAI: oai:DiVA.org:miun-6447DiVA: diva2:31486
Available from: 2008-11-30 Created: 2008-11-30 Last updated: 2009-03-11Bibliographically approved
In thesis
1. Mathematical modeling and numerical tools for simulation and design of light scattering in paper and print
Open this publication in new window or tab >>Mathematical modeling and numerical tools for simulation and design of light scattering in paper and print
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This work starts with a real industrial problem - the perceived need for a moredetailed and more accurate model for light scattering in paper and print than theKubelka‐Munk model of today. A careful analysis transfers this problem into aphysical description of the phenomena involved. This is then given a mathematicalformulation, and a detailed analysis leads to numerical solution procedures forspecific sub problems. Methods from scientific computing make it possible to meetindustrial demands made on speed and stability, and implementation in computercode is then followed by analysis of accuracy and stability.A problem formulation and a solution method are outlined for the forwardradiative transfer problem. First, all necessary steps to arrive at a numericallystable solution procedure are treated, and then methods are introduced to increasethe speed by a factor of several thousands or millions compared to a naiveapproach. The method is shown to be unconditionally stable, though the problemwas previously considered numerically intractable, and systematic studies ofnumerical performance are presented.The inverse radiative transfer problem is given a least‐squares formulation, anddifferent solution methods are analyzed and compared. Specifically, a two‐phasemethod for estimation of the scattering and absorption coefficients and theasymmetry factor (σs, σa and g) is presented. A sensitivity analysis is given, and it isshown how it can be used for designing measurements with minimal impact frommeasurement noise.It is shown how the standardized use of Kubelka‐Munk and the d/0°instrument leads to errors, and that the errors arising from an over‐idealized viewof the instrument - due to the fact that instrument readings are incorrectlyinterpreted - can be larger than any errors inherent in the Kubelka‐Munk modelitself. It is argued that the measurement device and the simulation model cannot beviewed as separate instances, which is a widespread implicit practice in appliedreflectance measurements. Rather, given a measurement device, measurement datashould be interpreted through a model that takes into consideration the actualgeometry, function and calibration of the instrument.The resulting tool, DORT2002, is in all aspects the Next Generation Kubelka‐Munk, and provides a greater range of applicability, higher accuracy and increasedunderstanding. It offers better interpretation of measurement data, and facilitatesthe exchange of data between the paper and graphical arts industries. It opens forunderstanding of anisotropic reflectance and for the utilization of the asymmetryfactor to design anisotropy, and thereby for the design of different visualappearance or optical performance in new printed or paper products.

Place, publisher, year, edition, pages
Sundsvall: Mittuniversitetet, 2007. 32 p.
Series
Mid Sweden University doctoral thesis, ISSN 1652-893X ; 22
Keyword
mathematical modeling, radiative transfer, integro-differential equations, inverse problems, parameter estimation, solution method, numerical performance, light scattering, paper industry applications, Kubelka-Munk
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-5908 (URN)5026 (Local ID)978-91-85317-50-9 (ISBN)5026 (Archive number)5026 (OAI)
Public defence
(English)
Available from: 2008-09-30 Created: 2009-05-06 Last updated: 2009-07-13Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Edström, Per
By organisation
Department of Natural Sciences, Engineering and Mathematics
In the same journal
Inverse Problems in Science and Engineering
MathematicsOther Engineering and Technologies

Search outside of DiVA

GoogleGoogle Scholar

Altmetric score

Total: 383 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf