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Applied problems and computational methods in radiative transfer
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
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: urn:nbn:se:miun:diva-19776ISBN: 978-91-87103-80-3 (print)OAI: oai:DiVA.org:miun-19776DiVA: diva2:643246
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
List of papers
1. A partial explanation of the dependence between light scattering and light absorption in the Kubelka-Munk model
Open this publication in new window or tab >>A partial explanation of the dependence between light scattering and light absorption in the Kubelka-Munk model
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. 

Keyword
Anisotropic reflectance; Kubelka-Munk; Paper optics; Parameter dependence; Reflectance measurements
National Category
Paper, Pulp and Fiber Technology
Identifiers
urn:nbn:se:miun:diva-16873 (URN)10.3183/NPPRJ-2012-27-02-p426-430 (DOI)000315696000035 ()2-s2.0-84865251384 (Scopus ID)
Available from: 2013-04-04 Created: 2012-08-28 Last updated: 2013-09-16Bibliographically approved
2. Angle resolved color of bulk scattering media
Open this publication in new window or tab >>Angle resolved color of bulk scattering media
2011 (English)In: Applied Optics, ISSN 1559-128X, E-ISSN 2155-3165, Vol. 50, no 36, 6555-6563 p.Article in journal (Refereed) Published
Abstract [en]

The angle resolved reflectance factor of matte samples is measured with a goniophotometer and simulated using radiative transfer theory. Both measurements and simulations display the same characteristic dependence of the reflectance factor on the observation angle. The angle resolved reflectance spectra are translated to CIELAB color coordinates and the angular color differences are found to be surprisingly large. A chromatic adaptation that is dependent on the observation angle is suggested, in which a nonabsorbing opaque medium is used as the reference white, and the angular color differences are then reduced. Furthermore, the use of an undyed paper as the reference white is evaluated. The angular lightness differences are then reduced further, but the angular differences in chroma are still large. It is suggested that smaller variations in perceived color could be explained by angle dependent chromatic adaptation and a limited sensitivity of the human visual system to changes in chroma.

Keyword
Angle resolved color; bulk scattering media
National Category
Other Physics Topics
Identifiers
urn:nbn:se:miun:diva-15157 (URN)10.1364/AO.50.006555 (DOI)000299166700002 ()2-s2.0-84255190004 (Scopus ID)
Projects
PaperOptOptics of paper and print: continuous models
Available from: 2011-12-12 Created: 2011-12-12 Last updated: 2016-04-19Bibliographically approved
3. A particle approach to the radiative transfer equation with fluorescence
Open this publication in new window or tab >>A particle approach to the radiative transfer equation with fluorescence
2013 (English)Article in journal (Refereed) Submitted
National Category
Other Physics Topics
Identifiers
urn:nbn:se:miun:diva-18693 (URN)
Available from: 2013-04-04 Created: 2013-04-04 Last updated: 2016-12-09Bibliographically approved
4. Anisotropic reflectance from turbid media. I. Theory
Open this publication in new window or tab >>Anisotropic reflectance from turbid media. I. Theory
2010 (English)In: Journal of the Optical Society of America A, ISSN 0740-3232, Vol. 27, no 5, 1032-1039 p.Article in journal (Refereed) Published
Abstract [en]

It is shown that the intensity of light reflected from plane-parallel turbid media is anisotropic in all situations encountered in practice. The anisotropy, in the form of higher intensity in large polar angles, increases when the amount of near-surface bulk scattering is increased, which dominates in optically thin and highly absorbing media. The only situation with isotropic intensity is when a non-absorbing infinitely thick medium is illuminated diffusely. This is the only case where the Kubelka-Munk model gives exact results and there exists an exact translation between Kubelka-Munk and general radiative transfer. This also means that a bulk scattering perfect diffusor does not exist. Angular resolved models are thus crucial for a correct understanding of light scattering in turbid media. The results are derived using simulations and analytical calculations. It is also shown that there exists an optimal angle for directional detection which minimizes the error introduced when using the Kubelka-Munk model to interpret reflectance measurements with diffuse illumination.

Keyword
MULTIPLE-SCATTERING CALCULATIONS; KUBELKA-MUNK MODEL; LIGHT-ABSORPTION; TECHNOLOGY; FLUX
National Category
Other Engineering and Technologies
Identifiers
urn:nbn:se:miun:diva-11429 (URN)10.1364/JOSAA.27.001032 (DOI)000277241200012 ()20448769 (PubMedID)2-s2.0-77955994658 (Scopus ID)
Projects
PaperOpt
Available from: 2010-04-19 Created: 2010-04-19 Last updated: 2016-09-22Bibliographically approved
5. Anisotropic reflectance from turbid media. II. Measurements
Open this publication in new window or tab >>Anisotropic reflectance from turbid media. II. Measurements
2010 (English)In: Journal of the Optical Society of America A, ISSN 0740-3232, Vol. 27, no 5, 1040-1045 p.Article in journal (Refereed) Published
Abstract [en]

The anisotropic reflectance from turbid media predicted using the radiative transfer based DORT2002 model is experimentally verified through goniophotometric measurements. A set of paper samples with varying amount of dye and thickness is prepared and their angle resolved reflectance is measured. An alleged perfect diffusor is also included. The corresponding simulations are performed. A complete agreement between the measurements and model predictions is seen regarding the characteristics of the anisotropy. They show that relatively more light is reflected in large polar angles when the absorption or illumination angle is increased or when the medium thickness is decreased. This is due to the relative amount of near-surface bulk scattering increasing in these cases. This affects the application of the Kubelka-Munk model as well as standards for reflectance measurements and calibration routines.

Keyword
KUBELKA-MUNK MODEL; RADIATION
National Category
Other Engineering and Technologies
Identifiers
urn:nbn:se:miun:diva-11430 (URN)000277241200013 ()20448770 (PubMedID)2-s2.0-77955987830 (Scopus ID)
Projects
PaperOpt
Available from: 2010-04-19 Created: 2010-04-19 Last updated: 2016-09-22Bibliographically approved
6. Point spreading in turbid media with anisotropic single scattering
Open this publication in new window or tab >>Point spreading in turbid media with anisotropic single scattering
2011 (English)In: Optics Express, ISSN 1094-4087, Vol. 19, no 3, 1915-1920 p.Article in journal (Refereed) Published
Abstract [en]

Point spreading is investigated using general radiative transfer theory. We find that the single scattering anisotropy plays a significant role for point spreading together with the medium mean free path, single scattering albedo and thickness. When forward scattering dominates, the light will on average undergo more scattering events to give a specific optical response in reflectance measurements. This will significantly increase point spreading if the medium is low absorbing with large mean free path. Any fundamental and generic model of point spreading must capture the dependence on all of these medium characteristics.

Place, publisher, year, edition, pages
OSA, 2011
Keyword
OPTICAL-PROPERTIES; PAPER; REFLECTANCE; MTF
National Category
Other Engineering and Technologies Computational Mathematics
Identifiers
urn:nbn:se:miun:diva-13113 (URN)10.1364/OE.19.001915 (DOI)000286807100026 ()21369006 (PubMedID)2-s2.0-79851482792 (Scopus ID)
Projects
PaperOptOptics of Paper and Print - Continuous Models
Available from: 2011-01-19 Created: 2011-01-19 Last updated: 2013-09-16Bibliographically approved
7. Lateral light scattering in paper - MTF simulation and measurement
Open this publication in new window or tab >>Lateral light scattering in paper - MTF simulation and measurement
2011 (English)In: Optics Express, ISSN 1094-4087, Vol. 19, no 25, 25181-25187 p.Article in journal (Refereed) Published
Abstract [en]

The modulation transfer function (MTF) of 22 paper samples is computed using Monte Carlo simulations with isotropic or strongly forward single scattering. The inverse frequency at half maximum of the MTF (kp) is found inappropriate as a single metric for the MTF since it is insensitive to the shape of the modeled and simulated MTF. The single scattering phase function has a significant impact on the shape of the MTF, leading to more lateral scattering. However, anisotropic single scattering cannot explain the larger lateral scattering observed in paper. It is argued that the directional inhomogeneity of paper requires a light scattering model with both the phase function and scattering distances being dependent on the absolute direction.

Place, publisher, year, edition, pages
Optical Society of America, 2011
Keyword
scattering turbid media lateral scattering paper
National Category
Other Physics Topics Paper, Pulp and Fiber Technology
Identifiers
urn:nbn:se:miun:diva-15014 (URN)10.1364/OE.19.025181 (DOI)000297702400033 ()2-s2.0-82955208266 (Scopus ID)
Projects
PaperOpt
Available from: 2011-12-02 Created: 2011-12-02 Last updated: 2013-09-16Bibliographically approved
8. Role of the particle method DFPM for solving linear equations
Open this publication in new window or tab >>Role of the particle method DFPM for solving linear equations
Show others...
(English)Manuscript (preprint) (Other academic)
National Category
Other Physics Topics
Identifiers
urn:nbn:se:miun:diva-18692 (URN)
Available from: 2013-04-08 Created: 2013-04-04 Last updated: 2016-12-09Bibliographically approved
9. Geometry Related Inter-Instrument Differences in Spectrophotometric Measurements
Open this publication in new window or tab >>Geometry Related Inter-Instrument Differences in Spectrophotometric Measurements
2010 (English)In: Nordic Pulp & Paper Research Journal, ISSN 0283-2631, E-ISSN 2000-0669, Vol. 25, no 2, 221-232 p.Article in journal (Refereed) Published
Abstract [en]

The L&W Elrepho d/0 and the Spectrolino 45/0 instruments are examined using paper samples with different properties. External factors that influence the measurements such as the sample background, the instrument calibration and the sample inhomogeneity are studied, and a methodology for their minimization is presented. Experimental measurements show that such external factors, if not minimized by proper routines, affect the inter-instrument differences far more (up to 4-5 Delta E-ab(star)) than the instrument geometry (the effect of which is small and of order 0.1 Delta E-ab(star)). The DORT2002 radiative transfer model is used to simulate differences caused by instrument geometry. The simulated and measured differences are found to agree in magnitude, and the differences are mapped against sample properties. It is observed that the 45/0 instrument detects higher reflectance from paper samples with negligible absorption and transmittance. When there is considerable absorption (dyed samples) or transmittance (thin samples), the d/0 instrument detects higher reflectance. The physical mechanism behind this behavior is studied and explained using DORT2002, and the instrument differences are shown to depend on the anisotropy of the reflected light. The model/measurement agreement is satisfactory as the characteristic behavior is captured in almost all cases studied. This new understanding is important for facilitating accurate data exchange between the paper and graphic arts industries, but also for interpretation of reflectance measurements in general.

Keyword
Absorption, Anisotropy, Instrument geometry, Measurement differences, Radiative transfer, Reflectance measurements, Spectrophotometry, Transmittance
National Category
Chemical Engineering
Identifiers
urn:nbn:se:miun:diva-11887 (URN)10.3183/NPPRJ-2010-25-02-p221-232 (DOI)000279341100011 ()2-s2.0-78649369333 (Scopus ID)
Available from: 2010-07-30 Created: 2010-07-30 Last updated: 2016-09-22Bibliographically approved

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