simulation of optical properties of inkjet prints with kubelka-munk...

Simulation of optical properties of inkjet prints with Kubelka-Munk theory

Nils Pauler, M-real, Corporate R&D TC, Örnsköldsvik

Jerker Wågberg, MoRe Research Örnsköldsvik AB Lars Eidenvall, Mid Sweden University, Örnsköldsvik

Rapportserie FSCN ISSN 1650-5387 2001:5 FSCN rapport R-01-18

October, 2001

Mid Sweden University Fibre Science and Communication Network SE-851 70 Sundsvall, Sweden Internet: http://www.mh.se/fscn

FSCN/DPC – Digital Printing Center Internet: Http/www.mh.se/fscn or http://www.ind.mh.se/dpc

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Table of Contents

SUMMARY

1 INTRODUCTION 4 1.1 Print tests with HP 970 on plain paper and photogloss paper 5

2 METHODS 6 2.1 Determination of light absorption of inkjet inks 6 2.2 Calculation of spectral reflectance factors and L*a*b* 9 2.3 Calculations of print density of the print D and the density of the ink-paper layer D∞ 10

3 RESULTS 11 3.1 Light absorption of the process inks 11 3.2 The influence of ink penetration on print density 12 3.3 The influence of ink penetration on L*a*b* values. 13 3.4 The influence of light scattering of the paper 15 3.5 The comparison between ideal ink and process inks 16 3.6 Different tone values 19 3.7 Comparison between measured and calculated values 19

4 CALCULATION OF COLOUR SPACE WITH OPTIMAL SURFACE COLOUR 20

5 DISCUSSIONS 21

6 REFERENCES 22

FSCN/DPC – Digital Printing Center Internet: Http/www.mh.se/fscn or http://www.ind.mh.se/dpc R-01-18 Page 3 (23)

Simulation of optical properties of inkjet prints with Kubelka-Munk theory Author: Nils Pauler, Jerker Wågberg and Lars Eidenvall SUMMARY Calculations based on Kubelka-Munk theory have been performed starting from spectral light scattering and light absorption of paper and inkjet inks. The calculations simulate the influence of ink penetration by assuming an additive behaviour of light absorption of ink and paper. Light scattering of the paper is assumed to be unaffected of the ink. The calculations demonstrate that ink penetration is the main reason why it is impossible to reach high colour strengths for uncoated fine papers. It is the light scattering of the paper that restrains the colour strength. Larger colour gamut is obtained if light scattering is decreased in the layer of the paper where the ink has penetrated. The simulations also indicate the existence of an optimum ink amount that gives the highest colour strength. The colour strength will decline if this amount is exceeded. This effect depends on the properties of process inks. Higher light absorption of ink is observed when the ink is distributed within the fibre structure of a paper compared to ink applied on a transparency. Colours for different halftones have also been calculated using a combination of Murray-Davids’ equation and Kubelka-Munk equation. Such a combination is discussed to be a realistic model to simulate optical properties of inkjet prints. The calculations are based on spectral light absorption values of inks of a HP 970 desktop printer and a fine paper that does not include any fluorescent whitening agent. So far the calculations has helped to understand how paper and process inks should be designed to give large colour gamut. It has to be further investigated if more parameters like mechanical and optical dot gain, equations for coloured dots (Neugenberger’s equations) and a more general ink penetration algorithm is a way to improve the accuracy of the calculations of colour for uncoated paper inkjet prints. Alternative methods to determine light absorption of inkjet inks should be considered. This way of calculating, using constants from ink and paper, may open up new possibilities to obtain correct colour, replacing the laborious colour management systems used today. Index Terms Ink Absorption, Ink Jet Printing, Kubelka Munk Equation, Optical Properties, Print Quality, Simulation


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1 INTRODUCTION

The Kubelka-Munk (K-M) theory (1–4) has been used to analyse the print through for uncoated paper within the paper industry. It is then assumed that inks penetrate and distribute homogeneously to a certain depth into the paper. The print through can be divided into a show through component and an ink penetration component (5,6) expressed as print density units. The ink penetration can also be expressed as a percentage of the paper grammage. It has been shown for uncoated paper that offset ink penetrates homogeneously to a depth that is almost linear to the ink amount, up to a depth of about 50 % of the paper The K-M equations can be solved explicitly in either direction. This means that if ink penetration and lighscattering (s) and lightabsorption (k) of the ink are known, the optical properties of the printed paper can be calculated. The calculation is performed in two steps; firstly the s and k of the ink-paper layer is calculated by combining the s and k of the paper and ink using the additivity rule. The print density of the printed paper can thereafter be calculated using the K-M equation (7). The following observations were made from these simulations: • Print density reaches a plateau when the ink penetrates linearly vs. ink amount. • A barrier is needed in order to overcome the low plateau behaviour of print density.

The plateau will then appear at a higher print density level. • The print density increases when light scattering of paper is decreased These observations can explain the low print density of uncoated papers, the increased colour strength of coated paper and the increased ink demand observed for fillers with high light scattering. As inkjet also show a high degree of ink penetration, the same K-M equation may be useful for predicting print density for inkjet. When calculations are performed using spectral reflectances, the impact of ink penetration on colour can be calculated. Different approaches for the simulation of inkjet print has been reported in the graphical research literature. The K-M equations have been used for simulations for non-absorbent materials and fairly good agreements between calculated and measured values have been reported. The overall most common approach is however to use the Murray-Davids’ or Neugenberger’s equations since they describe the dependence of the different tone values normally used to produce colours in prints. A combination of the Kubelka-Munk equation and Murray-Davids' equation is often reported, (8, 9). In these works, efforts have been made to include phenomena like optical and mechanical dot gain. So far, the influence of ink penetration has been paid very little attention in theoretical models for inkjet print. Li and co-workers (10) have however derived more general equations for ink penetration that may find application for inkjet print.


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The HP DeskJet 970, an inkjet printer for small office use, offers the possibility to vary the ink amount in five steps. These steps are available under all major settings of the printer, like Photogloss, Plain paper and Transparency. Preliminary investigations show that ink amount increases from about 1 g/m2 to 2–3 g/m2 when ink level is changed from 1 to 5. This opens up new possibilities to study the inkjet process, as ink amount is a main parameter in graphical research.

1.1 Print tests with HP 970 on plain paper and photogloss paper

Intensive lab studies have been performed varying the ink levels and measurements have confirmed that colour strength increases with higher ink levels. Figure (1a–c) (11). The difference between uncoated fine papers and special inkjet paper like "Photogloss quality" papers is also clearly seen in the figures. As the ink amount reaches the higher levels, a typical bending behaviour of the colour values is observed. These tests also shows that ink penetration is considerable and increases with ink amount when the printing is made on plain papers, Figure1 d.

Full-tone

-100

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0

50

100

150

-70 -20 30 80

a*

b*

Full -tone

20

40

60

80

100

-70 -20 30 80a*

L*

Full-Tone

20

40

60

80

100

-60 -10 40 90

b*

L*

01020304050

0 1 2 3 4 5Ink level

Pene

tratio

n (%

)

Plainpaper setting Photopaper setting

Figure 1a–. a* vs. b*, L* vs. a* and L* vs. b* for print on photo paper and uncoated fine paper (outlined filled circles) at ink levels 1 to 5. Figure 1d ink penetration vs. ink levels 1 to 5. Printing with HP 970, Plain paper setting.


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The normal way to create different colour strength in print is to vary the halftone values. In Figure 2, L*a*b* is shown for tone values 30, 50, 80 and 100 %. Ink level 3 and 5 were used in the printing. Note the similar curvature of the plots in Figure 2 and Figure 1 above.

Inklevel 3

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a*

b*

Inklevel 5

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-25

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25

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-50 -30 -10 10 30 50 70 90

a*b*

Inklevel 3

30

50

70

90

110

-50 0 50 100

a*

L*

Ink level 5

30

50

70

90

110

-50 0 50 100

a*

L*

Figure 2 a–d. a* vs. b*, L* vs. a* and L* vs. b* for print on photo paper and uncoated fine paper (outlined filled circles) at ink levels 3 and 5 for half tone values 0 % 30% 50% 90% and 100%. Inkjet setting was Plain Paper for all prints with HP 970.

2 METHODS

2.1 Determination of light absorption of inkjet inks

Light absorption of inkjet ink was determined in two different ways, denoted i and ii: i) Variable Rg method by printing process ink, fulltone, on transparency. 1. Cyan, magenta, yellow and black fulltone surfaces were printed on transparencies with

a HP 970 with ink level settings 1, 2, 3, 4 and 5. The transparency was allowed to dry and the ink amounts were determined by weighing with high accuracy.

The reflectances of unprinted and printed areas were measured with an Elrepho 2000 with white and black paper as backing.


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2. The light absorption was calculated using equation 1–4 for wavelengths 400, 420…700 nm

( )( ) ( )( )

gsvgvs

gsgvsvsvgsgv

RRRRRRRRRRRR

a−

+−−+−⋅=

1121 (1)

12 −−=∞ aaR (2)

( )( )( )( )sgs

gss

RRRRRRRR

RR

ws

−−−−

⋅

−

=∞∞

∞∞

∞∞

11

ln1

1 (3)

( )

∞

∞−=

RRsk

21 2

(4)

where Rgv = reflectance factor for transparency with white background Rgs = reflectance factor for transparency with black background Rvs = reflectance factor for printed transparency with white background Rs = reflectance factor for printed transparency with black background R∞ = reflectivity of the print s = light scattering of the ink layer k = light absorption of the ink layer ii) Inverse calculation, knowing ink penetration on uncoated paper Fulltone patches in cyan, magenta and yellow were printed on uncoated paper. The ink penetration was determined using the K-M equation according to Bristow(6). The amount of process inks for the five different ink levels were assumed to be the same as for the printing on transparency, see above. The results from the test printings are summarised in Table 1. Table 1. Ink amount and ink penetration measured for prints on uncoated papers. Ink amount, g/m2 Penetration, % Level Cyan Magenta Yellow Cyan Magenta Yellow 1 0,61 0,87 0,99 15,61 8,7 0 2 0,93 1,26 1,4 16 15 17,8 3 1,24 2,0 2,9 19 28,3 39,1 4 1,9 3,0 3,2 32,7 37,1 38,3 5 2,1 2,8 2,9 47,5 43,7 39,3 The values of levels 3,4 and 5 were used for the determination of light absorption of inkjet inks. It is assumed that light scattering of paper is not affected of the inks. The light absorption of the inkjet ink was determined by inverse calculation using the solver add–in in Excel. The solver algoritm vary the papameter kInk until RCalc=RMeasured where RCalc = f(kInk, p, wInk, wPaper ,kPaper) is calculated using equation 5 to 13.


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If the general K-M equation to calculate R ∞ from light scattering s and light absorption k is denoted:

sk

sk

skksR ⋅+

−+=∞ 21),(

2

(5)

and the K-M equation to calculate R over a background Rg with grammage w and reflectivity R ∞ is denoted

( )

( )∞∞∞∞

∞

∞∞

∞∞∞

∞

−+

−

−

−+

−

−

=

RRRR

swRR

RRR

RR

swRR

RRRwsR

gg

gg

g1exp1

1exp1

),,,( (6)

the calculation of RCalc can be described by equations 7–13:

InkPaperPaperInk wpww +⋅=100

(7)

InkPaperInk

Ink

wwwx

+= (9)

xkxkk InkPaperPaperInk +−= )1( (10)

),( PaperPaperPaper, ksRR ∞∞ = (11)

),( PaperInkPaperPaperInk, ksRR ∞∞ = (12)

),,,( ,, PaperPaperInkPaperInkPaperCalc ∞∞= RRwsRR (13)

where kInk = light absorption of the ink wInk = grammage of ink p = penetration depth of ink expressed as % of paper thickness wPaper = grammage of paper sPaper = light scattering of paper kPaper = light absorption of paper


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2.2 Calculation of spectral reflectance factors and L*a*b*

The same spectral s and k value of uncoated paper, without any FWA (fluorescent whitening agent) has been used in all calculations. The spectral reflectance of an inkjet printed paper was calculated using ordinary K–M equations under the following assumptions: 1. The light scattering coefficient of paper is unaffected by inkjet inks. 2. The inks are evenly distributed down to a certain depth of the paper. This layer is

denoted the ink–paper–layer. 3. The light absorption coefficients of both inks and paper can be added in the ink–

paper–layer, in accordance with the Kubelka-Munk theory.

The colour gamut, the maximum volume in L*a*b* space that the printer can produce, was calculated by simulating different amounts of ink, from no ink at all to the amount corresponding to level 5 of the printer. The calculation was performed over 16 wavelength bands from 400 nm to 700 nm using the D65/10° colour matching functions. Different colours were calculated by using an additive blending algorithm for the light absorption of process inks and paper. Blue was thus simulated by adding equal parts of cyan and magenta, green as equal parts of yellow and cyan and red as equal parts of yellow and magenta. In order to determine the color gamut, the gamut was split up into two parts. In the first part, inks were blended in steps were each colour points comprises of one or two process inks. The inks were blended so that colour hues from 0 to 360 and colour strengths from no ink to ink levels 5 were realised. In the second part, the remaining third process colour was added in steps, so that a composite black point were reached as the final point. Composite black was thus simulated by adding equal parts of ’level 5’ cyan, magenta and yellow. The calculations were done following equations, 14–21.

100pww ⋅= PaperPaperPen (14)

)( InkYellowInkMagInkCyanPaperPen

InkCyanCyan wwww

wx

+++= (15)


InkMagMag wwww

wx

+++= (16)


InkYellowYellow wwww

wx

+++= (17)


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YellowYellowMagMagCyanCyanYellowMagCyanPaperPaperInk kxkxkxxxxkk +++−−−= )1( (18)

),(, PaperPaperPaper ksRR ∞∞ = (19)

),(, PaperInkPaperInkPaperInk ksRR ∞∞ = (20)

),,,( Paper,PaperInk,PaperInkPaperCalc ∞∞= RRwsRR (21)

The calculation was repeated for wavelength 400,420…700 nm. Tristimulus values X, Y and Z were calculated for D65/10º colour matching function and L*a*b* was calculated according CIE Lab 76.

2.3 Calculations of print density of the print D and the density of the ink-paper layer D∞

The print density was calculated for cyan according to eqn. (22), at the wavelength where light absorption has its maximum, 640 nm.

= ∞

Print

Paper

RR

D ,log10 (22)

where R∞,Paper is reflectivity of the paper and RPrint is reflectance factor of print with R∞,Paper as backing. In order to clarify how print density is influenced by ink amount a value denoted D ∞ was calculated. D∞ is the print density of an infinitely thick ink-paper layer.

=

∞

∞∞

PaperInk,

Paper

RR

D ,log10 (23)

Colour of different tone values has also been calculated. The reflectances for different tone values were calculated using Murray-Davids’ equation, where the fulltone was calculated according to K-M equation taking the ink penetration into consideration.

)( ,, FullTonePaperPaperTone RRToneValueRR −−= ∞∞ (24)


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3 RESULTS

3.1 Light absorption of the process inks

Light absorption values for cyan, magenta, yellow and black inks are shown in Figure 3.

lightabsorption

050

100150200250300350400450500

400 450 500 550 600 650 700

nm

m2 /K

g

Figure 3. Light absorption for the cyan, magenta, yellow and black ink determined from measurement of inks on transparencies. The light absorption of black ink follows the coloured inks. This is probably because this black ink also includes coloured inks. The calculation gave small s values around 1, but for the black ink s was about 5 m2/kg. This may be an indication that the black ink has some pigments since pigmented ink is likely to have more light scattering than black inks composed of organic dyes. When the light absorption was determined by inverse calculation the values were about 10 times higher than the measured values, Figure 4. The reason for the big difference in light absorption between the two methods may be that light absorption is influenced by the light scattering of the fibres/fillers in the paper structure (see also discussion).

lightabsorption

0

1000

2000

3000

4000

5000

6000

400 450 500 550 600 650 700

nm

Figure 4. Light absorption of cyan, magenta and yellow inkjet ink determined by inverse calculation.


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3.2 The influence of ink penetration on print density

The impact of ink penetration on print density is shown in Figure 5. The calculations are performed for increasing ink amount from 1 to 2 g/m2 with penetration depths as parameters. When the ink penetrates in a linear fashion from 1 to 50 % of the paper, the print density shows an initial rapid increase and then flattens out into a plateau at print density level of about 1,0. If the ink is allowed to distribute evenly into 50 % of the paper for all ink amounts, the print density will increase monotonously, albeit more slowly, until it reaches the final value. When the ink stays in the upper part of the paper (homogeneously distributed in 5 % of the paper), print density will reach a higher level about 1,8 for the highest ink amounts. A way to obtain an even higher print density is to reduce light scattering of the ink-paper layer, denoted ‘5 % Pen Red Lsc’ in the figure.

0

0,5

1

1,5

2

2,5

3

0 0,5 1 1,5 2 2,5

Ink grammage g/m2

Prin

t Den

s Liniear 1-50Evenly 50Evenly 5Red Scatt

Figure 5. Print density vs. ink amount for four different penetrations. From bottom and up in the figure, ink is distributed: 1) evenly in the upper 50 % layer of the paper 2) linearly to ink amount from 1 to 50 % depth 3) evenly in the upper 5% part of the paper 4) evenly in the upper 5% part of the paper and the light scattering in this part is reduced to 1%

of the paper. The print density dependence of different penetration profiles is a combined effect of increasing print density of the ink-paper layer and a covering effect of the ink paper layer, Figure 6. As can be seen from Figure 6b, the print density of the ink-paper layer, denoted D ∞ in the figure, increases very fast with ink amount in the case of a linear penetration from 1 to 50 %. As this dark ink-paper layer becomes thicker it will cover the paper and the print density will reach the plateau value. In the case of evenly distributed ink into 50 % of the paper, increased ink amount means higher ink concentration in the ink-paper layer and D ∞ and D increases moderately.


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Ink G ram m age

Ink P enetra tion %

1-50%

50%

0

0,2

0,4

0,6

0,8

1

1,2

0 1 2

Ink G ram m age g /m 2

Den

sity

P en 1 ,50

P en 50,50

D

D oo

D ,D oo

Figure 6 a–b. Print density of the paper, D, and print density of the print/paper layer, D ∞ , vs. ink amount for two different penetrations. From bottom and up the figure, ink is distributed:

1) evenly in the upper 50 % layer of the paper 2) linearly to ink amount from 1 to 50 % depth

3.3 The influence of ink penetration on L*a*b* values.

A calculation of a* and b* for increasing ink amounts is shown in Figure 7. A typical bending behaviour is noticed for high ink amounts. This bending behaviour will be discussed more in chapter 2.5, where process inks are compared to what is called ideal inks. As expected, higher colour strength is obtained when the ink is concentrated to the upper part of the paper, as can be seen in Figure 5a and b, where the ink penetrations are 1–50 % and 1–5 % respectively.

Figure 7 a–b. Calculation of a* and b* for increasing ink amounts when the inks penetrate from 1 to 50 % of the paper (left) as opposed to when the ink is concentrated to the first 1 to 5 % of the paper (right). In Figure 8, corresponding calculations for L* vs. a* and L* vs. b* also demonstrates the impact of ink penetration. Note the differences in composite black (the lowest point of the graph); a blacker print (lower L* value) is obtained when the ink is concentrated towards the surface of the paper.


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Figure 8 a–c. Calculation of L* and b* for increasing ink amounts when the inks penetrate from 1 to 50 % of the paper (left) as opposed to when the ink is concentrated to the first 1 to 5 % of the paper (right). The colour gamut will be larger the less it penetrates into the paper. This is illustrated below, where an assumed penetration linear to the ink amount is compared to the case where the ink is assumed to always penetrate down to the middle of the paper, Figure 9.

Figure 9. Calculation of L*a*b* for increasing ink amounts when the inks is evenly distributed in 50 % of the paper (left), compared to when the inks penetrate from 1 to 50 % of the paper (right).


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It is interesting to notice that the ink penetration distribution does have influence on the shape of the colour space. Calculations where only two process colour define the colour points, i.e. the upper part of the colour gamut, clarify that there exists an optimal ink amount. When the ink penetrates linear to the ink amount, these maximums are obvious, which is not the case when the ink is evenly distributed, Figure 10.

Figure 10. Calculation of L*a*b* for increasing ink amounts when the inks is evenly distributed in 50 % of the paper (left), compared to when the inks penetrate from 1 to 50 % of the paper (right).

3.4 The influence of light scattering of the paper

Low light scattering in the ink-paper layer has a positive influence on the colour strength for inkjet prints. This is shown in figure 11, where the calculation has been made for uncoated paper and a paper were the light scattering has been decreased by 95% in the ink-paper layer. Photogloss papers, with their high colour strengths, are contructed this way.


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Figure 11 a–d. Calculation of L*a*b* for increasing ink amount when the inks penetrate from 1 % to 50 % of the paper and the light scattering of the ink layer is reduced by 95 %. In the upper two figures this situation can be seen, as the reduced light scattering case totally encloses the case of unmodified light scattering. In the lower figures, the cases are shown in separate figures, where the right figure shows the case when the light scattering of the ink-paper layer has been reduced.

3.5 The comparison between ideal ink and process inks

If light absorption of three inks cover the whole visual spectrum according to figure 12, these inks can be regarded as ideal inks. The absorption intervals have been chosen manually just to illustrate one set of ideal inks. Probably there are more favourable intervals that could be denoted as an optimal ideal CMY set.


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Figure 12 Light absorption for the ideal inks used. Yellow absorbs light in the interval 360 to 500 nm, magenta from 500 to 580 nm and cyan from 580 to 780 nm. The light absorption was set to 5000 m2/kg. The behaviour of these ideal inks is illustrated by letting their light absorption go into the calculation. In Figure 13 process inks are compared with ideal inks. The calculation is made with the assumption of linear penetration from 20–40 % for increasing ink levels.

Figure 13 a–d. Calculation of L*a*b* for increasing ink amount for process inks (left) and ideal inks (right) corresponding to level 1 to 5. The ink penetration is assumed to be linear from 1 % to 50 %.


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It is obvious from figure 14 (left), that ideal inks do not hook or bend towards the grey L* axis for high ink levels. The figure 14 (right), which covers the whole colour gamut, shows that these ideal process inks do not embrace all colours obtained by process inks. A black process ink is probably needed to reach the dark green colours.

Figure 14 a–b. Calculation of L*a*b* for increasing ink amount for ideal inks and process inks corresponding to level 1 to 5. The ink penetration is assumed to be linear from 1 % to 5 %. The left figure is calculation of the upper part of the gamut, the right hand side is for the whole colour gamut. Figure 15 below clearly shows the differences between ideal inks and process inks. The figure shows spectral values for cyan at 10 different ink levels where the ink penetration is linear from 0 to 40 %. The ideal inks do not give any decline in the reflectance in the non-absorbent part of the spectrum, whereas the process cyan shows a clearly decreasing behaviour in this region.

Figure 15 a–b. Spectral reflectance values calculated for ideal cyan ink (left) and process cyan at 10 increasing ink levels (right), when ink penetrates from 1 to 50 % At high ink levels, the reflectances of the process inks tend to reach low levels for the whole spectrum. This explains the hook tendency for process inks.


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3.6 Different tone values

In Figure 16 different tone values calculated with Murray-Davids’ equation has been compared with different ink amounts calculated with the Kubelka-Munk equation. It is obvious that Murray-Davids’ equation, where the reflectances are calculated according to the coverage of ink on the surfaces, gives a more linear behaviour of a* vs. b* whereas different ink amounts give a bend or hook behaviour. In the halftones, the coloured parts with ink are assumed to have an ink penetration of 50 % and an ink level of 5.

Figure 16 a–c. Calculation of L*a*b* for increasing ink amount (left) and increasing tone values (right). The ink penetration is assumed to be 50 %, and the ink amount at level 5 for the parts of the surface covered with ink.

3.7 Comparison between measured and calculated values

In Figure 17, calculated and measured values are compared when ink level increases from 1 to 5. It is obvious from the figures that the simulation fairly well agrees with measured data.


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Ink=1-10, Pen=0,01%-40%

-50

0

50

100

-60 -40 -20 0 20 40 60

a*

b*

hbbb

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100

0

10

20

30

40

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-100 -50 0 50 100

Figure 17 a–c Measured (lines) and calculated values (square points) for inkjet prints on uncoated papers. The calculations were made for ink penetration from 20–45 % for all three process inks.

4 CALCULATION OF COLOUR SPACE WITH OPTIMAL SURFACE COLOUR

Calculation of the maximum perceivable colour space according to Rösch (11) has been performed. In Figure 17 this calculation is compared with inkjet were the ink is concentrated to upper parts of an uncoated paper. It is obvious from this figure that there still much room for improvement of the inkjet process colour system.


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Figure 18. Optimal colour gamut according to Rösch compared with the much smaller gamut obtained by simulation where the ink is concentrated to the 5% upper parts of an uncoated paper.

5 DISCUSSIONS

The calculations have demonstrated how the Kubelka-Munk theory can be used to simulate the interaction between inkjet inks and paper. It was possible to study the influence of different penetration depths into the paper, to simulate the influence of different optical paper properties and to make calculations for different tone values and compare ideal inks with process inks. The simulations show that light scattering in the ink-paper/coating layer and the non ideal behaviour of the inkjet inks are the main reasons to limits in colour gamut. The paper and ink should be designed so that the ink stays close to the surface. The light scattering should be low in the ink paper layer. The process ink should be designed so that it absorbs light only in the interval intended. Preliminary studies show that the simulated bending or hook tendency at high ink amounts of a* and b* values, can be verified for real inkjet prints. Print tests also demonstrate the influence of ink penetration by comparing photogloss and uncoated papers although it was not possible to get a value of the ink penetration depth of photogloss paper. The finding that lightabsorption of the inks determined by variabel Rg method for prints on transparency was different from the determination made on uncoated paper, has to be investigated. It should be possible to make a rigorous evaluation of the relevance of these types of simulations. With HP 970, the ink amount can be varied in up to seven different ink levels, and the ink penetration can be determined by using the K-M equation. Corresponding calculations can be made and the reflectances and L*a*b* values compared. Screened surfaces can also be evaluated by comparing measured colour with calculations, where Murray-Davids’ equations are combined with K-M penetration calculations.


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The simulations can be extended to include gradual ink penetration, comparison of subtractive and additive screened dots and simple simulation of optical dot gain using the following approaches: . • study different gradual concentrations of the ink in the paper by including equations

for layered structures • compare additive and subtractive screened surfaces by using layer equations where the

process inks are placed on top of each other for the subtractive blending • simulate the optical dot gain by letting the ink layer be reduced to half its original value

and combine K-M and Murray David’s equations

6 REFERENCES

1. Kubelka P. and Munk F., "A contribution to the optics of colorant layers", (In German). Z. Phys. 12(11a):503-66101 (1931)

2. Kubelka P., "New contributions to the optics of intensely light scattering materials. II.

Non homogeneous layers", J.Opt. Soc. Am. 44(4): 330–336 (1954) 3. Pauler N., ”Opacity and Reflectivity of Multilayer Structures”, Structure and properties,

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0 5. Pauler N., ”Opacity is not always a direct guide to print-through”, Paper in Advances in

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simulation of optical properties of inkjet prints with kubelka-munk...

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