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Anisotropic reflectance from turbid media. II. Measurements
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics. (Pappersoptik och färg)
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics. (Pappersoptik och färg)ORCID iD: 0000-0002-0529-1009
2010 (English)In: Journal of the Optical Society of America A, ISSN 0740-3232, Vol. 27, no 5, p. 1040-1045Article 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.

Place, publisher, year, edition, pages
2010. Vol. 27, no 5, p. 1040-1045
Keywords [en]
KUBELKA-MUNK MODEL; RADIATION
National Category
Other Engineering and Technologies
Identifiers
URN: urn:nbn:se:miun:diva-11430ISI: 000277241200013PubMedID: 20448770Scopus ID: 2-s2.0-77955987830OAI: oai:DiVA.org:miun-11430DiVA, id: diva2:310958
Projects
PaperOptAvailable from: 2010-04-19 Created: 2010-04-19 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Angle Resolved Light Scattering in Turbid Media: Analysis and Applications
Open this publication in new window or tab >>Angle Resolved Light Scattering in Turbid Media: Analysis and Applications
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Light scattering in turbid media is essential for such diverse application areas as paper and print, computer rendering, optical tomography, astrophysics and remote sensing. This thesis investigates angular variations of light reflected from plane-parallel turbid media using both mathematical models and reflectance measurements, and deals with several applications. The model of most widespread use in industry is the Kubelka-Munk model, which neglects angular variations in the reflected light. This thesis employs a numerical solution of the angle resolved radiative transfer problem to better understand how the angular variations are related to medium properties. It is found that the light is reflected anisotropically from all media encountered in practice, and that the angular variations depend on the medium absorption and transmittance and on the angular 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 are confirmed by measurements using a set of paper samples. The only situation with isotropic reflectance is when a non-transmitting, non-absorbing medium is illuminated diffusely. This is the only situation where the Kubelka-Munk model is exactly valid. The results also show that there is no such thing as an ideal bulk scattering diffusor, and these findings can affect calibration and measurement procedures defined in international standards.The implications of the presented results are studied for a set of applications including reflectance measurements, angle resolved color and point spreading. It is seen that differences in instrument detection and illumination geometry can result in measurement differences. The differences are small and if other sources of error - such as fluorescence and gloss - are not eliminated, the differences related to instrument geometry become difficult to discern. Furthermore, the angle resolved color of a set of paper samples is assessed both theoretically and experimentally. The chroma decreases and the lightness increases as the observation polar angle increases. The observed differences are clearly large, and it is an open issue how angle resolved color should be handled. Finally, the dependence of point spreading in turbid media on the medium parameters is studied. The asymmetry factor is varied while maintaining constant the optical response in a standardized measurement geometry. It is seen 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 mean free path. A generic model of point spreading must therefore capture the dependence on all of these medium parameters.This thesis shows that turbid media reflect light anisotropically, and angle resolved radiative transfer models are therefore necessary to capture this. Using simplified models can introduce errors in an uncontrolled manner. The results presented potentially have consequences for all applications dealing with light scattering, some of which are studied here.

Place, publisher, year, edition, pages
Härnösand: Mid Sweden University, 2011. p. 17
Series
Mid Sweden University licentiate thesis, ISSN 1652-8948 ; 56
National Category
Other Engineering and Technologies
Identifiers
urn:nbn:se:miun:diva-13154 (URN)978-91-86694-22-7 (ISBN)
Presentation
2011-02-16, O111, Gånsviksvägen 2, Härnösand, 10:00 (English)
Opponent
Supervisors
Available from: 2011-01-25 Created: 2011-01-25 Last updated: 2011-01-25Bibliographically approved
2. 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. p. 25
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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