ink-paper interaction

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Linkoping Studies in Science and Technology

Dissertations No. 806

INK-PAPER INTERACTION

A study in ink-jet colorreproduction

Li Yang

Department of Science and Technology

Linkoping University, SE-601 74 Norrkoping, SwedenNorrkoping, April 2003


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INK-PAPER INTERACTIONA study in ink-jet color

reproduction

c Li Yang

Department of Science and Technology

Linkoping University

SE-601 74 NorrkopingSweden

ISBN 91-7373-613-9 ISSN 0345-7524

Printed in Sweden by UniTryck, Linkoping, 2003


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AbstractAn ink jet printing system consists of three fundamental parts: inks, printingengine, and substrates. Inks are materials creating color by selectively absorb-ing and scattering the visible illumination light. The printer acts as an inkdistributor that governs the ink application. Finally, the substrate acts as areceiver of the inks and forms the images. Ink setting on the substrate is acomplex process that depends on physical and chemical properties of the inksand the substrates, and their bilateral interactions. For a system consisting ofdye based liquid inks and plain paper, the ink moves together with the liquidcarrier before the pores absorb the liquid. This process contributes to seriousink spreading on the surface along the paper fibers. At the same time theink spreads down into the pore structure. This causes severe dot deformation,physical dot gain and ink penetration. Understanding the consequences ofthese phenomena and above all being able to characterize their impact on colorreproduction is of great importance. Moreover this knowledge is fundamentalfor finding solutions to ink-penetration related problems. This thesis presentsstudies of some important issues concerning image reproduction quality for dyebased ink-jet printing on ordinary plain paper (office copy paper), such as inkpenetration, optical dot gain, and even physical dot gain. The thesis beginswith theoretical developments to the Kubelka-Munk theory, which allows oneto study even non-uniform ink penetration into the substrate. With the knowl-edge of scattering and absorption coefficients and ink thickness, reflectance canbe computed by solving differential equations. Three forms of ink penetra-tion, uniform, linear, and exponential have been studied. A method is then

presented for obtaining fundamental properties of the inks from spectral re-flectance measurements, like the scattering- and absorption-power of inks, inklayer thickness, and ink mixing scheme for the generation of secondary colors.The method is further developed for modelling the ink penetration in printingsystems consisting of dye based liquid inks and plain paper. By combiningthe spectral reflectance measurements with theoretical simulations, quantitieslike the depth of ink penetration is determined. These quantities, in turn, areused to predict the spectral reflectance of prints. Simulated spectral reflectancevalues have been in fairly good agreement with experimental results. Modelsdealing with light scattering inside the substrate resulting in optical dot gainfor halftone printing, in the case of existing ink penetration, have been devel-oped for both mono- and multi-color printing. It is shown that the optical dotgain leads to higher color saturation than predications from Murray-Davis ap-proximation. Additionally, tentative studies for physical dot gain were made.Finally, an evaluation of the chromatic effects of the ink penetration for print-ing on office copy paper has been carried out based on both experimental dataand simulations. It is found that ink penetration has a dramatic impact onchroma and hue of the color, and the color saturation is significantly reduced


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by the ink penetration. Consequently, the capacity for color representation, orthe color gamut, is dramatically reduced by the ink penetration.


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AcknowledgementsDuring the years spent on this thesis work I got a lot of help from many peopleand in many ways.

First of all, I would like to express my sincere gratitude to my supervisorProfessor Bjorn Kruse for giving me the opportunity to pursue the study inhis group, sharing his broad and deep knowledge and experiences in GraphicArts. His suggestions, comments, and inspiration have sparked initiatives ofthe researches. His continuous efforts for establishing contacts with researchinstitutes and industries have been very helpful for promoting and improvingour work. His encouragement, appreciation, and sharp view of the subjects andworks have been particularly important. Words like I trust you have meanta lot.

Associate professor Reiner Lenz, has acted as co-supervisor in the last coupleof years. His questions, comments, criticisms, and discussions have been veryimportant inputs to the researches and the formulation of the dissertation. Hisenthusiasm and research style have been strong influence.

Senior researcher, Nils Pauler, in M-Real Research (Sweden), has been aparticularly important person outside of the university. He, together withProfessor Kruse, initiated collaboration in the studies of ink penetration. Hishelp in spectral reflectance measurement has been very important for havinga good start. His kindness and hospitality when I visited Ornskoldsvik havemade the research visits not only rewarding but also enjoyable. He and his teammember, Jerker Wagberg, have been wonderful people to collaborate with.

I would like to thank all group members, for creating an amicable and ac-

tive research atmosphere, providing courses and holding interesting seminars.Thanks Arash, Daniel, Linh, Sasan, and Thanh for pleasant coffee breaks andfree talks, and interesting discussions of various topics, from football to uni-verse.

Special thanks to Professor Hans Agren at Royal Technology Institute(KTH) for inviting me to Sweden, and for very fruitful collaborations duringthe time when we were at Physics Department (IFM) of Linkoping University.

Many thanks to our research engineers, especially Sven Franzen, for main-taining the office- and Lab-systems. Thanks to our secretaries, especially So-phie Lindesvik, for being very helpful in arranging conferences, travel affairs,and taking care of administrative tasks.

Thanks associated professor Stan Miklavcic who made a careful linguisticreading and valuable technical comments during the time he had to meet a fewdeadlines of himself. Thanks Dr. Sasan Gooran for a helpful proof reading.

I also wish to thank all my Chinese friends in Linkoping, Norrkoping, andother places, for their friendship and constant help, especially Fang Hong andLin Dan, Luo Yi and KeZhao, and QinZhong and ZhuangWei.

Thanks to Swedish Foundation for Strategic Research for financial support


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through the Surface Science Printing Program (S2P2).At last I wish to express my deepest gratitude to my wife Yan and our son

YiChen (Mikael), for their understanding and support, and the joys of our life.


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List of publications1. L. Yang and B. Kruse,Scattering and absorption of light in turbid

media, in Advance in Printing and Science and Technology 26 (2000)199-218;

2. L. Yang and B. Kruse,Ink penetration and its effects on printing,in Proc. IS&T SPIE Conf., 3963, 365-375, Jan. 2000, San Jose, CA;

3. L. Yang and B. Kruse,Yule-Nielsen effect and ink-penetration inmulti-chromatic tone reproduction, in Proc. IS&T NIP16 Conf.,363-366, Oct. 2000, Vancouver, Canada;

4. L. Yang, R. Lenz, and B. Kruse, Light scattering and ink penetra-

tion effects on tone reproduction, J. Opt. Soc. Am. A, 18 (2001)360-366;

5. L. Yang, S. Gooran and B. Kruse, Simulation of optical dot gain inmulti-chromatic tone production,J. Imaging. Sci. Tech.,45 (2001)198-204;

6. L. Yang and B. Kruse, Chromatic variation and color gamut re-duction due to ink penetration, inProc. TAGA Conf., 399-407, May6-9, 2001, San Diego, CA;

7. L. yang, B. Kruse, and N. Pauler,Modelling ink penetration in ink-jet printing, in Proc. IS&T NIP17 Conf., 731-734, Oct. 2001, FortLauderdale, FL;

8. L. Yang, R. Lenz, and B. Kruse, Light scattering and ink pene-tration effects on tone reproduction, in Proc. IS&T PICS Conf.,pp.225-230, Mar. 26-29, 2001, Oregon, PL;

9. L. Yang, Characterization of the inks and the printer in ink-jetprinting, in Proc. TAGA Conf., 255-265, Apr. 2002, Asheville, NC;

10. L. Yang,Modelling ink-jet printing: Does Kubelka-Munk theoryapply ?, in Proc. IS&T NIP18 Conf., 482-485, Sep. 2002, San Diego,CA;

11. L. Yang,Color reproduction of inkjet printing: model and sim-

ulation, J. Opt. Soc. Am. A, 2003 (accepted for publication);12. L. Yang, Determination for depth of ink penetration in ink-jet

printing, to be presented in TAGA Conference, May 2003, Montreal,Canada.


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Contents

Abstract iv

Acknowledgements vi

List of publications viii

Table of Contents ix

1 Introduction 11.1 Goal of the study . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Status of studies and our contribution . . . . . . . . . . . . . . 2

1.2.1 Extension to Kubelka-Munk theory . . . . . . . . . . . . 2

1.2.2 Evaluation of effects of ink penetration . . . . . . . . . . 31.2.3 Optical dot gain . . . . . . . . . . . . . . . . . . . . . . 51.3 Structure of the dissertation . . . . . . . . . . . . . . . . . . . . 6

2 Paper 92.1 Structures and properties of paper . . . . . . . . . . . . . . . . 9

2.1.1 Fibres, fillers and coating . . . . . . . . . . . . . . . . . 92.1.2 Density and porosity . . . . . . . . . . . . . . . . . . . . 10

2.2 Optical properties and measurements . . . . . . . . . . . . . . . 122.2.1 Brightness, opacity and gloss . . . . . . . . . . . . . . . 122.2.2 Optical measurements . . . . . . . . . . . . . . . . . . . 14

2.3 Paper permeability and mechanism of ink penetration . . . . . 18

3 Ink-jet printers and inks 213.1 Ink-jet technologies . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.1 The continuous ink-jet . . . . . . . . . . . . . . . . . . . 223.1.2 Drop-on-demand ink-jet . . . . . . . . . . . . . . . . . . 23

3.2 Characteristics of ink-jet printers . . . . . . . . . . . . . . . . . 25


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3.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2.2 HP970Cxi ink-jet printer . . . . . . . . . . . . . . . . . 27

3.3 Ink-jet ink technologies . . . . . . . . . . . . . . . . . . . . . . 273.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.2 Dye-based and pigment-based inks . . . . . . . . . . . . 28

4 Optical modelling: an overview 314.1 Radiative Transfer Theory . . . . . . . . . . . . . . . . . . . . . 314.2 Phase function . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.3 Multi-flux theory . . . . . . . . . . . . . . . . . . . . . . . . . . 334.4 Kubelka-Munk method . . . . . . . . . . . . . . . . . . . . . . . 344.5 Monte-Carlo simulation . . . . . . . . . . . . . . . . . . . . . . 35

5 Extended Kubelka-Munk theory and applications 395.1 Assumptions in Kubelka-Munk theory . . . . . . . . . . . . . . 395.2 Differential equations . . . . . . . . . . . . . . . . . . . . . . . . 40

5.2.1 Boundary conditions . . . . . . . . . . . . . . . . . . . . 425.2.2 Boundary reflection . . . . . . . . . . . . . . . . . . . . 43

5.3 Models of ink penetration . . . . . . . . . . . . . . . . . . . . . 455.3.1 Uniform distribution . . . . . . . . . . . . . . . . . . . . 455.3.2 Linear distribution . . . . . . . . . . . . . . . . . . . . . 465.3.3 Exponential distribution . . . . . . . . . . . . . . . . . . 46

5.4 Solutions of the differential equations . . . . . . . . . . . . . . . 475.4.1 Uniform ink distribution . . . . . . . . . . . . . . . . . . 475.4.2 Linear ink distribution . . . . . . . . . . . . . . . . . . . 505.4.3 Exponential distribution . . . . . . . . . . . . . . . . . . 54

5.5 Simulations for uniform- and linear-ink distribution . . . . . . . 555.5.1 Convergency of the series expansion. . . . . . . . . . . . 555.5.2 Optical effects of ink penetration . . . . . . . . . . . . . 575.5.3 Correction for boundary reflection . . . . . . . . . . . . 605.5.4 Effect on color gamut . . . . . . . . . . . . . . . . . . . 61

5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6 Characterization of inks and ink application 636.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.2 Experiment, data analysis and simulation . . . . . . . . . . . . 64

6.2.1 Samples and measurements . . . . . . . . . . . . . . . . 646.2.2 Data analysis and simulation . . . . . . . . . . . . . . . 65

6.3 Results and discussions . . . . . . . . . . . . . . . . . . . . . . 676.3.1 Spectral characteristics of the primary inks . . . . . . . 676.3.2 Spectral reflectance values and relative ink thicknesses of

the primary inks . . . . . . . . . . . . . . . . . . . . . . 68


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6.3.3 Spectral reflectance values and relative ink thickness ofsecondary colors . . . . . . . . . . . . . . . . . . . . . . 70

6.4 Remarks for application of Kubelka-Munk theory . . . . . . . . 72

6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

7 Characterization of ink penetration 75

7.1 Optical properties of plain paper . . . . . . . . . . . . . . . . . 75

7.2 Assumptions and notations . . . . . . . . . . . . . . . . . . . . 78

7.2.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 78

7.2.2 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . 79

7.3 Simulation of print on office copy-paper . . . . . . . . . . . . . 80

7.3.1 Primary colors . . . . . . . . . . . . . . . . . . . . . . . 80

7.3.2 Secondary colors . . . . . . . . . . . . . . . . . . . . . . 83

7.4 Optical effect of ink penetration . . . . . . . . . . . . . . . . . . 84

7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

8 Dot gain in black and white 89

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

8.1.1 Murray-Davis equation . . . . . . . . . . . . . . . . . . . 89

8.1.2 Yule-Nielsen equation . . . . . . . . . . . . . . . . . . . 90

8.1.3 Status of the studies . . . . . . . . . . . . . . . . . . . . 92

8.2 Model and methodology . . . . . . . . . . . . . . . . . . . . . . 93

8.2.1 Point spread function approach . . . . . . . . . . . . . . 93

8.2.2 Probability approach . . . . . . . . . . . . . . . . . . . . 968.2.3 Impacts of the optical dot gain . . . . . . . . . . . . . . 100

8.3 Overall dot gain of monochromatic colors . . . . . . . . . . . . 101

8.3.1 A model for overall dot gain . . . . . . . . . . . . . . . . 101

8.3.2 Simulation of the overall dot gain . . . . . . . . . . . . . 103

8.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

9 Dot gain in color 107

9.1 Reflectance of a multi-color image . . . . . . . . . . . . . . . . 107

9.2 Optical dot gain in multi-color tone reproduction . . . . . . . . 110

9.3 Simulation for multi-layer color image . . . . . . . . . . . . . . 111

9.3.1 Two inks of round dots: dot on dot . . . . . . . . . . . . 1129.3.2 Two inks of square dots: dot on dot . . . . . . . . . . . 115

9.3.3 Two inks of round dots: random dot distribution . . . . 117

9.4 The effects of optical dot gain on color reproduction . . . . . . 119

9.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119


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10 Chromatic effects of ink penetration 12110.1 Basics in colorimetry . . . . . . . . . . . . . . . . . . . . . . . . 121

10.1.1 C I E X Y Z color space . . . . . . . . . . . . . . . . . . . 12110.1.2 Chromaticity diagram . . . . . . . . . . . . . . . . . . . 12210.1.3 CIELAB color space . . . . . . . . . . . . . . . . . . . 122

10.2 Evaluation of chromatic effects from experimental data . . . . . 12310.2.1 Parallel comparison of prints on two types of substrates 12310.2.2 Two-dimensional representations of chromatic effects . . 125

10.3 Evaluation in 3D color space: simulations . . . . . . . . . . . . 12910.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

11 Summary and future work 13311.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

11.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

12 Appendix 137A Mathematical derivation for Equation (6.4) . . . . . . . . . . . 137B Probability model for optical gain . . . . . . . . . . . . . . . . . 138

Bibliography 140


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Chapter 1

Introduction

Ink-jet printing a is commercially young but rapidly developing printing tech-nology. Success in making printers of high print resolution, color capacity, yetvery affordable price has made ink-jet printers available not only for big com-panies, but also for private users and small business units. According to CapVentures [Ash01], of all the printing applications, 60% was printed on uncoatedstocks, like plain paper or office copy paper during year 2000. This figure willreach 90% by year the 2005. Studies of ink-jet printing on uncoated substratesis therefore of great importance not only from an academic perspective but alsofrom application perspective.

1.1 Goal of the study

To build up a model that can be used for prediction of ink jet color reproduction,methods that help characterize the printing materials, printing systems, andfinal printout are necessary. This thesis thus consists of various study phasesand goals.

One goal is to establish a general method that deals with various typesof ink penetration, uniform or non-uniform, whatsoever. Because of existingwidely diversified ink-paper combinations, mechanisms that are responsible forink-paper interaction differ from one combination to another.

A second goal is to characterize printer and optical properties of inks. It in-cludes information about scattering and absorption characteristics of the inks,the volume of the inks being printed, and color mixing schemes for the genera-tion of secondary colors. In the case of having ink-penetration, this informationserves as an input for further studies.

The underlining phenomenon of ink penetration is formation of a layer ofan ink-paper mixture. Based on knowledge from the first two phases, the study


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2 Introduction

moves naturally to the third phase. The third goal is to understand the fun-damentals of how the ink-paper interaction affects color reproduction and tocharacterize optical effects of ink penetration. Basic quantities that character-ize ink-penetration, such as penetration depth, is indirectly determined fromexperimental spectral reflectance values. A model that takes into account inkand paper mixing is developed allowing prediction of spectral reflectance of realprints.

That ink penetration into an uncoated substrate impact strongly on colorrepresentation of the printed images is an experimentally known fact. One ofthe goals is therefore to evaluate the impact of ink penetration from experimen-tal data and simulations. The focus of the evaluation is on color, i.e., chroma,hue, and color gamut etc.

In order to correctly predict color of halftone images, the dot gain proba-

bly has to be considered. Thus, model development for dot gain description,including optical dot gain and physical dot gain, is an important feature of ourstudy.

Modelling and simulation are important tools contributing to our under-standing, deeper insights into the problems. Moreover, they serve also to guideus on the way toward finding solutions.

1.2 Status of studies and our contribution

This section briefly outlines the status of studies on the topics related to thework presented in this thesis. It also provides a brief description of our contri-

bution as well.

1.2.1 Extension to Kubelka-Munk theory

The original theory of Kubelka-Munk (K-M) was developed for light propaga-tion in parallel colorant layers of infinite xy-extension [KM31, Kub48]. Thefundamental assumptions of the K-M theory are that the layer is uniform andthat light distribution inside the layer is completely diffused. From these as-sumptions, the light propagation in the layer was simplified into two diffuse lightfluxes through the layers, one proceeding upward and another simultaneouslydownward. After its introduction in the 1930s, K-M theory was subjected toextensions by removal of some of the assumptions. Among others, the bound-ary reflection at the interface bewteen two adjacent media was introduced bySaunderson [Sau42], i.e, the well-known Saunderson correction. Kubelka him-self also made an attempt to extend the applicability of the theory to opticallyinhomogeneous samples [Kub54]. However, this extension was only applied toa special case of inhomogeneous media, in which the ratio of the absorption tothe scattering is constant.


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1.2 Status of studies and our contribution 3

Recently, Emmel and Hersch introduced an elegant mathematical formula-tion of the Kubelka-Munk theory, based on matrices [Emm98, EH99]. Theyproposed also a mathematical framework unifying the K-M model with theNeugebauer model [EH00]. This allowed them to apply the K-M theory to ahalftone image. Therefore optical dot gain was studied. Very recently, Mouradextended the 1-dimensional K-M theory representation (2 flux) to 3-dimensions(6 flux). Such an extension made it possible to account for the light scatteringin the substrate and therefore the optical dot gain.

The object of our studies is mainly on optical performance of a layer con-sisting of non-uniform media concentration. This is a topic that has not beenexplored theoretically. One of the applications of the study is ink penetration,where the ink distribution inside the substrate may be nonuniform, dependingon the mechanism of ink penetration. Phenomenon of non-uniform ink pen-

etration has been observed experimentally (cross section image) by means ofmicrotomy, in ink jet printing [GKOF02]. In Chapter 5, we work out a frame-work that is applicable to both uniform and non-uniform ink penetration cases.Expressions for reflectance and transmittance of three types of ink penetration,uniform, linear, and exponential (ink penetration) are derived. Moreover, appli-cations of the K-M theory to ink jet printing has substantiated the applicabilityof the theory. Explanations and discussions around these issues are given inChapter 6.

1.2.2 Evaluation of effects of ink penetration

Absorption of ink constituents by the substrate, or ink penetration is significant

over a range of timescales, from the first stages of ink-transfer and ink-dryingby absorption, through to long-term stability [Voe52, Oit76, Str88, MK00].Studies of ink penetration related issues have long been important topics inoffset printing and cover a wide range of topics, such as print gloss and printdensity, print defects (unevenness and mottle), print through, separation of inkconstituents [SGS00, Rou02], etc.

Studies have so far mainly concentrated on understanding the mechanismsof ink penetration and developing materials for paper coating. Reported stud-ies of the optical and chromatic effects of ink penetration are few, even thoughsuch studies have recently intensified [McD02, PL02, NA02]. Among others,Bristow and Pauler proposed a method by which the depth of ink penetra-tion could be determined indirectly from spectral reflectance measurementdata [Bri87, Pau87], in offset printing. The method was based on K-M the-ory, the additivity assumption and a uniform ink distribution. In recent years,Pauler and his research group have been very active in modelling and simulatingink penetration in ink jet printing [PWE02a, PWE02b, PWE02c].

Experimental measurements and theoretical simulations for the optical andchromatic effects of ink penetration have not been conducted without difficulty.


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From the experimental side, the measurements may be made by comparingprints having ink penetration with those that dot not. Unfortunately, onecan not obtain prints with and without ink penetration (into the celluloseporous structure of the substrate) by using the same ink-substrate combination.Different types of substrate, like plain paper and high grade photo paper haveto be used when comparisons are made. For halftone images, differences incolor and optical dot gain characteristics for different substrates, will contributeto the color difference between the prints. Moreover, differences in surfacecharacteristics between the substrates used for the prints may lead to significantdifference in physical dot gain.

Theoretical simulations have the advantages that one can use exactly thesame ink-substrate combinations when the effects of ink penetration is evalu-ated. One has the possibility to manipulate the ink penetration by switchingit

onor offin the simulation. The underlining difficulty is to establish a theoret-ical model that can properly describe a complex problem like ink penetration.So far K-M theory has been the only model that has been applied to the inkpenetration problems, even though more sophisticated theories like Multi-fluxRadiative Transfer Theory (or Discrete Ordinate Radiative Transfer (DORT)theory [Eds02]) may be possible candidates in the future.

Studies carried out in this dissertation represent a combination of the K-M model with spectral reflectance measurements. We present a systematicframework stretching from the characterization of inks and ink application,to the modelling and the simulation of ink penetration. It begins with thedetermination of the scattering and absorption characteristics of pure ink layersof primary colors, as well as thickness of the ink layers. The scattering and

absorption characteristics of the primary inks are then applied to determine thecolor mixing scheme for the generation of secondary colors. The applicationsserve not only as tests to the quality of data, but also to the applicability ofthe model (see Chapter 6, for details).

The characteristics of the inks (scattering and absorption, and ink thickness)and that of the paper, are in turn used to simulate ink penetration (ink-papermixture). The additivity assumption is modified by considering the correlationbetween the light scattering (from the paper) and the absorption (from theinks). With the help of our model, the depth of ink penetration is indirectlydetermined from the measured reflectance values. Spectral reflectance of inkjet prints on office copy paper (in both primary- and secondary-colors) havefairly well been reproduced by the simulation (see Chapter 7, for details).

Evaluation of the impact of ink penetration is obtained from both exper-iment and simulation perspectives. Color difference between prints with andwithout ink penetration are represented in chromaticity diagrams (2D) andCIELAB color space (3D). It shows that ink penetration has a dramatic im-pact on the chroma of the print and even on the hue. This leads to a dramaticreduction of color gamut which is absolutely negative for color reproduction


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1.2 Status of studies and our contribution 5

(see Chapter 10, for details).

1.2.3 Optical dot gain

The physical phenomenon behind the so-called optical dot gain, or Yule-Nielseneffect, is basically light scattering within the substrate paper. Light scatteringinside the substrate of a printed image is a very complex process. Studies ofthe effects on color rendition of a print has attracted constant research interest,since it was first studied by Yule and Nielsen in 1950s [YN51]. Yule and Nielsenfound that the optical dot gain can be well approximated by introducing anempirical factor, n, into the Murray-Davis equation (see Eq. (8.2) and (8.5)),although the physical meaning of the n factor was not clear. Shortly after,Clapper and Yule extended the work of Yule and Nielsen by including a contri-

bution from multiple internal reflections between upper and lower boundariesof the substrate [CY53]. The assumptions made in the Clapper and Yule modelare that the ink layer is uniform and that the light is completely scattered bybulk scattering. Complete light scattering is a physical approximation whenthe average lateral light scattering distance is much greater than the size of thehalftone element.

In 1978, Ruchdeschel and Hauser [RH78] provided a physical explanation forthenfactor and showed that 1 n 2, if only optical dot gain involved. n= 1and 2 represent two extremes for the light scattering, where n = 1 correspondsto no light scattering while n = 2 corresponds to complete scattering. Theoriginal intention of the Yule-Nielsen model was to involve the optical dotgain. Nevertheless, it has often been applied to cases where there was also

physical dot gain involved. Unsurprisingly, they got n factor bigger than 2 andsometimes much bigger than 2 [BT96]. Consequently, the physical meaning ofsuch nfactor is difficult to explain.

In the past 10 years, Kruse and Wedin [KW95], among many others, pro-posed an approach which was thoroughly studied and fully implemented byGustavson [Gus97a, Gus97b]. The approach simulated the light scatteringprocess from a fundamental level. It was based on direct numerical simulationof scattering events which depend on the optical properties of the materials,the halftone frequency and the halftone geometry. This approach is similar innature to the Monte-Carlo method that is briefly explained in Sec. 4.5. Statis-tics are recorded over a large number of light scattering events. From these theprobability of an event can be established. Arney [Arn97] and Hubler [Hub97]independently proposed similar models based on probability descriptions of thelight scattering. In their models, the light scattering inside the paper was de-scribed by the probabilities that a photon emerges from the inked and non-inkedareas. These probabilities depend on the positions where the photon enters thepaper and emerges from the paper, as one will see in Sec. 8.2.2. A point spreadfunction (PSF) is a different representation of light scattering. Using the PSF


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6 Introduction

approach, Rogers [Rog97, Rog98a, Rog98b, Rog98c] presented a method deal-ing with the light scattering process. He proposed a matrix approach wherethe tristimulus values of a halftone image could be calculated as the trace ofa product of two matrices. So far, the studies have not provided any explicitexpression for the reflectance or tristimulus as a function of dot percentage(as it was given by the Neugebauer equation). Moreover, the studies have sofar been limited to the mono-color or black-and-white case and no studies formulti-color have been reported. Furthermore, the subject of ink penetration(into the substrate) has barely been touched.

Our work makes contributions in these three areas, i.e., explicit expressionsfor reflectance and optical dot gain have been worked out, studies of the opticaldot gain have been extended to multi-color cases, and ink penetration has beenincluded in the model. Detailed descriptions can be found in Chapters 8 and

9.

1.3 Structure of the dissertation

This thesis consists of 6 parts and 11 chapters. The contents of the presenta-tion are organized in such a way that they follow a logical path for reasoning.Apart from the introduction (Chapters 1-4), the thesis begins with a theoret-ical extension of Kubelka-Munk theory (Chapter 5). This provides us with ageneral description of ink penetration. It is then applied to determine ink char-acteristics, ink application, and ink penetration in full tone prints (Chapters6 and 7). Furthermore, the model and application are extended to halftone

cases, where dot gain plays an important role (Chapters 8 and 9). Finally, thechromatic effects from the ink penetration and dot gain are evaluated with helpof experimental data, as well as simulations.

Each chapter is intended to be self consistent and sufficiently independentof all others, that a reader only interested in a given topic needs only viewthat particular chapter. However, the chapters are also arranged according toa common theme.

A brief description about the contents of the thesis is given as following.Part Iconsists of the first four chapters. Chapter 2 describes the basics of

paper structures, properties, and relevant measurement technologies. Chapter3 briefly describes ink jet technologies, inks, and printers used in the thesisstudy. Chapter 4 provides an overview of optical modelling and simulations.

Part II consists of a single chapter (Chapter 5). A theoretical frameworkis proposed as an extension of the Kubelka-Munk theory. The extension allowsone to deal with both uniform and nonuniform ink distribution in cases of inkpenetration. Expressions for reflectance and transmittance of three types ofink penetration, uniform, linear, and exponential, have been worked out.

Part III has the goal of characterizing ink penetration for solid tone printed


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1.3 Structure of the dissertation 7

patches and consists of two chapters, Chapters 6 and 7. In studying ink pene-tration, one actually deals with an ink-paper mixture. It is therefore essentialto know what kind of ink, in terms of its optical properties (scattering andabsorption), has been printed and how much ink has penetrated into the sub-strate. Chapter 6 aims at characterizing inks and ink application controlledby ink-jet printer, such as scattering- and absorption-power of the inks, theamount of ink printed onto a substrate, and color mixing scheme in generationof secondary colors. Results of Chapter 6 serve as input for Chapter 7 whereink penetration into plain paper is studied. Quantity alike depth of the inkpenetration has been determined from simulations.

Part IV presents models and simulations for halftone-image-related is-sues, such as optical dot gain in both monochromatic (Chapter 8) and multi-chromatic (Chapter 9) printing cases. Even overall dot gain (physical- plus

optical-dot gain) has been tentatively studied (Chapter 8). The model hasbeen applied to simulating optical dot gain for different dot shapes and lo-cations. It is found that the optical dot gain results in more saturated colorsensation. Applications of the model to overall dot gain is tested by applyingit to a digital image.

Part V consists of two chapters, Chapters 10 and 11. In Chapter 10, theimpact of the ink penetration on capacity for color representation was evaluatedfrom both experimental and simulation perspectives. The impact is representedin (2D) chromaticity diagram and 3D color gamut (in CIELAB color space).It is found that ink penetration has a dramatic impact on chroma and evenon hue, and leads to a dramatic reduction in color gamut. Chapter 11 gives asummary of the thesis.

Part VI consists of an Appendix and the Bibliography.


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Chapter 2

Paper

2.1 Structures and properties of paper

In the Graphic Arts industries, paper is the most commonly used substratethat receives the inks and colorants to form images. The properties of thepaper substrate are important partly because the substrate is visible betweenthe printed areas, and partly because the substrate defines the background re-flectance for the ink layer. Moreover, optical properties, mechanical properties,permeability to liquids, and so on, directly affect the quality of the images andthe production practices. Paper-making is a multi-disciplinary subject involv-ing mechanics, physics, optics, chemistry, etc. Interested readers can find more

detailed descriptions elsewhere [NKP98, Ran82, Bri86, Bak97]. In this chapterwe give a brief overview of the structures and properties of paper which areeither directly or indirectly related to the current work.

2.1.1 Fibres, fillers and coating

Paper is a stochastic network of fibers as seen in Fig. 2.1. Since the fibersare much longer than the thickness of the paper sheet, the network is more orless flattened out [Nor91] and therefore almost two-dimensional (in xy-plane).For paper-making fibers, the basis weight is about 5 10g/m2, which meansthat ordinary printing and writing papers consist of normally 5-20 layersof fibers [NKP98]. The two-dimensional (2D) structure governs many paperproperties, such as in-plane mechanical properties. The fibre network in paperis normally built up of mechanical pulp fibres and/or chemical pulp fibres.They form the backbone of the paper.

Graphic Arts industries have continuously placed stringent demands onthe paper-making industries, such as high productivity, wide diversity, and


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10 Paper

Figure 2.1: Micrograph of paper surface area of ca. 1 mm2 (from K. Niska-

nen [NKP98]).

improved product quality etc. Paper that only consists of fibres can hardly meetthese demands. As a result chemicals and post paper making processes are nowcommonly applied. For example, by adding fillers such as kaolin clay or calciumcarbonate to the furnish one can increase the specific scattering strength andin turn improve the opacity. Additionally, a post paper-making process whichis usually called coatingis employed in order to improve both mechanical andoptical properties. The main constituents of the coating layer are pigments( 50 v %), polymers ( 20 30v %) and air ( 25 35v %) [Rou02].The coating can be composed of one structure or of multi-layer structures,containing one or several pigments and a binder. Detailed studies and reviewsabout the relation between the addition of fillers, coating constituents and theproperties of the paper can be found in references [FBP90, Bro85, Lep89]

2.1.2 Density and porosity

Closer examination using microphotography reveals that paper is actually threedimensional [Fay02]. The z-directional structure and material distribution af-fect paper properties such as bulk, bending stiffness, optical properties, andsurface roughness. The distribution of fines and fillers are particularly impor-tant.

Density and thickness are basic macroscopic characteristics of paper struc-ture. Density, (g/m3), is defined as the ratio of the basis weight, b (g/m2),


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2.1 Structures and properties of paper 11

and thickness, d (m).

= b/d. (2.1)

Its inverse value, termed bulk(m3/g), is more convenient to use in the paper-making industry.

Figure 2.2: Micrograph of pore structure of a paper sheet (from A. Fayyazi [Fay02]).

In a 3D perspective (see Fig. 2.2), the paper is not merely a network offibers but more strictly an aerogel. The network of fibers embraces and createsa network of pores, and paper is thus a two-phase system in which the pores orvoids between the fibers are an important part of the paper structure [Bri86].The 3D pore structure controls the density and optical properties directly, whilethe mechanical properties and dimensional stability are indirectly controlledthrough the relative bonded area [NKP98]. It is therefore useful to introducea term called porosity, , that is defined as the ratio of pore volume to totalvolume,

=V Vf

V = 1

f(2.2)

where V is the volume of the entire sheet, Vf

is the volume occupied by thefibres, and fare the paper and the fibre wall densities.

Paper porosities range from 0.1 for glassine to 0.87 for filter paper. Thevariation of is controlled by the paper-making furnish and its beating level.Mechanical pulps with stiff and bulky fibers usually give higher paper porositythan chemical pulps. The beating of chemical pulp decreases porosity since


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12 Paper

fiber flexibility and collapse increase during beating. Therefore, a sandwichtype of layer structure using chemical pulps in the upper- and lower-surfacelayers and a mechanical pulp in the middle layer, will make paper with goodsurface properties (smoothness, printability, and bending stiffness) and highporosity at the same time. In practice, for example, newsprint often primarilyconsists of mechanical pulp while copy paper mostly of chemical pulp. Mixtureof mechanical and chemical pulps finds use especially in printing papers andmultiply boards [RNN98].

The pore size distribution is also influenced by operation such as calen-dering, the mean pore size becoming smaller as a result of such compressivetreatments. Additionally, measurements made, for example by immersing asheet in a low viscosity oil show that virtually all the pore volume is accessibleto the liquid and it can be assumed that there are no isolated inaccessible voids

within the structure [Bri86].Surface roughness is another important characteristic of paper. It influences

the optical properties such as gloss. High roughness reduces the contact areabetween the ink film and paper and gives low ink transfer in Offset printing.On the other hand a rough surface contains leaks and holes that lead to inkpenetrating into the paper sheet. Ink penetration determines how much of thetransferred ink remains on the surface of paper. Small penetration gives highprint density. It has been observed that unevenness in offset printing comesfrom the spatial variation in surface roughness and ink penetration [Kaj89].Detailed studies on the ink penetration for ink jet printing will be presented inChapter 7.

2.2 Optical properties and measurements

Optical properties such as opacity, brightness, and gloss are important to usersof most paper and board grades. In order to successfully manufacture paperwith desired optical properties, it is important to understand the physical prin-ciples of sheet structure and composition that determine these characteristics.Measurements of these optical properties can in turn provide information forcharacterizing the sheet structure.

2.2.1 Brightness, opacity and gloss

When light of intensity, I0, hits a paper surface, a fraction of intensity, Isurf,reflects back (surface reflection), and the remainder enters the sheet. Inside thesheet, light spreads and scatters in all directions. Some light (Ibulk) eventuallyreflects back from the sheet, another part transmits through the sheet ( Itran),and the rest is absorbed. Thereflectance, R, is defined as the ratio of the


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2.2 Optical properties and measurements 13

reflected intensity to the incident intensity, i.e.

R= Isurf+ Ibulk

I0. (2.3)

Similarly transmittance, T, is defined as the ratio of the transmitted intensityto the incident intensity,

T = Itran

I0. (2.4)

The sum ofR and Tis less than unity when there is absorption.Brightness, R( = 457nm), is the reflectance of an infinitely thick pile

paper sheet, which is measured by adding sheets to the pile until there is nochange in the intensity of reflected light at wavelength of 457 nm (blue light).The use of blue light arises because paper-making fibers have a yellowish color

and because the human eye perceives blue colors as brightness.Opacitycharacterizes the ability of a single sheet to hide text or pictures

on the back side of the sheet. Quantitatively, opacity is defined as a ratio ofreflectance of a single sheet, R1, to that of an infinite number of sheets, R,at wavelength = 557 nm [Les98a]

Opacity = R1(= 557nm)

R(= 557nm) (2.5)

One should be aware that opacity is defined at a different wavelength ( =557nm) from that of the brightness (= 457nm).

Gloss is an optical phenomenon caused by light reflection from a smoothtop surface. A glossy material is characterized by a high reflectance in the

direction of regular reflection or close to that direction. If the illuminationis white, the glossy reflection is normally colorless despite the color pigmentsunder the surface of the print [Gra01]. Every day experience tells us that thegloss of printed paper depends considerably on the illumination and detectionangles.

Gloss paper has a high specular reflectance that is closely related to thesurface smoothness or in other words, surface roughness of the paper. Thesurface roughness of paper can be sorted into three categories according to thein-plane resolution: Optical roughness at length scale < 1m; micro roughnessat 1100m; and macro roughness at 0.11mm. Gloss is a combination of theeffects of micro roughness and optical roughness of the paper surface. Microroughness affects gloss because titled surface facets reflect light in differentdirections as shown in Fig. 2.3

The scale of optical surface roughness has the same magnitude as the wave-length of the light. Optical roughness therefore causes light diffraction. Thetotal reflection, Rt, from a surface of normally distributed height is [Mic84]

Rt = R0exp[(4)2

2 ] + R0

254

m2 (

)4()2 (2.6)


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14 Paper

where is the wavelength of light, the root mean square (RMS) surfaceroughness,m the mean gradient of the surface, R0 the reflectivity of fibers orcoating color, and the solid angle of measurement. The first term is thespecular component responsible for the gloss of paper. Clearly, as roughness,, increases the exponential function decays to zero and gloss vanishes. Incontrast, the diffuse reflectance increases with roughness as 4.

Figure 2.3: Schematic effects of micro roughness on paper gloss. The randomly titledsurface facets reflect light to different directions and reduce gloss.

High print gloss on paper also requires that the paper itself has high gloss.To achieve high gloss or good surface smoothness, coating is usually needed,and higher coating weight generally gives better gloss. However, proper choiceof pigments and binders, together with the average size and distribution of thecoating materials controls the behavior of the coating layer and the gloss [Lep89,Les98a].

2.2.2 Optical measurements

Optical measurements is an important issue in paper-making and Graphic Artsindustries. In general, the measurements need to be relevant to what the humansees. For a reflective sample, an image for example, the light that stimulateshuman vision depends not only on the optical properties of the image butalso on the illumination and observation geometries. International standardsspecify the procedures for the reflectance measurements including the spectral


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16 Paper

(45o/0o) geometries as these are the instruments we have used in our stud-ies. More information about other geometric implementations may be foundin Ref. [Ryd97], and references therein.

Elrepho 2000 belongs to the (D/0o) category and is one of the most widelyused instruments in paper making industry. A typical implementation of theinstrument is shown in Fig. 2.5. The instrument consists of an integratingsphere with holes for illumination, sample, and detector. The inside surface ofthe sphere is covered with white pigments that ideally scatter light isotropically.Inside the sphere there are baffles whose surfaces are also covered by the whitepigments. Using such an arrangement, light from the light sources is scatteredonto the inside surface of the sphere and no light from the light sources canshine directly onto the sample.

detector

light light

sample

gloss trap

baffle

Figure 2.5: Instrument ofD/0o geometry for measurement of reflectance.

The accuracy of which the illumination mimics the ideal diffuse light de-pends on the optical properties of the white pigments and the sizes of the holeson the sphere. Generally speaking, the smaller the holes the closer the illu-mination to ideal diffuse light. Nevertheless, too small holes may cause largererrors in the measurement. For example, too small holes for the sample mayresult in lower signal/noise ratio. Additionally, it may also lead to less statis-tically meaningful measurements when the characteristics of a relatively large


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2.2 Optical properties and measurements 17

area, say reflectance of a piece of paper, is of interest (this is exactly the casefor paper-making and Graphic Arts industries). Therefore, the implementationof diffuse illumination into a real instrument is a compromise between manyfactors. More detailed descriptions of the (D/0o) geometry instrument may befound in the international standard ISO 2469 [24694]. It should be pointed outthat measurements using Elrepho2000 are very time consuming because eachpatch has to be manually positioned.

In Graphic Arts, (45o/0o) or (0o/45o) -observing geometry (Fig. 2.6) is rec-ommended by CIE and well applied in practice. The illumination unit consistsgenerally of a cone shape glass illuminated by up to three different unpolar-ized light sources. This setup leads to an approximately circular illuminationcondition which helps to diminish the measurement dependencies on the sam-ple orientation. The spectrophotometer Gretag MachbethTM Spectrolinoused

in our measurements belongs to this category. In a reflectance measurement,the sample gets circularly illuminated from the top with the collimated fluxI0. By using this instrument in combination with the software called Spec-troChart [GM01], one can measure many patches automatically in sequence.This makes the measurements used for system calibration, such as color gamutmapping, much easier. Comparative measurements made by applying bothElrepho 2000 and Spectrolino have shown excellent agreement in spectral re-flectance values for plain paper [Pau01].

monochromator& detector

broadbandlight source

45o/0

o 0

o/45

o

broadbandlight source

Figure 2.6: Instrument of 45o

/0o

and 0o

/45o

geometry for reflectance measurement.

An angle-resolved spectrophotometer operating with a collimated illumi-nation (laser) [Gra01] is one of the high grade instruments. With it one canmeasure the monochromatic reflectance of a sample at any illumination- anddetection-geometries, which is particularly useful when there is specular re-


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18 Paper

flection involved. Nevertheless, it is still too early to generally implement suchmeasurements in industrial practice because of the limitation of the instrumentitself (monochromatic illumination and extremely time consuming for the spacesampling). A more serious obstacle, though, is the lack of a simple theoreticalmodel that copes with the measurement.

2.3 Paper permeability and mechanism of ink

penetration

Most end uses of paper involve transport phenomena in some form that requiresa specific level of permeability. Printing paper has medium permeability, filter

papers, facial tissues, and sanitary papers must have high permeability, and inmany packaging papers and so-called barrier papers, low permeability [Les98b].The permeability of paper is closely related to its porosity, . One usuallyassumes that the structure consists of ellipsoidal cavities connected throughnarrow channels. Comparing the ideal model system with measurements offluid penetration or fluid flow through paper determines the apparent pore sizedistribution [Les98b].

For graphic arts industry, liquid (water, oil, etc.) penetration into paper hastremendous impact on the quality of the print. Absorption of ink constituentsby paper is driven by thermodynamic interaction between the ink and the pa-per, by capillary forces and by chemical diffusion gradients. Capillary pressureis acknowledged to be the main driving force in the offset ink oil transport in atypical paper coating porous structure. With increased latex content diffusion-driven transport of ink chemicals into the latex counterpart of the coating layerbecomes important [Rou02]. The penetration can also be driven by the print-ing nip during the printing and converting processes. Therefore, theoreticalhandling of the penetration process is complicated. Moreover, experimentalverifications of theory are challenged by the small dimension and by the rele-vance of both short and long time-scale. In the following, we will only mentionsome theoretical background for capillary driven penetration process that maybe relevant to ink penetration for ink jet printing on un-coated paper.

The capillary force (pressure) is described by Youngs equation,

p=2cos

r (2.7)

where the surface tension, r the capillary radius, and the contact anglebetween the liquid and the capillary wall as shown in Fig. 2.7. Accordingto the Young equation, penetration occurs when the contact angle is smallerthan 90o (f > 0). However, experiments showed that even if the contactangle >90 and the external pressure zero, surface tension can drive a liquid


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2.3 Paper permeability and mechanism of ink penetration 19

into paper, if there are converging capillaries. With irregularly shaped pores,capillary penetration accelerates in converging parts of the pore and deceleratesin diverging parts [Lyn93].

Liquid (ink)

Air

Solid (paper)

Figure 2.7: Contact angle, , of a wetting liquid on a solid surface.

In the printing processes, the capillary force together with the externalpressure govern the penetration. The time dependence of the penetration isdescribed by the Lucas-Washburn equation,

h2 = r2t

4(

2cos

r +pE) (2.8)

where h is the thickness of the ink penetration, the fluid viscosity, and pEthe external pressure difference. The first term is the penetration driven by thecapillary force. It says that the depth of penetration is proportional to squareroot of the capillary radius, but inversely proportional to the square root of theviscosity of the ink solvent.

In practice, the mechanism of the ink penetration depends significantly onthe printing process. For offset printing, it is the nip pressure that dominates

in the printing and converting processes. This is followed up by the capillarydriven penetration afterwards. Similar process occurs in Toner Fusing Printingprocess [Hwa99]. For an ink jet, the external pressure comes from the kineticimpact (a pulse) when the ink droplet hits the paper substrate. Comparatively,capillary driven penetration may play an important role.


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Chapter 3

Ink-jet printers and inks

3.1 Ink-jet technologies

Ink-jet is a non-impact, dot-matrix printing technology. Ink droplets are emit-ted from nozzles of the printer directly to a specified position on a substrateto create an image. The operation of the ink-jet printer is easy to visualize: aprinthead scans the page in horizontal strips, using a motor assembly to moveit from left to right and back, as another motor assembly rolls the paper invertical steps (see Fig. 3.1). A strip of the image is printed, then the papermoves on, ready for the next strip. To speed things up, the printhead does notprint just a single row of pixels in each pass, but a vertical row of pixels at a

time.

Figure 3.1: A four-color ink-jet printer. The printhead moves along the drum per-

pendicular to the rotation of the drum facilitating the deposition of ink droplets of

all colors in each pixel (from L. Palm [Pal99]).

Ink-jet printing is a relatively young commercial industry. It b egan about


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22 Ink-jet printers and inks

20 years or so ago, even though the mechanism for breaking up a liquid streaminto droplets was described more than 120 years ago by Lord Rayleigh [Ray78].Efforts to make an ink-jet printer started about 50 years ago [Elm51]. Afterthat, continuous efforts have been made to improve the reliability of drop for-mation, to reduce the size of the ink droplets, while at the same time to increasethe jetting speed etc. This continuous development has led to continuous im-provement of printed images [Le98]. The state of the art ink-jet technology cangenerate ink droplet as small as 2 pico-liter (pL) in volume. Today, the ink-jetprinters can produce images of photo-quality with reasonable printing speed.

Ink Jet Printing

Drop on DemandContinuous Ink Jet

Raster

Binary

Hertz

Airbrush

Electrostatic

Piezoelectric

ThermalDuPont

Iris Graphics Stork

Domino Imaje LinxVideojet

ScitexVideojet

LACSign Tech Vutex

Epson iTi

AprionBrotherDataproductsEpsonMIT/XaarSpectraTektronicsTriden

CanonHPLexmarkOlivettiXerox

Figure 3.2: Ink-jet technology map. Vendors that employ the technologies have been

listed in the figure.

Ink-jet printing has been implemented in many different designs with awide range of potential applications. Fundamentally, the technologies for inkapplication is divided into two groups,continuousand drop-on-demand(DOD)as shown in Fig 3.2.

3.1.1 The continuous ink-jet

In a continuous ink-jet, the creation of ink droplets is controlled by periodicsignals (not the printing signal) which lead to a constant ink droplet genera-


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3.1 Ink-jet technologies 23

tion. The generated droplets are selectively charged, a feature controlled bythe printing signals. The charged droplets correspond to no print and are de-flected into a gutter for recirculation when they pass through the electric field,while the uncharged droplets fly directly to the media and form an image (seeFig. 3.3). The advantage of the continuous ink-jet technology lies at its higherprinting speed compared to the drop-on-demand technology.

Figure 3.3: Schematic drawing of the principle for controlling droplet flight in a

continuous ink-jet printer through charging and deflection (a binary deflection system)

of individual droplets. (From L. Palm [Pal99]).

3.1.2 Drop-on-demand ink-jet

In contrast to the continuous ink-jet technology, impulse ink-jet technology

generates ink droplets when they are needed for printing. In the literature,this technology is more commonly called drop-on-demand (DOD).

In DOD design, technologies of ink drop formation and ejection can becategorized into four major methods: thermal, piezoelectric, electrostatic, andacoustic. The first two are the dominant technologies for products on markettoday, while the other two are still in the developmental stage.

In a printhead of a thermal ink-jet, there is an electric heater which isattached to the ink chamber. Heat is transferred from the surface of the heaterto the ink. The heater is controlled by an electric current pulse. When thecurrent is on, the ink is superheated to the critical temperature for bubblenucleation (about 300 oC for water based ink). When nucleation occurs, awater vapor bubble instantaneously expands to force the ink out of the nozzle.Once the current is off and all the energy stored in the ink is used, the bubblebegins to collapse on the surface of the heater. Concurrently, with the bubblecollapse, the ink drop breaks off and accelerates toward the paper as shownin Fig. 3.4. Once the ink droplet is ejected, ink is refilled into the chamberand the process is ready to begin again. Because the ink droplet is essentiallygenerated by the growth and the collapse of the vapor bubble, the thermal


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Printhead Body Ink Supply

Heater Chip

Nozzle Plate

Substrate

Figure 3.4: A schematic diagram of thermal jet technology.

jet is also called a bubble jet. The simple design of a bubble jet printheadalong with its semiconductor fabrication process allow printheads to be built

at low coat and with high packing density. These made the thermal ink-jettechnology the most successful one on the market today [Le98]. Moreover, thebubble ink-jet with a high printing resolution and color capacity is availableat a very affordable price. On the market, there are many vendors who haveadapted this technology in their ink-jet products, such as, Hewlett-Packard,Lexmark, Olivetti, Canon, and Xerox.

In the printhead of a piezoelectric ink-jet, there are piezo-ceramic platesbonded to the diaphragm (electrodes) as shown in Fig. 3.5. Similar to thebubble jet, the piezoelectric material is also controlled by a current pulse. Inresponse to the electric pulse, the piezo-ceramic plates deform in shape whichcauses the ink volume change in the chamber to generate a pressure wave thatpropagates toward the nozzle. Consequently, an ink droplet is ejected out.Depending on the mode of shape deformation of the piezoelectric plates, thereare different printhead designs, such as, push-mode, bent-mode, shear-mode,etc, and Fig. 3.5 is an example of the shear-mode design. Piezoelectric ink-jetis also very popular among the ink-jet manufacturers, such as, Epson, Xaar,Tektronix, etc.

Unlike the continuous ink-jet, drop-on-demand ink-jet technology means


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3.2 Characteristics of ink-jet printers 25

Figure 3.5: A shear mode piezoelectric ink-jet design [Le98].

that ink droplets are generated and ejected when they are used in imaging. Thistechnology eliminates the complexity of drop charging and deflection hardwareas well as the inherit unreliability of the ink recirculation systems required forthe continuous ink-jet technology. The drop-on-demand ink-jet technology isthe most common technology on the market today.

The trend in the development of ink-jet technology is toward jetting smallerdroplets for image quality, fast drop frequency and a higher number of nozzleson the printhead for print speed.

3.2 Characteristics of ink-jet printers

3.2.1 General

The performance of an ink-jet printer may be characterized by its printingspeed and resolution. The speed depends above all on the jetting frequency orthe time interval between two consecutive ink-jets. On an ordinary ink-jet, theprinthead takes about half a second to print a strip across a page. Since A4paper is about 21 cm wide and the ink-jet operates at a minimum of 300 dpi,this means there are at least 2,475 dots across the page. The printhead has,therefore, about 1/5000th of a second to respond to whether or not a dotneeds printing. Nevertheless, higher printing speed may also be achieved by


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adapting bigger printheads with more nozzles which enables it to deliver nativeresolutions of up to 1200 dpi and print speeds approaching those of currentcolor laser printers: 3 to 4 pages per minute (ppm) in color, and 12 to 14 ppmin monochrome.

Table 3.1: Descriptions for some desk ink-jet printers

Canon S300

Jet type drop size Number of nozzles Resolution (dpi)1 Speed (ppm)2

(picoliter) black color black color black color

Thermal 5 320 1283 600600 24001200 11 7.5

Epson C60Piezo 4 144 483 up to 2880720 12 8

HP 920c

Thermal N/A N/A N/A up to 24001200 9 7.5

Lexmark Z53

Thermal N/A N/A N/A up to 24001200 16 8

1 - it consists generally of 3 categories, draft, normal and best. Only the

highest possible resolution of the printer has been listed here.

2 - the speed of printing, pages per minute (ppm), decreases when higher reso-

lution is chosen in the printing. Only the higher possible speed (draft) is listed

here.

Resolution of the print depends on the volume of the ink droplet. Thesmaller the ink droplet the higher the possible printing resolution. The volumeof the ink droplet is determined by the diameter of the nozzle as well as thewidth of the current pulse (in time). Therefore, to be able to manufacturethe printhead with a very fine nozzles is of great importance for achievinghigh printing quality. For example, for 10 pL droplet, HP DeskJet 890C colorprinthead has nozzle diameter of around 20 m. Apart from the printhead,the substrate onto which the ink drops can also have great impact on theprinting resolution, due to the ink-substrate interaction, such as ink spreadingand penetration. Ink bleeding can actually have significant impact on theimage resolution. Finally, it should be borne in mind that print speeds mayvary, depending on the document, software program, and computer settings.Table 3.1 is a collection of technical descriptions for some ink-jet printers thathave been available on the market over recent years.


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3.3 Ink-jet ink technologies 27

3.2.2 HP970Cxi ink-jet printer

In this dissertation, the test charts were printed by employing a HP970Cxiink-jet printer, which is of the drop-on-demand ink-jet design. It uses dye-based liquid inks (water resolution). The technological characteristics of thisprinter is summarized in Tab. 3.2.

Table 3.2: Description of HP970Cxi ink-jet.

Document type Draft Normal Best

Resolution (black-white, dpi) 300 x600 600 x 600 600 x 600

Resolution (color, dpi) 300 x 600 Color layering 2400 x 1200

Print speed (black text, ppm) 12.0 6.5 4.7

Print speed (Mixed text/graphics) 10.0 5.0 3.1

Print speed (Full page color) 2.9 0.6 0.3

Type of ink Water-based organic dyes

Printer command language HP PCL level 3 enhanced

dpi - dots per inch.

3.3 Ink-jet ink technologies

3.3.1 General

Inks are probably the most critical components in the ink-jet printing. Thedevelopment of ink-jet inks has been an important part of ink-jet technology.This is because the ink properties not only dictate the quality of the printedimages, but they also determine the characteristics of the drop ejection and thereliability of the printing system.

The ink-jet inks consist normally of colorants, an ink vehicle, and additivematerials. The ink vehicle like water, oil, solvent, resin, etc., governs the dy-namic properties of ink distribution. The ink vehicle is the major componentof the ink, whose amount in percentage varies from 40 90% depending onthe ink type. The colorants are the materials that create color of the printedimage, whose amount lies between 1 10%. The rest of the ink is generallyreferred to as additives. These improve the chemical and physical properties ofthe ink, such as ink viscosity, adhesion strength, heat stability, cure rate (forlight inks), surface tension (for liquid ink), etc.

Ink-jet inks can be sorted into different groups based on the different per-spectives, as shown in Tab. 3.3. Ink vehicle is one perspective: ink-jet inksare usually divided into 4 groups. They are, aqueous-based, nonaqueous-based, phase-change, and reactive.


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Aqueous and nonaqueous inks use water or other solvents as ink vehicleswhose drying mechanism depends on penetration and absorption of the receiv-ing media (substrate). When ordinary copy or plain paper is used, the inktogether with the ink-vehicle are absorbed by the porous material. The mixingof the ink with the pores, lowers the color density and spot resolution.

Phase-change ink is also called solid ink which is solid at room tempera-ture. The ink is jetted out from the printhead as a molten liquid. When themolten ink drop hits the substrate surface, it solidifies immediately. The quicksolidification prevents the ink from spreading or penetrating the substrate, andensures good image quality for a wide variety of substrates.

Detail descriptions of the groups of inks may be found in references [Le98,HF97, III99].

Table 3.3: An ink-jet ink technologies map.

Category according to ink bases

Aqeous-Based Solution, Dispersed, Microemulsion

Nonaqeous-Based Oil, Solvent

Phase-change Liquid to Solid, Liquid to Gel

Reative UV Cured, Two parts

Category according to colorants

Organic Dyes Direct, Acid, Reactive, Disperse, Solvent

Polymeric Dyes Aqueous, Nonaqueous, Polymer Blend

Pigments Carbon Black, Organic

3.3.2 Dye-based and pigment-based inks

Inks can be divided into 3 groups based on colorants: organic dye,polymericdyes, andpigments. The organic dyes consist of organic dye molecules, whilethe polymeric dyes consist of dye p olymers. The pigmented inks are mainlyinorganic powders even though there are few organic pigments.

In the case of color the use of a dye or a pigment is one of the most widelydebated topics in the industry. Dyes and pigments are different in many ways,which contributes to their different color performances for the printed images.In this section, we briefly compare these in terms of their color performance.

Most dyes are soluble synthetic organic materials, as opposed to pigmentswhich are generally insoluble. Chemically, dyes exist in the ink as individualmolecules, while the pigments exist as clusters that consist of thousands ofcolorant molecules.

Generally speaking, the dye-based inks have superior color representationcapability or greater color gamut than the pigment-based inks. By printing on


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3.3 Ink-jet ink technologies 29

high grade substrates, dye-based ink-jet printing can deliver images of com-patible quality as those produced by silver halide. The disadvantages of thedye-based inks are their relatively poor (long term) image performance whichincludes light fastness (light fading stability), dark storage stability, humidityfastness, and water fastness.

One explanation to poor image stability for images produced by dye-basedinks, is that the dye consists of individual molecules which are chemically lessstable in terms of light exposure, oxidation, and humidity. Being a clusterof many molecules, the pigment inks have greater resistance to the impactof the environment and therefore possess better light fastness and humidityfastness. In terms of dye design, chromophore chosen has a dominant impacton the spectral characteristics and color stability achieved. Additionally, theirphysical and chemical properties also have great impact on color stability.

Trying to achieve a high degree of light fading stability and large color gamutat the same time can pose a challenge for ink development due to the rarity ofpigments and dyes that have both of these desirable properties [ADT+]. Overthe years, it has been a hot topic for debate in ink chemistry studies and ink-jettechnologies. Hopefully, we are now seeing a rapid closing of the gap in colorand image performance, between pigments and dyes [IB01].


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Chapter 4

Optical modelling: an

overview

Reflectance, such as, brightness, opacity, etc, characterize the paper sheet quan-tities, but not the general material properties of the paper. Optically, thefundamental events that govern reflection are light scattering and absorption.Therefore, quantities that parameterize the fundamental processes, such ascoefficients of scattering (s) and absorption (a), are fundamental materialproperties. To link measured reflectance values with the material properties,one needs an optical model.

Basically, there exist two groups of models for optical modelling. One groupof models is based on Radiative Transfer Theory [Cha60]. Another group usesMonte-Carlo methods [Jam80, Rub81] to simulate light scattering and absorp-tion. In this chapter we highlight the fundamental concepts of these methodsas well as their application to Paper Optics and Graphic Arts.

4.1 Radiative Transfer Theory

Radiative Transfer Theory (RTT) based approaches start with solving integro-differential equations which describe light propagation in media. According toRTT, the radiance L(r,u) (W m2 sr1) of light at position r travelling in

a direction of unit vector u is decreased by absorption and scattering but isincreased by light that is scattered from u into the direction u. The radiativetransfer equation which describes this light interaction is [Cha60]

u L(r,u) = (a+ s)L(r,u) + s4

4

q(u,u)L(r,u)d (4.1)


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32 Optical modelling: an overview

where a (m1) is the absorption coefficient, s (m

1) is the scattering co-efficient, d is the differential solid angle, and q(u,u) is a phase function.The total extinction coefficient, t, is a sum of the absorption and scatteringcoefficients,

t= a+ s (4.2)

The phase function,q(u,u), describes angular distribution of a single scat-tering event. If the integral of the phase function is normalized to equal tounity, i.e.

1

4

4

q(u,u)d = 1 (4.3)

then it is the probability density function of scattering from direction, u todirection u. Assume the directions of the incident and the scattered light

are u(, ) and u

(

,

). It is reasonable to assume that the phase functiondepends only on the scattering angle (cos = uu) rather than the incomingor the outgoing angles, i.e.

q(u,u) = q(cos) (4.4)

wherecos = coscos + sinsincos( ) (4.5)

A complete description of light transfer requires knowledge ofa, s, andq(u,u). These quantities depend not only on the properties of the raw mate-rials, but also on their distribution (or the structure of the system). To obtainthese quantities for various papers is not trivial and remains an open problem.

4.2 Phase function

The key in solving the integro-differential equation (Eq. 4.1) depends largely onthe form of the phase function, q(cos). Different phase functions have beenproposed to physically describe different types of scattering. Among the well-known are the Rayleigh phase function [Ray71], Mie phase functions [Mie08],and Henyey-Greenstein phase function [HG41]. These phase functions wereoriginally proposed for studying radiative transfer in atmospheric gaseous sys-tems and in the galaxy. Later, they found applications in other fields.

Mie theory describes light scattered by isolated spherical particles of arbi-trary size and refractive index. Taking particle size (radiusr) and refractive

index as input parameters, Mie theory calculates efficiency parameters, i.e.,scattering efficiency Qsca and absorption efficiency Qabs. The angular distri-bution of the scattered light, or the phase function, is calculated by

q(cos) = i()

22Qsca(4.6)


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4.3 Multi-flux theory 33

where = 2r/ is the particle size parameter relative to the wavelength ofthe light, i() is called the Mie theory intensity function. Mie theory found itsoriginal application in gaseous systems where the particles are well isolated.However, it has also been applied to systems that are closely packed such as,paint film [JVS00].

Henyey-Greenstein phase function is a one parameter analytical approxi-mation to a real phase function. It is expressed as [HG41]

q(cos) = 1 g2

(1 + g2 2gcos)3/2 (4.7)

where g is called an asymmetry factor which controls the scattering pattern.g = 0 corresponds to isotropic scattering, which is the case in the Kubelka-Munk approach. Clearly, = 0, are two singular points for g = 1, respec-tively. It is easy to see that when 0 and g 1

limg1

q(cos 1) = limg1

(1 + g)

(1 g)

(1 + g2 2gcos)

() (4.8)

Consulting the normalization condition given by Eq. (4.3), one can concludethat g = 1 corresponds to complete forward scattering. Similarly, g = 1corresponds to complete backward scattering. One of the greatest advantageof the Henyey-Greenstein phase function is its simple form under the Legendreexpansion,

q(cos) = 1 + 3gcos + 5g2P2(cos) + 7g3P3(cos) + ... (4.9)

This makes it a popular choice in applications, for example, in studying ra-diative transfer in biological tissues (dermal and aortic tissues) [Pra88, Yoo88,CPW90]. Very recently, it has been even considered for application in simula-tions for light transfer in paper [Eds02].

4.3 Multi-flux theory

Mathematically, the radiative transfer equation (Eq. 4.1) has no analytic so-lutions except in a few special cases, such as q(cos) = const. To solve theproblem with the help of computers, one must to divide the direction in spaceinto channels as shown in Fig. 4.1. All light travelling in a direction within a po-lar angle1 of the positive direction of the axis perpendicular to the boundaryplane is said to be in channel 1. All light travelling at a polar angle between1and2 is allocated to channel 2, etc. Such a discrete ordinate method is calledDiscrete-Ordinate-Method Radiative Transfer [Cha60, STWJ88] or Multi-fluxRadiative Transfer Method [MR71].


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Figure 4.1: The division of the directions in space into channels (provided by

H. Granberg).

The number of channel divisions depends on the nature of the application.Many papers involving radiative transfer calculations have been written byauthors using 2, 3, or 4 channels [Sch05, MR71]. A general mathematicaltreatment using this coordinate discretion, was first developed by Wick [Wic43].

It was then thoroughly exploited by Chandrasekhar [Cha44] and applied to theproblem of radiative transfer.

Mudgett and Richards [MR71, MR72] reformulated this method in a morecomprehensive way and applied it to parallel layered media, such as paintfilm [Ric70]. Their work was well followed up by other authors in modellingand predicting the optical characteristics of paint films [JVS00, All73].

In principle, by applying the Multi-flux approach with a sufficient numberof channels, one can accurately solve the radiative transfer problem. Never-theless, the solution depends directly on the knowledge of the phase function.Therefore, finding the proper phase functions for different types of papers isessential for optical modelling and simulations.

4.4 Kubelka-Munk method

The Kubelka-Munk (K-M) approach is actually a two-flux version of the multi-flux method for solving the radiative transfer problem. Here the ordinate isonly divided up into an up- and a low-hemisphere by the bounding plane (paper


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4.5 Monte-Carlo simulation 35

sheet). In the K-M approach, the light propagation depends on the K-M coeffi-cients of light absorption (k) and scattering (s). The fundamental assumptionof this approach is that light distribution in the media is ideally diffuse. It re-quires the media to be of little absorption, while at the same time of involvingstrong and angle-independent scattering (q(cos) = 1). Indeed, a compari-son between the more accurate multi-flux calculation with the Kubelka-Munkapproximation reveals that the two-flux approximation gives excellent resultsprovided the absorption is small compared to scattering, and the optical thick-ness is greater than 5 [MR71]. A key factor for a successful application ofthis method lies at finding the so-called K-M absorption coefficients, k, whichdepends not only on the physical properties of a medium but also on light dis-tribution in the medium. Detailed discussions about this issue is presented inSecs. 5.2 and 7.2.

The K-M approach has probably been the most widely used approach inpaper-making and color-using industries since it was introduced more than70 years ago [KM31, Kub48]. The continued popularity of this approach isattributable to the simple analytical solutions. Nevertheless, the solutions pro-vide insights to the processes of the light transfer and can be used to predict thereflectance of the specimen with reasonable accuracy. In addition, the simpleprinciples involved in the theory are easily understood by the non-specialist. Anexcellent review about the advantages and disadvantages of the K-M methodcan be found in [Nob85].

In the ordinary K-M method, the surface reflection is usually neglected,even though it may be an important contribution sometimes. In addition, theanalytical solution that has widely been used, is only applicable to layered

media that has a uniform concentration along the ordinate z-axis within thelayer, and the layer has infinite horizontal extension in the xy-plane. When thedistribution is non-uniform one has to work directly with the integro-differentialequation. In the next chapter, we extend the K-M method to cope with thenon-uniform ink distribution and surface reflection.

4.5 Monte-Carlo simulation

The Monte-Carlo approach belongs to another category of radiative transfersimulations. It was first used by Fermi, Von Neumann and Ulam who developedit for the solution of problems related to neutron scattering during the devel-opment of the atomic bomb. The name Monte-Carlo is used since the methodis based on the selection of random numbers. In this sense it is related to thegambling casinos at the city of Monte Carlo in Monaco. As shown in Fig. 4.2,the light scattering process can be considered as a random walk which con-sisting of straight paths between points of interaction with the media, suchas fibres or fillers in paper and colorant particles in print. The Monte Carlo


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method can be considered as a very general mathematical method to solve agreat variety of problems. In the following, we will only highlight the basicconcepts of this method for the simulation of light propagation. More detaileddescription of this method may be found in references [Jam80, Rub81, Gus97b].

1 2

A

B

l1

l2

l3

C

DA

B

3 1

3

Figure 4.2: Random walk of photons in a turbid medium (2D diagram).

For simplicity of description, we shall trace the random walks of photons ina 2D scene (Fig. 4.2). The length, li, of an undisturbed straight path of onephoton is a stochastic variable. Its statistical expectance value, lp, is called themean free pathand is inversely proportional to the extinction coefficient, t,i.e.

lp = limN

Ni=1 liN

= 1

t(4.10)

When the photon hits the media, it will either be absorbed (like photon 2 at siteB), or be scattered randomly. On average, the probability of a photon beingabsorbed is related to the relative strength of the absorption coefficient to thetotal extinction coefficient, i.e. a/t, and similarly s/t, for the scattering.

From a physics point of view, scattering means that a photon is absorbedand then re-emitted with the same (elastic scattering) or different (inelasticscattering or Raman Scattering) energy in a different direction. The lattercase is out of the scope of this work. The direction of the re-emission is atrandom. In a 3D scenario, the direction is specified by a pair of angles, polarand azimuth angles, (, ).


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4.5 Monte-Carlo simulation 37

By applying a large number of photons or equivalently by repeating the onephoton process a large number of times, one can obtain statistically meaningfulquantities (probability) that characterize the properties of the studied system.Assume that the total number of incident photons is Ntot. If there areNrefphotons that have returned to the same hemisphere (1) as the incident pho-tons, and Ntran photons that have reached the opposite hemisphere (3

), thenreflectance (R) and transmittance (T) can be computed as

R = Nref

Ntot(4.11)

T = Ntran

Ntot(4.12)

A useful concept that describes light propagation in the media is the pointspread function(PSF). If a photon hits the surface of a sheet of paper atr, theprobability that the photon exits the paper at r is described by the PSF anddenoted asp(r, r). If the PSF of the paper is known, quantities like reflectanceand transmittance can easily be computed. Therefore, to obtain the PSF ismore essential in the Monte-Carlo simulation. Recently, Gustavson [Gus97b]developed methods for computing the PSF of paper and simulated the opticaldot gain in halftone prints.


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Chapter 5

Extended Kubelka-Munk

theory and applications

5.1 Assumptions in Kubelka-Munk theory

The original theory of Kubelka-Munk (K-M) was developed for light propaga-tion in parallel colorant layers of infinite xy-extension [KM31, Kub48]. Thefundamental assumptions of the K-M theory are that the layer is uniform andthat light distribution inside the layer is completely diffused. From these as-sumptions, light propagation in the layer was simplified into two diffuse light

fluxes through the layers, one proceeding upward and the other simultaneouslydownward. After its introduction in the 1930s, K-M theory was extended byremoving some of the original assumptions. Among others, a correction to theboundary reflection at the interface of two adjacent media was introduced bySaunderson [Sau42], i.e., the well-known Saunders

ink-paper interaction

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