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A partial explanation of the dependence between light scattering and light absorption in the Kubelka-Munk model
Mid Sweden University, Faculty of Science, Technology and Media, Department of applied science and design. (FSCN)
Mid Sweden University, Faculty of Science, Technology and Media, Department of applied science and design. (DPC)
Mid Sweden University, Faculty of Science, Technology and Media, Department of applied science and design. (FSCN)ORCID iD: 0000-0002-0529-1009
2012 (English)In: Nordic Pulp & Paper Research Journal, ISSN 0283-2631, Vol. 27, no 2, 426-430 p.Article in journal (Refereed) Published
Abstract [en]

The Kubelka-Munk scattering and absorption coefficients of a set of paper samples are assessed using reflectance measurements in d/0 geometry. The coefficients display the widely studied dependence between light scattering and light absorption, since the light scattering coefficient decreases in regions of high absorption. It is shown using general radiative transfer theory that part of this dependence can be explained and eliminated by taking into account the geometry of the d/0 instrument and the single scattering anisotropy, thus capturing the angular variations of the light reflected from the samples. These findings allow the papermaker to better predict the reflectance from mixtures of pulps, fillers, dye, and FWA, and to better evaluate bleaching efforts. 

Place, publisher, year, edition, pages
2012. Vol. 27, no 2, 426-430 p.
Keyword [en]
Anisotropic reflectance; Kubelka-Munk; Paper optics; Parameter dependence; Reflectance measurements
National Category
Paper, Pulp and Fiber Technology
Identifiers
URN: urn:nbn:se:miun:diva-16873DOI: 10.3183/NPPRJ-2012-27-02-p426-430ISI: 000315696000035Scopus ID: 2-s2.0-84865251384OAI: oai:DiVA.org:miun-16873DiVA: diva2:547458
Available from: 2013-04-04 Created: 2012-08-28 Last updated: 2013-09-16Bibliographically approved
In thesis
1. Applied problems and computational methods in radiative transfer
Open this publication in new window or tab >>Applied problems and computational methods in radiative transfer
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Light scattering in turbid media is essential for such diverse applications as paperand print, computer rendering, optical tomography, astrophysics and remote sensing.This thesis investigates angular variations of light reflected from plane-parallelturbid media using both mathematical models and reflectance measurements, dealswith several applications and proposes novel computational methods for solving thegoverning equations.Angular variations of light reflected from plane-parallel turbid media is studiedusing both mathematical models and reflectance measurements. It is found that thelight is reflected anisotropically from all media encountered in practice, and that theangular variations depend on the medium absorption and transmittance and on theangular distribution of the incident light. If near-surface bulk scattering dominates,as in strongly absorbing or highly transmitting media or obliquely illuminated media,relatively more light is reflected in large polar (grazing) angles. These results areconfirmed by measurements using a set of paper samples. The only situation withisotropic reflectance is when a non-transmitting, non-absorbing medium is illuminateddiffusely, and it is shown that this is the only situation where the widely usedKubelka-Munk model is exactly valid.A number of applied problems is studied, including reflectance measurements,angle resolved color and point spreading. It is seen that differences in instrumentdetection and illumination geometry can result in measurement differences. The differencesare small and if other sources of error — such as fluorescence and gloss— are not eliminated, the differences related to instrument geometry become difficultto discern. Furthermore, the dependence of point spreading in turbid mediaon the medium parameters is studied. The asymmetry factor is varied while maintainingconstant the optical response in a standardized measurement geometry. It isseen that the point spreading increases as forward scattering becomes more dominant,and that the effect is larger if the medium is low-absorbing with large meanfree path. It is argued that the directional inhomogeneity of the scattering mediummust be captured by the model to reproduce experimental results. Finally, the angleresolved color of a set of paper samples is assessed both theoretically and experimentally.The chroma decreases and the lightness increases as the observation polarangle increases. The observed differences are clearly large, and a modification ofthe L∗a∗b∗ formalism including angle dependent chromatic adaptation is suggestedhere to handle this situation.

The long standing issue of parameter dependence in the Kubelka-Munk modelis partially explained by recognizing that light reflected from paper samples in standardizedmeasurements has angular variations, and by using the appropriatemodelin the calculation of the scattering and absorption coefficients.The radiative transfer (RT) equation is solved with a recently proposed particlemethod (DFPM), both in standard cases and in cases previously considered intractable.Fluorescence is added to the RT equation, thus including wavelength asan additional dimension, and this equation is solved using DFPM. The discrete RTequation can be written as a system of linear equations, and a comprehensive analysisof the convergence properties of DFPM when solving this type of problems ispresented.

Place, publisher, year, edition, pages
Härnösand: Mittuniversitetet, 2013. 25 p.
Series
Mid Sweden University doctoral thesis, ISSN 1652-893X ; 151
National Category
Other Physics Topics
Identifiers
urn:nbn:se:miun:diva-19776 (URN)978-91-87103-80-3 (ISBN)
Public defence
2013-09-20, Alfhild Agrell-salen, Universitetsbacken 3, Härnösand, 10:00 (Swedish)
Opponent
Supervisors
Funder
Vinnova
Available from: 2013-09-16 Created: 2013-08-26 Last updated: 2013-09-16Bibliographically approved

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