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Angle Resolved Light Scattering in Turbid Media: Analysis and Applications
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
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: urn:nbn:se:miun:diva-13154ISBN: 978-91-86694-22-7 (print)OAI: oai:DiVA.org:miun-13154DiVA, id: diva2:391548
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
List of papers
1. 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, p. 1032-1039Article 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: 2017-12-12Bibliographically approved
2. 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, 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.

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: 2017-12-12Bibliographically approved
3. 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, p. 221-232Article 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: 2017-12-12Bibliographically approved
4. Angular Variations of Color in Turbid Media – the Influence of Bulk Scattering on Goniochromism in Paper
Open this publication in new window or tab >>Angular Variations of Color in Turbid Media – the Influence of Bulk Scattering on Goniochromism in Paper
Show others...
2010 (English)In: 5th European Conference on Colour in Graphics, Imaging, and Vision and 12th International Symposium on Multispectral Colour Science 2010, CGIV 2010/MCS'10, 2010, p. 407-413Conference paper, Published paper (Refereed)
Abstract [en]

The angular variations of color of a set of paper samples are  experimentally assessed using goniophotometric measurements.  The corresponding simulations are done using a radiative transfer based simulation tool, thus considering only the contribution  of bulk scattering to the reflectance. It is seen that measurements  and simulations agree and display the same characteristics, with  the lightness increasing and the chroma decreasing as the observation  polar angle increases. The decrease in chroma is larger  the more dye the paper contains. Based on previous results about  anisotropic reflectance from turbid media these findings are explained.  The relative reflectance in large polar angles of wavelengths  with strong absorption is higher than that of wavelengths  with low absorption. This leads to a loss of chroma and color information  in these angles. The increase in lightness is a result  of the anisotropy affecting all wavelengths equally, which is the  case for transmitting media and obliquely incident illumination.  The only case with no color variations of this kind is when a nonabsorbing,  non-transmitting medium is illuminated diffusely. The  measured and simulated color differences are clearly large, and  it is an open issue how angle resolved color should be handled  in standard color calculations.

National Category
Materials Engineering
Identifiers
urn:nbn:se:miun:diva-11758 (URN)2-s2.0-78649358316 (Scopus ID)978-161738889-7 (ISBN)
Conference
5th European Conference on Colour in Graphics, Imaging, and Vision and 12th International Symposium on Multispectral Colour Science 2010, CGIV 2010/MCS'10; Joensuu; 14 June 2010 through 17 June 2010; Code 82712
Funder
Available from: 2010-06-23 Created: 2010-06-23 Last updated: 2011-01-25Bibliographically approved
5. 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, E-ISSN 1094-4087, Vol. 19, no 3, p. 1915-1920Article 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: 2017-12-11Bibliographically approved

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