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  • 1.
    Bohlin, Erik
    et al.
    Karlstad Universitet.
    Gustafsson Coppel, Ludovic
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Johansson, Caisa
    Karlstads Universitet.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Modelling of brightness decrease in coated cartonboard as an effect of calendering: Microroughness and effective refractive index aspects2010Ingår i: 11th Advanced Coating Fundamentals Symposium Proceedings: The Latest Advances in Coating Research and Development, Norcross, GA, USA: TAPPI Press, 2010, s. 51-65Konferensbidrag (Refereegranskat)
    Abstract [en]

    Calendering of coated paper leads to a brightness decrease. The mechanism for this is not clear, although it has been discussed in the past. One common explanation is that the porosity of the coating layer decreases and hence scattering. By comparing simulated and measured results this paper shows that modifications of the surface properties account for the brightness decrease of GCC coated substrates with calendering. The effect of a deformable cartonboard substrate is investigated here and compared to a less deformable plastic film substrate. From simulations based on a two-layer Kubelka-Munk model, it is shown that the brightness decrease of the cartonboard due to calendering has a negligible contribution to the brightness decrease of the coated cartonboard. The brightness decrease was similar for coated plastic film and coated cartonboard. The thickness of GCC coated plastic films was not affected by calendering irrespectively of the pigment and latex size distribution. Monte Carlo light scattering simulations, taking into account the measured decrease of surface microroughness and increased effective refractive index, showed that surface modifications accounted for most of the observed brightness decrease of the GCC coated substrate, whereas the bulk scattering and absorption coefficients were not affected by calendering. It is also shown that the scattering coefficient is significantly dependent on the coat weight whereas the physical absorption coefficient is not.

  • 2.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    A Comparison Between the Coefficients of the Kubelka-Munk and DORT2002 Models2003Rapport (Övrigt vetenskapligt)
    Abstract [en]

    This paper gives the exact translation and between the scattering and absorption coefficients of the Kubelka-Munk and DORT2002 models. It is shown that the conditions, under which this exact translation is valid, are perfectly diffuse light, perfectly isotropic scattering, and only two channels in the DORT2002 model. Reasons for non-validity in other cases are given. It is also shown that it is possible to use grammage instead of thickness for DORT2002, as has previously been shown for Kubelka-Munk. Since the s and k values of the Kubelka-Munk model are so well known and in such widespread use, a translation to and from the DORT2002 coefficients will make it easy to use the models together, to compare results, and to change from one model to the other.

  • 3.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    A Fast and Stable Solution Method for the Radiative Transfer Problem2005Ingår i: SIAM Review, ISSN 0036-1445, E-ISSN 1095-7200, Vol. 47, nr 3, s. 447-468Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Radiative transfer theory considers radiation in turbid media, and is used in a wide range of applications. This paper outlines a problem formulation and a solution method for the radiative transfer problem in multilayer scattering and absorbing media, using discrete ordinate model geometry. A selection of different steps is brought together. The main contribution here is the synthesis of these steps, all of which have been used in different areas, but never all together in one method. First all necessary steps to get a numerically stable solution procedure are treated, and then methods are introduced to increase the speed by a factor of several thousand. This includes methods for handling strongly forward-scattering media. The method is shown to be unconditionally stable, whilst the problem was previously considered numerically intractable.

  • 4.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    A Two-Phase Parameter Estimation Method for Radiative Transfer Problems in Paper Industry Applications2008Ingår i: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 16, nr 7, s. 927-951Artikel i tidskrift (Refereegranskat)
    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.

  • 5.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Comparison of the DORT2002 Radiative Transfer Solution Method and the Kubelka-Munk Model2004Ingår i: Nordic Pulp & Paper Research Journal, ISSN 0283-2631, E-ISSN 2000-0669, Vol. 19, nr 3, s. 397-403Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The need for optical modeling of paper is obvious to provide connections between its optical response and the actual properties of the paper. It is argued that modern solution methods from radiative transfer theory could be considered instead of the Kubelka-Munk model, and a specific example, DORT2002, is tested. It is shown that Kubelka-Munk is a simple special case of DORT2002, and the two models and their coefficients are compared. A comprehensive list of advantages for the applied user of a model with higher dimensionality is supplied. It is shown, by the use of DORT2002, that when the medium has finite thickness, the light distribution deviates from the perfectly diffuse even under the theoretically ideal conditions for which Kubelka-Munk was created. This effect causes errors in Kubelka-Munk reflectance calculations that may be up to 20% and more, even for a grammage of 80 g/m2. The magnitude of the error shows a strong dependence on the degree of light absorption, with higher absorption giving greater error. DORT2002 can well be considered for increased understanding in cases where the level of accuracy of Kubelka-Munk reflectance calculations is not sufficient.

  • 6.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Efficient Reflectance Calculations and Parameter Estimation Methods for Radiative Transfer Problems in Paper Industry Applications2007Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Very fast code for standardized d/0° reflectance calculations and an efficient Gauss-Newton parameter estimation method are introduced into the radiative transfer based light scattering simulation tool DORT2002, which makes it competitive in paper industry applications. Outstanding problems in general radiative transfer theory are addressed in a paper industry application. The parameter estimation problem is given a least-squares formulation, different solution methods are evaluated, some characteristics of the problem are found, and the sensitivity of the solution is analyzed. Tests show that Gauss-Newton type methods are most suitable for the studied parameter estimation problem; superior performance was shown with respect to both robustness and speed. The parameter estimation problem is shown to be non-trivial and sometimes ill-conditioned. The type of analyses made in this work give good insight in the character of the problem, and similar studies will be valuable in the future design of measurements and parameter estimation methods when using angle-resolved measurements to estimate also the asymmetry factor.

  • 7.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Examination of the Revised Kubelka-Munk Theory: Considerations of Modeling Strategies2007Ingår i: Journal of the Optical Society of America A, ISSN 0740-3232, Vol. 24, nr 2, s. 548-556Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The revised Kubelka-Munk theory is examined theoretically and experimentally. Systems of dyed paper sheets are simulated, and the results are compared with other models. The results show that the revised Kubelka-Munk model yields significant errors in predicted dye-paper mixture reflectances, and is not self-consistent. The absorption is noticeably overestimated. Theoretical arguments show that properties in the revised Kubelka-Munk theory are inadequately derived. The main conclusion is that the revised Kubelka-Munk theory is wrong in the inclusion of the so-called scattering-induced-path-variation factor. Consequently, the theory should not be used for light scattering calculations. Instead, the original Kubelka-Munk theory should be used where its accuracy is sufficient, and a radiative transfer tool of higher resolution should be used where higher accuracy is needed.

  • 8.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Fast and Stable Solution Method for Angle-Resolved Light Scattering Simulation2002Rapport (Övrigt vetenskapligt)
    Abstract [en]

    This report extensively treats a problem formulation of and a solution method to the radiative transfer problem, including some adaptations to the area of light scattering in paper and print. The resulting model is referred to as DORT2002, and has been implemented in MATLAB using a discrete ordinate model geometry. The main steps to get a numerically stable solution procedure include the continuous formulation with expansion in Legendre functions and Fourier cosine series, the evaluation of normalized associated Legendre functions, the choice of numerical quadrature, the matrix formulation of the discretization, the reduction of the eigenvalue problem, the preconditioning of the system of equations for the boundary conditions, and the avoidance of over- and underflow in the solution and interpolation formulas. Important are also the recognition of potential divide-by-zero situations, and reformulation of those. Comments are given on possible applications in the paper and printing industries. It is suggested that the Kubelka-Munk model should be replaced with DORT2002 in most applications.

  • 9.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Fast and Stable Solution Method for Angle-Resolved Light Scattering Simulation III: Handling Refractive Index Discontinuities2005Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The change in refractive index that occurs at the interface between air and an ink-paper substrate causes effects such as refraction and total reflection. This report uses radiative transfer theory to account for these effects exactly, and for any measurement geometry, without approximations and without unknown constants. This is in contrast with Kubelka-Munk and the Saunderson correction, which is only an approximation and only for integrating sphere geometry, and which requires non-trivial determination of unknown constants. This report continues previous work, and extends the solution procedure of DORT2002 to handle a discontinuous change in refractive index at the interface between two perfectly flat layers. The result of a large number of consistency and accuracy tests are presented, and they are all positive. Some comments on planned and suggested future work are given regarding direct and inverse model development, but also for comparative studies. Comments are also given on the benefit of this work for the paper and printing industries. It is suggested that the Kubelka-Munk model should be replaced with DORT2002 in most applications.

  • 10.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Inverse Scattering: athematical Modelling in a Changing World, Berlin2001Konferensbidrag (Övrigt vetenskapligt)
  • 11.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Ljus idé kastar nytt ljus på ljusspridning i papper och tryck: Ekmandagarna, Stockholm2007Konferensbidrag (Övrigt vetenskapligt)
  • 12.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Made in Sweden – Future Textiles and Paper: Strategic research and innovation agenda for the joint paper and textile industries in Sweden2013Övrigt (Övrig (populärvetenskap, debatt, mm))
  • 13.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Mathematical modeling and numerical tools for simulation and design of light scattering in paper and print2007Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    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.

  • 14.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Mathematical Modelling of Light Scattering in Paper and Print2004Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    A problem formulation and a solution method are outlined for the radiative transfer problem in vertically inhomogeneous scattering and absorbing media, using discrete ordinate model geometry. The treatment spans from the physical problem via a continuous formulation, a discretization and a numerical analysis, to an implementation with performance evaluation and application to real-world problems. The thesis clearly illustrates how considerations in one step affect other steps, and thus provides an example of an overall treatment of mathematical modeling of a large applied problem. A selection of different steps is brought together. First all the steps necessary to get a numerically stable solution procedure are treated, and then methods are introduced to increase the speed by a factor of several thousand. The solution procedure is implemented in MATLAB under the name of DORT2002, and is adapted primarily to light scattering simulations in paper and print. A confined presentation is given of the effect of the steps that are needed, or possible, to make any discrete ordinate radiative transfer solution method numerically efficient. This is done through studies of the numerical performance of DORT2002. Performance tests show that the steps that are included to improve stability and speed of DORT2002 are very successful. Together they give an unconditionally stable solution method to a problem previously considered numerically intractable, and decrease computation time compared to a naive implementation with a factor of 1 000 � 10 000 in typical cases and with a factor up to and beyond 10 000 000 in extreme cases. It is also shown that the speed increasing steps are not introduced at the cost of reduced accuracy, and that DORT2002 converges to the true value as the discretization is made finer. It is shown by the use of DORT2002 that when a medium has a finite thickness, the light distribution deviates from the perfectly diffuse even under the theoretically ideal conditions for which the Kubelka-Munk model was created. This effect, which is in opposition to what one would intuitively expect, is caused by light escaping through the lower boundary of the medium, and causes errors in Kubelka-Munk reflectance calculations that can be up to 20% and more, even for a grammage of 80 g/m2. The magnitude of the error shows a strong dependence on the degree of absorption, with higher absorption giving greater error. This confirms previously reported problems with Kubelka-Munk for strongly absorbing media, and DORT2002 offers a partial explanation of these problems, as it can describe this effect and quantify the Kubelka-Munk errors. It is argued that DORT2002 could well be considered for increased understanding in cases where the level of accuracy of Kubelka-Munk reflectance calculations is not acceptable. A comprehensive list of advantages for the applied user of a model with higher dimensionality is supplied.

  • 15.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Modeller och metoder för ljusspridning i papper: Ekmandagarna, Stockholm2002Konferensbidrag (Övrigt vetenskapligt)
  • 16.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Next Generation Simulation Tools for Optical Properties in Paper and Print2008Ingår i: Proc. International Conference Modelling and Simulation in the Pulp and Paper Industry, Madrid, 2008Konferensbidrag (Refereegranskat)
  • 17.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Next Generation Simulation Tools for Optical Properties in Paper and Print2008Ingår i: International Conference Modeling and Simulation in the Pulp and Paper Industry, 2008, s. 156-169Konferensbidrag (Refereegranskat)
    Abstract [en]

    A large number of optical properties in paper and print are determined by measuring the light reflected from an illuminated paper surface. These measurements are interpreted through a model, and the one that has been in use in the paper industry since the 1930’s (Kubelka-Munk) is deficient in some respects. This paper presents a selection of issues that will be in focus for future optical modeling, and shows what the next generation simulation tools may look like.

    The anisotropy of the scattered light becomes increasingly important, and this will open up a large area of research that will both explain a number of outstanding issues and open for a new kind of material property design. Physically objective material parameters will be introduced instead of phenomenological model parameters. The wish to model the real structure of paper and printed paper products instead of homogenized approximations will drive the development of Monte Carlo models with greater explanative power, which in turn will give an increased need for characterization methods. Differences in optical standards between the paper and graphic arts industries will force harmonization or models for data exchange. The treatment of UV and fluorescence will be included in both light scattering simulation tools and color management tools, and there will be attempts of merging these two types of tools, which will open for another view on color reproduction. The directions of development outlined above are exemplified with recent results.

  • 18.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för informationsteknologi och medier.
    Numercal performance of the DORT2002 radiative transfer Solution methodManuskript (preprint) (Övrigt vetenskapligt)
  • 19.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Numerical Performance of Stability Enhancing and Speed Increasing Steps in Radiative Transfer Solution Methods2009Ingår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 228, nr 1, s. 104-114Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Methods for solving the radiative transfer problem, which are crucial for a number of sectors of industry, involve several numerical challenges. DORT2002 is a fast and numerically stable solution method for this problem, and has been implemented in MATLAB. This paper studies the numerical performance of DORT2002, in terms of stability, speed and accuracy. Focus is on the effects of the steps that are needed to make the method numerically efficient, and that differ from a naive implementation. Performance tests show that the steps that are included to improve stability and speed of DORT2002 are very successful. Together they give an unconditionally stable solution method to a problem previously considered numerically intractable, and decrease computation time compared to a naive implementation with a factor 1 000-10 000 in typical cases and with a factor up to and beyond 10 000 000 in extreme cases. It is also shown that the speed increasing steps are not introduced at the cost of reduced accuracy. Further studies and developments, that can have a positive impact on computation time, are suggested.

  • 20.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Radiative transfer i pappersindustriella tillämpningar2010Ingår i: Thule: Kungl. Skytteanska Samfundets Årsbok 2010 / [ed] R. Jacobsson, Umeå: Kungl. Skytteanska Samfundet , 2010, s. 115-124Kapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 21.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Simulation and modeling of light scattering in paper and print applications2010Ingår i: Light Scattering Reviews, vol 5, Part 3 / [ed] Kokhanovsky, A., Springer, 2010, s. 451-475Kapitel i bok, del av antologi (Övrigt vetenskapligt)
    Abstract [en]

    When developing and applying models to light scattering problems, things usually turn very mathematical. This is all in good order, but it may also be a hindrance for a broader audience to gain insight into the overall issues. This chapter aims at discussing a range of light scattering simulation and modeling issues with a minimum of mathematics involved, and with the specific perspective of paper and printing industry applications. Shorter sections of mathematical content are included, but the mathematically interested reader is here pointed to selected references and other chapters in this volume.

  • 22.
    Edström, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Bohlin, Erik
    Coppel, Ludovic
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för informationsteknologi och medier.
    Andersson, Caisa
    Characterization and modelling of the effect of calendering on coated polyester film2009Ingår i: Advances in Printing and Media Technology, vol 36, International Association of Research Organizations for the Information, Media and Graphic Arts Industrie (IARIGAI), 2009Konferensbidrag (Refereegranskat)
  • 23.
    Edström, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Granberg, H
    Gulliksson, Mårten
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Some Ideas on Models and Methods for Light Scattering in Paper2001Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this report a short overview is given on existing models for simulating light scattering in paper. The well known Kubelka-Munk model somewhat oversimplifies the problem. Newer discrete ordinate models take into account more aspects, e.g. angle resolved scattering, but have intrinsic ill-conditioned problems that have to be overcome. No existing models are designed to solve the inverse problem, i.e. finding model parameters given real light scattering measurements. Therefore we propose a Stable Multilayer Discrete Ordinate Radiative Transfer model, SM-DORT, to simulate the scattering of light in coated paper and similar structures, and to solve the corresponding inverse problem. We discuss improvements of existing models, for making SM-DORT stable to give reliable results in spite of intrinsic ill-conditioned problems, and for making it fast to efficiently solve the inverse problem. In this report we also cover some aspects of inverse problems in general, we give some ideas on further model improvement to take into account more aspects of light scattering in paper, and we discuss model validation, using experiments and existing models.

  • 24.
    Edström, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gustafsson Coppel, Ludovic
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Open PaperOpt – A Monte Carlo Simulation Tool for Simulating Light Scattering in Paper and Print2010Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The Kubelka-Munk model and extensions thereof are extensively used in product development, thanks to their simplicity and the fact that they are invertible. However, their explanative power is limited to distinguishing processes that affect scattering properties from those that affect absorption properties, an example being the frequently observed decrease of the scattering coefficient with calendering. Better understanding of how internal structural changes affect the optical properties requires modelling the composite structure of a paper layer. We propose a modular object-oriented Open Source Monte Carlo simulation platform, Open PaperOpt, which allows different geometrical representations of the inner paper structure. The proposed file formats open for a standardisation that facilitates data exchange between different simulation tools and measuring instruments, and supports a broad dissemination of the simulation software.

  • 25.
    Edström, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Lehto, Marcus
    DORT2002 version 2.0 User Manual2003Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The DORT2002 software is a fast and accurate tool for solving radiative transfer problems in vertically inhomogeneous turbid media, using a discrete ordinate model geometry. DORT2002 is implemented in MATLAB, and is adapted to light scattering simulations in paper and print. The DORT2002 Graphical User Interface is a tool developed to provide users with a fast and easy way of performing DORT2002 simulations. It works as a shell that encapsulates the parameters and the function calls, and offers powerful simulations through a mouse click. This report gives a thorough description of how to install and use DORT2002, version 2.0, and the Graphical User Interface.

  • 26.
    Edström, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Lehto, Marcus
    Fast and Stable Solution Method for Angle-Resolved Light Scattering Simulation II - Model Enhancements2003Rapport (Övrigt vetenskapligt)
    Abstract [en]

    This report continues previous work to extensively treat a solution method to the radiative transfer problem. Several enhancements have been made, including handling of multilayer structures, handling of sharply peaked phase functions, and code optimization. The resulting model is referred to as DORT2002, now in version 2.0, and has been implemented in MATLAB using a discrete ordinate model geometry. The introduction of a graphical user interface makes the model easy to use, and any desired simulation is just a button-click away. The main steps to get a numerically stable multilayer solution procedure include the preconditioning of the system of equations for the boundary and continuity conditions, and the avoidance of over- and underflow in the multilayer solution and interpolation formulas. Important are also the recognition of potential divide-by-zero situations, and reformulation of those. Several measures are taken to make the code fast. This includes exploitation of the sparse structure of the system of equations for the boundary and continuity conditions. Several features allow high speed by maintaining accuracy at significantly lower number of channels than would otherwise be needed, or by automatically stopping calculations earlier when certain convergence criteria have been met. Comments are given on possible applications in the paper and printing industries. It is suggested that the Kubelka-Munk model should be replaced with DORT2002 in most applications.

  • 27.
    Edström, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Lehto, Marcus
    Performance and application of the DORT2002 light scattering simulation model2003Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Models for calculating the light intensity inside an illuminated turbid medium, e.g. paper, involve several numerical challenges, and are crucial for the paper and printing industries. DORT2002 is a fast and numerically stable solution procedure for this problem, which has been implemented in MATLAB. This report studies the performance and application of DORT2002, and is the documentation of an extensive test series. All major steps that are taken to improve stability and speed of DORT2002 are discussed, and the resulting improvements are illustrated. Comparison of accuracy, applicability and speed between DORT2002 and three other models when applied to different sets of relevant test problems is covered. The performance tests show that the steps that are taken to improve stability and speed of DORT2002 are very successful, together giving an unconditionally stable solution procedure to a problem previously considered numerically intractable, and together decreasing computation time with a factor 1 000-10 000 in typical cases and with a factor up to and beyond 10 000 000 in extreme cases. Further investigations and developments are suggested, that can have a large positive impact on computation time. The application tests show very good agreement with three other model types. DORT2002 is shown to have better accuracy and much larger range of applicability than Kubelka-Munk, and to be much faster than Grace in relevant test cases. It is also shown that DORT2002 and Grace have good agreement, and that the agreement between the results from DORT2002 and DISORT  which is claimed to be the finest radiative transfer software available - is very good without exception, which gives strong support for the accuracy of DORT2002. The conclusion is that Kubelka-Munk should be replaced with DORT2002 for most applications, and that a combination of Grace and DORT2002 should be used for accurate modeling of paper and print.

  • 28.
    Edström, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Neuman, Magnus
    Avramidis, Stefanos
    Andersson, Mattias
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Geometry Related Inter-Instrument Differences in Spectrophotometric Measurements2010Ingår i: Nordic Pulp & Paper Research Journal, ISSN 0283-2631, E-ISSN 2000-0669, Vol. 25, nr 2, s. 221-232Artikel i tidskrift (Refereegranskat)
    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.

  • 29.
    Edström, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Pauler, Nils
    Norberg, Ole
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Mechanisms involved in the optical interaction between ink and substrate2009Ingår i: Advances in Printing and Media Technology, vol 36, International Association of Research Organizations for the Information, Media and Graphic Arts Industrie (IARIGAI), 2009Konferensbidrag (Refereegranskat)
    Abstract [en]

    It is known that colour reproduction of inkjet comprises a range of mechanisms. It was possible to understand and

    explain some of these mechanisms by evaluating print tests with standard optical measurement and by calculations

    using algorithms of the Kubelka Munk and Murray Davies theories. The combined interaction of the substrate, the

    ink penetration, the optical properties of the inks and the dot size were clarified. Large colour gamut is governed by

    low ink penetration, low light scattering of the substrate and small dot size. The non-ideal property of process inks

    and the continuous tone character of colour reproduction of the studied desktop inkjets explained the observed

    convex shape of the colour gamut. For plain paper, dye-based and pigment-based inks were shown to follow different

    mechanisms, with lower penetration of the pigment-based ink. Colour gamut could be increased by a surface

    treatment that further reduced the penetration, but this treatment worked only for the pigment-based inks. Internal

    sizing of plain paper had only a very small influence on colour gamut for dye-based ink, even though the ink

    penetration was reduced.

  • 30.
    Edvardsson, Sverker
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Neuman, Magnus
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Gulliksson, Mårten
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Olin, Håkan
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Role of the particle method DFPM for solving linear equationsManuskript (preprint) (Övrigt vetenskapligt)
  • 31.
    Edvardsson, Sverker
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Neuman, Magnus
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Olin, Håkan
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Solving equations through particle dynamics2015Ingår i: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 197, s. 169-181Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The present work evaluates a recently developed particle method (DFPM). The basic idea behind this method is to utilize a Newtonian system of interacting particles that through dissipation solves mathematical problems. We find that this second order dynamical system results in an algorithm that is among the best methods known. The present work studies large systems of linear equations. Of special interest is the wide eigenvalue spectrum. This case is common as the discretization of the continuous problem becomes dense. The convergence rate of DFPM is shown to be in parity with that of the conjugate gradient method, both analytically and through numerical examples. However, an advantage with DFPM is that it is cheaper per iteration. Another advantage is that it is not restricted to symmetric matrices only, as is the case for the conjugate gradient method. The convergence properties of DFPM are shown to be superior to the closely related approach utilizing only a first order dynamical system, and also to several other iterative methods in numerical linear algebra. The performance properties are understood and optimized by taking advantage of critically damped oscillators in classical mechanics. Just as in the case of the conjugate gradient method, a limitation is that all eigenvalues (spring constants) are required to be of the same sign. DFPM has no other limitation such as matrix structure or a spectral radius as is common among iterative methods. Examples are provided to test the particle algorithm’s merits and also various performance comparisons with existent numerical algorithms are provided.

  • 32.
    Engström, Clas
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för informationsteknologi och medier.
    Pauler, Nils
    Wågberg, Jerker
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för informationsteknologi och medier.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Final Report on the Project: Optical Interaction between Ink and Paper2007Rapport (Övrigt vetenskapligt)
  • 33.
    Feng, Tao
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Gulliksson, Mårten
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Levenberg-Marquardt Methods for Parameter Estimation Problems in the Radiative Transfer Equation2007Ingår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 23, nr 3, s. 879-891, artikel-id 002Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A discrete ordinate method is developed for solving the radiative transfer equation, and the corresponding parameter estimation problem is given a least-squares formulation. Two Levenberg-Marquardt methods, a feasible-path approach and an SQP type method, are analyzed and compared. A sensitivity analysis is given, and it is shown how it can be used for designing measurements with minimal impact of measurement noise. Numerical experiments are performed to exemplify the usefulness of the theory.

  • 34. Granberg, H
    et al.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Quantification of the intrinsic error of the kubelka–munk model caused by strong light absorption2003Ingår i: Journal of Pulp and Paper Science (JPPS), ISSN 0826-6220, Vol. 29, nr 11, s. 386-390Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The Kubelka-Munk (KM) model is widely used within the paper industry to interpret diffuse reflectance factor measurements of paper and its components. It has been found in the literature that the addition of a dye colorant to a paper sheet not only increases its KM light absorption coefficient, but for strong absorption also decreases its KM light scattering coefficient. This effect has previously been attributed to the intrinsic error of the KM model induced by light absorption that tends to orient of the light fluxes perpendicular to the sheet. In the present work we have mapped the intrinsic error of the KM model by comparing light scattering calculations from the KM model with the more accurate Discrete Ordinate Radiative Transfer model DORT2002. We found that the models agree within 2.3% in reflectance, and that the intrinsic error in the KM model explains about 1/5 of the previously observed interdependence of the KM coefficients for heavily dyed sheets.

  • 35.
    Gustafsson Coppel, Ludovic
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för informationsteknologi och medier.
    Andersson, Mattias
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för informationsteknologi och medier.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för informationsteknologi och medier.
    Determination of quantum efficiency in fluorescing turbid media2011Ingår i: Applied Optics, ISSN 1559-128X, E-ISSN 2155-3165, Vol. 50, nr 17, s. 2784-2792Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A method is proposed to estimate the optical parameters in a fluorescing turbid medium with strong absorption for which traditional Kubelka–Munk theory is not applicable, using a model for the radiative properties of optically thick fluorescent turbid media of finite thickness proposed in 2009[J. Opt. Soc. Am. A26, 1896 (2009)JOAOD60740-323210.1364/JOSAA.26.001896]. The method is successfully applied to uncoated papers with different thicknesses. It is found that the quantum efficiency of fluorescent whitening agents (FWAs) is nearly independent of the fiber type, FWA type, FWA concentration, and filler additive concentration used in this study. The results enable an estimation of the model parameters as function of the FWA concentration and substrate composition. This is necessary in order to use the model for optimizing fluorescence in the paper and textile industries.

  • 36.
    Gustafsson Coppel, Ludovic
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Andersson, Mattias
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för informationsteknologi och medier.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Kinnunen, Jussi
    Univ Eastern Finland, Dept Math & Phys, FI-80101 Joensuu, Finland.
    Limitations of the efficiency of fluorescent whitening agents in uncoated paper2011Ingår i: Nordic Pulp & Paper Research Journal, ISSN 0283-2631, E-ISSN 2000-0669, Vol. 26, nr 3, s. 319-328Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The fluorescence efficiency of one fluorescent whitening agent (FWA) inuncoated and unfilled paper was characterised at different FWA concentrations. An extendedKubelka-Munk model proposed earlier by several authors was applied to quantify the effect onCIE whiteness of absorption of the FWA in the visible spectrum . At high FWA concentration,chemical interactions slightly modify the emission spectrum of the FWA, and the quantumefficiency depends on the FWA concentration. This effect has however a negligible effect onthe CIE whiteness for FWA concentrations used in practice. The overlap of the absorption andemission bands of the FWA is shown to be the main cause of greening (a shift of thechromaticity towards green) and saturation of the fluorescence effect. With increasing FWAconcentration, the positive effect of fluorescence is neutralised by the reduction of thereflectance factor in the violet-blue region of the spectrum induced by a significant absorptionof the FWA in that region.

  • 37.
    Gustafsson Coppel, Ludovic
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Andersson, Mattias
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Neuman, Magnus
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Fluorescence model for multi-layer papers using conventional spectrophotometers2012Ingår i: Nordic Pulp & Paper Research Journal, ISSN 0283-2631, E-ISSN 2000-0669, Vol. 27, nr 2, s. 418-425Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present an extension of a Kubelka-Munk based fluorescence model in which we introduce an apparent scattering (SUV) and absorption (KUV) coefficient for all wavelengths below 400 nm. We describe a method for modelling the total radiance factor of multi-layer papers and for estimating the optical parameters (S, K and Q) of each layer. Assuming that the fluorescent whitening agent only absorbs below 400 nm, we are able to determine SUV, KUV and the apparent quantum efficiency, Q(UV,l) for 400 nm<l<700 nm, from spectral radiance measurements in the visual part of the electromagnetic spectrum. We test the proposed method on different layered constructions made of three individual pilot paper layers. The proposed method allows the papermaker to determine the illumination independent fluorescence characteristics of single- and multilayer paper layers using a conventional single-monochromator spectrophotometer operating in the visible part of the electromagnetic spectrum, and also to predict the radiance factor of fluorescing layered papers.

  • 38.
    Gustafsson Coppel, Ludovic
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Open source Monte carlo simulation platform for particle level simulation of light scattering from generated paper structures2009Ingår i: Papermaking Research Symposium, 2009Konferensbidrag (Refereegranskat)
  • 39.
    Gustafsson Coppel, Ludovic
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Neuman, Magnus
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Extension of the Stokes equation for layered constructions to fluorescent turbid media2012Ingår i: Journal of the Optical Society of America A, ISSN 1084-7529, Vol. 29, nr 4, s. 574-578Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Expressions relating the bispectral reflectance of a stack of n fluorescinglayers to each individual layer's reflectance and transmittance arederived. This theoretical framework is used together with recentlyproposed extensions of the Kubelka--Munk model to study the fluorescencefrom layered turbid media. For one layer over a reflecting background,the model is shown to give the same results as a previous model.The extension to n layers with different optical properties allowssimulating the bispectral reflectance from a pad of layered turbidmedia. The applicability of the model is exemplified with an optimizationof fluorophore distribution in layered turbid media.

  • 40.
    Gustafsson Coppel, Ludovic
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Neuman, Magnus
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för informationsteknologi och medier.
    Lateral light scattering in paper - MTF simulation and measurement2011Ingår i: Optics Express, ISSN 1094-4087, E-ISSN 1094-4087, Vol. 19, nr 25, s. 25181-25187Artikel i tidskrift (Refereegranskat)
    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.

  • 41.
    Hägglund, Håkan
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Norberg, Ole
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Non-destructive high resolution measurements of spatial filler content distribution in paper2013Ingår i: Nordic Pulp & Paper Research Journal, ISSN 0283-2631, E-ISSN 2000-0669, Vol. 28, nr 1, s. 131-136Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this work, a non-destructive method is presented that enables the measurement of filler content in paper with high spatial resolution. The method uses an X-ray fluorescence setup that enables high resolution measurements of calcium content in the paper, together with a beta radiography measurement method, to assess the local filler content in the paper. An image registration method is used to combine the two measurement maps, and a calibration polynomial is applied to the point-wise values in order to calculate the local filler content. The measurement methods show good accuracy. The grammage and the calcium content can be measured at a spatial resolution of 0.1 mm × 0.1 mm but the resolution for the filler content map was in this work chosen to 1 mm × 1 mm in order to minimize image registration errors. The method is illustrated using two paper samples, a laboratory paper and a commercial 80 g/m2 copy paper. From the methods used in this work, a difference is shown between the two paper samples in how the filler content distribution is related to the paper formation. With the help of image registration, point-wise measurements of filler content from both sides of the samples can be compared. The method can be used together with other high resolution measurements in order to analyze the simultaneous interrelation between different paper properties. The high resolution measurements of filler content will be particularly valuable for the analysis of the underlying causes to optical variations in paper and print.

  • 42.
    Hägglund, Håkan
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap. Metsa Board Sverige AB, Husum Mill, SE-89680 Husum, *Sweden.
    Norberg, Ole
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap. Umea Univ, SE-90187 Umea, Sweden.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Prediction of optical variations in paper from high resolution measurements of paper properties2013Ingår i: Nordic Pulp & Paper Research Journal, ISSN 0283-2631, E-ISSN 2000-0669, Vol. 28, nr 4, s. 596-601Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A method to predict optical variations from high resolution measurementsof paper properties is evaluated in this work. The method combines thepoint-wise values of high resolution maps of filler content and grammagewith an empirical model derived in an earlier study to predict thespatial optical variations in paper.The method has been applied on two paper samples, a laboratory paper anda commercial 80 g/m(2) copy paper. The optical variations have beenpredicted at a scale of 1 mm(2). Validation has been made by using ahigh resolution spectrophotometric setup to measure the spatialreflectance variations in the paper. The results show that for thesamples used, the influence of filler content variations and densityvariations on the optical variations is small compared to influence ofthe grammage variations.

  • 43.
    Hägglund, Håkan
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Norberg, Ole
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Neuman, Magnus
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för informationsteknologi och medier.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Dependence between paper properties and spectral optical response of uncoated paper2012Ingår i: Nordic Pulp & Paper Research Journal, ISSN 0283-2631, E-ISSN 2000-0669, Vol. 27, nr 2, s. 440-444Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper presents a method to describe, with good accuracy, the relation between variations in paper properties and variations of the spectral optical response of an uncoated paper. The dependence between density, filler content, grammage, and the spectral optical response is characterized by a multivariate model. The model is based on large-scale measurements data on a set of paper samples that have been produced with different values of grammage, density and filler content, representing the variations within a normal 80 g/m2 uncoated paper. From the optical measurements the light scattering (s) and light absorption (k) coefficients have been estimated according to the Kubelka-Munk theory.The results from this study will give valuable input to optical modeling activities, where the optical variations are predicted from measured small-scale variations in underlying paper properties.The variations in the paper properties can be used to model the light scattering coefficient, s, but there were too small variations in the light absorption coefficient, k, to find any significant dependence to the paper properties for the samples studied in this work. Furthermore, linear models give sufficient accuracy in the intervals studied. Additional findings from this study are the different effects of wet-pressing and calendering on the light scattering coefficient. 

  • 44.
    Johansson, Niklas
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Neuman, Magnus
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Andersson, Mattias
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Influence of finite-sized detection solid angle on bidirectional reflectance distribution function measurements2014Ingår i: Applied Optics, ISSN 1559-128X, E-ISSN 2155-3165, Vol. 53, nr 6, s. 1212-1220Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper deals with limitations and often overlooked sources of error introduced in compact double-beam goniophotometers. It is shown that relative errors in measured radiance factor, comparable to the total measurement uncertainty, can be introduced if recommended corrections are not carried out. Two different error sources are investigated, both related to the size of the detection solid angle. The first is a geometrical error that occurs when the size of the illuminated area and detector aperture are comparable to the distance between them. The second is a convolution error due to variations in radiant flux over the detector aperture, which is quantified by simulating the full 3D bidirectional reflectance distribution function (BRDF) of a set of samples with different degrees of anisotropic reflectance. The evaluation is performed for a compact double-beam goniophotometer using different detection solid angles, and it is shown that both error sources introduce relative errors of 1%–3%, depending on viewing angle and optical properties of the sample. Commercially available compact goniophotometers, capable of absolute measurements, are becoming more and more common, and the findings in this paper are therefore important for anyone using or planning to use this type of instrument.

  • 45.
    Johansson, Niklas
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Neuman, Magnus
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Andersson, Mattias
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Separation of surface and bulk reflectance by absorption of bulk scattered light2013Ingår i: Applied Optics, ISSN 1559-128X, E-ISSN 2155-3165, Vol. 52, nr 19, s. 4749-4754Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A method is proposed for separating light reflected from turbid media with a rough surface into a bulkand a surface component. Dye is added to the sample, thereby increasing absorption and canceling bulkscattering. The remaining reflected light is surface reflectance, which can be subtracted from the totalreflectance of an undyed sample to obtain the bulk component. The method is applied to paper wherethe addition of dye is accomplished by inkjet printing. The results show that the bulk scattered light isefficiently canceled, and that both the spectrally neutral surface reflectance and the surface topographyof the undyed paper is maintained. The proposed method is particularly suitable for characterization ofdielectric, highly randomized materials with significant bulk reflectance and rough surfaces, which aredifficult to analyze with existing methods. A reliable separation method opens up for new ways of analyzing,e.g., biological tissues and optical coatings, and is also a valuable tool in the development of morecomprehensive reflectance models.

  • 46.
    Johansson, Niklas
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Neuman, Magnus
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Andersson, Mattias
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    The inverse radiative transfer problem - considerations for optically thick mediaArtikel i tidskrift (Refereegranskat)
  • 47.
    Karlsson, Anette
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Enberg, Sofia
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Rundlöf, Mats
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Paulsson, Magnus
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Determining optical properties of mechanical pulps: Sheetmaking procedure and investigation of different ways to evaluate light absorption2012Ingår i: Nordic Pulp & Paper Research Journal, ISSN 0283-2631, E-ISSN 2000-0669, Vol. 27, nr 3, s. 531-541Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A method to produce representative sheets for determination of optical properties of mechanical pulps has been developed. It reduces the risk of contamination and discoloration and can be used with small pulp quantities. The deviation from the expected linear behaviour of the light scattering coefficient, s, at wavelengths corresponding to strong light absorption, has been studied using the Kubelka-Munk model and the angular resolved DORT2002 radiative transfer solution method. This decrease in s could not be explained by errors introduced in the Kubelka-Munk modelling by anisotropic scattering. Linear extrapolation of s can therefore not be justified as a way to obtain a more correct light absorption coefficient, k. For thepulps studied, the decrease in s at short wavelengths had little effect on k at 457 nm.

  • 48.
    Linder, Tomas
    et al.
    Department of Computer Science, Electrical and Space Engineering Luleå University of Technology.
    Löfqvist, Torbjörn
    Department of Computer Science, Electrical and Space Engineering Luleå University of Technology.
    Gustafsson Coppel, Ludovic
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Neuman, Magnus
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Lateral light scattering in fibrous media2013Ingår i: Optics Express, ISSN 1094-4087, E-ISSN 1094-4087, Vol. 21, nr 6, s. 7835-7840Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Lateral light scattering in fibrous media is investigated by computing the modulation transfer function (MTF) of 22 paper samples using a Monte Carlo model. The simulation tool uses phase functions from infinitely long homogenous cylinders and the directional inhomogeneity of paper is achieved by aligning the cylinders in the plane. The inverse frequency at half maximum of the MTF is compared to both measurements and previous simulations with isotropic and strongly forward single scattering phase functions. It is found that the conical scattering by cylinders enhances the lateral scattering and therefore predicts a larger extent of lateral light scattering than models using rotationally invariant single scattering phase functions. However, it does not fully reach the levels of lateral scattering observed in measurements. It is argued that the hollow lumen of a wood fiber or dependent scattering effects must be considered for a complete description of lateral light scattering in paper.

  • 49.
    Namedanian, Mahziar
    et al.
    Department of Science and Technology, Linköping University, Norrköping, Sweden .
    Gustafsson Coppel, Ludovic
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Neuman, Magnus
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Gooran, Sasan
    Department of Science and Technology, Linköping University, Norrköping, Sweden .
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Kolseth, Petter
    Nsieme Consulting, Sweden .
    Koh, Wei
    Analysis of Optical and Physical Dot Gain by Microscale Image Histogram and Modulation Transfer Functions2013Ingår i: Journal of Imaging Science and Technology, ISSN 1062-3701, E-ISSN 1943-3522, Vol. 57, nr 2, s. 020504-1-020504-5Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The color of a print is affected by ink spreading and lateral light scattering in the substrate, making printed dots appear larger. Characterization of physical and optical dot gain is crucial for the graphic arts and paper industries. We propose a novel approach to separate physical from optical dot gain by use of a high-resolution camera. This approach is based on the histogram of microscale images captured by the camera. Having determined the actual physical dot shape, we estimate the modulation transfer function (MTF) of the paper substrate. The proposed method is validated by comparing the estimated MTF of 11 offset printed coated papers to the MTF obtained from the unprinted papers using measured and Monte Carlo simulated edge responses.

  • 50.
    Neuman, Magnus
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Coppel, Ludovic
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Edström, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Point spreading in turbid media with anisotropic single scattering2011Ingår i: Optics Express, ISSN 1094-4087, E-ISSN 1094-4087, Vol. 19, nr 3, s. 1915-1920Artikel i tidskrift (Refereegranskat)
    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.

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