Multispectral Analysis of Paper Production Phases

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Department of Information Technology

Multispectral Analysis of Paper Production Phases

The topic of the Thesis has been confirmed by the Departmental Council of the Department of Information Technology on 22nd of January, 2003.

Supervisor: Professor Pekka Toivanen Examiner: D. Sc. Lasse Lensu

in Lappeenranta on 25.04.2003 Irina Mironova

Ruskonlahdenkatu 13-15, D 12/2 53850 Lappeenranta

FINLAND +358 400693922

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ABSTRACT

Lappeenranta University of Technology Department of Information Technology Irina Mironova

Multispectral Analysis of Paper Production Phases Master’s Thesis

2003

61 pages, 45 figures, 2 tables

Supervisor: Professor Pekka Toivanen Examiner: D.Sc. Lasse Lensu

Keywords: color of paper, multispectral imaging, similarity metrics

Paper mills estimate color of paper based on L*a*b values. This approach lacks for accuracy, which leads the paper of the same type to have different color. This thesis is dealing with color estimation based on multispectral approach. The idea of the method is to compare standardized spectral reflectance curve and spectral reflectance curve of a current paper roll using metrics. 12 metrics from literature [27] and 1 metric constructed by our group were examined to find the most effective ones. The effectiveness means the ability to recognize differences in hue, saturation, and brightness. The experiment was carried out on artificial images and actual paper samples. As a result, maximum-minimum, arithmetic- mean minimum and geometric-mean minimum metrics were the best.

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“Multispectral Analysis of Paper Production Phases ”, Irina Mironova, 2002

TIIVISTELMÄ

Lappeenrannan Teknillinen Yliopisto Tietotekniikan osasto

Irina Mironova

Paperintuotannon vaiheiden multispektraalinen analyysi Diplomityö

2003

61 sivua, 45 kuvaa, 2 taulukkoa Ohjaaja: Professori Pekka Toivanen Tarkastaja: TkT Lasse Lensu

Avainsanat: paperin väri, multispektraalinen kuvantaminen, samankaltaisuuden mittaustavat

Paperitehtaissa paperin väriä arvioidaan L*a*b –arvojen perusteella. Tämä lähestymistapa ei ole tarkka ja johtaa siihen, että saman luokkaan kuuluvat paperit saatetaan havaita eri värisinä. Tässä diplomityössä tarkastellaan värien arviointia multispektraalisen

kuvantamisen avulla. Menetelmän ajatuksena on verrata standardoidun heijastuman spektriä kohteena olevan paperirullan heijastuman spektriin mittaustapojen avulla. 12:n kirjallisuuteen perustuvan ja yhden tutkimusryhmämme kehittämän mittaustavan joukosta pyrittiin valitsemaan parhaat mittaustavat tutkimuksien perusteella. Mittaustavan tehokkuus tarkoittaa kykä tunnistaa eroavaisuuksia värisävyn, värikylläisyyden ja valoisuuden

perusteella. Mittaustapoja tutkittiin sekä keinotekoisilla kuvilla että aidoilla paperinäytteillä. Tuloksena maksimi-minimi-, aritmeettisen keskiarvon minimi- ja geometrisen keskiarvon minimimenetelmä olivat parhaita mittaustapoja.

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Foreword

I wish to express my gratitude to all the people who contributed to this thesis. I would like to thank my supervisor Pekka Toivanen who introduced me into the project and gave me valuable advices. I appreciate Lasse Lensu for his worth comments and suggestions. He put a lot of work into thesis examination. I am grateful to the thesis coordinator Pasi Saarinen for the help in cooperation with UPM-kymmene. I would like to thank Raimo Kaljunen from UPM-kymmene for furnished materials. Special gratitude goes to Petri Aijo who accompanied me to the physical laboratory. He spent much time waiting until I carried out measurements. I would like to thank Alexander Davydov who furthers my English improvement. I appreciate Vladimir Botchko for the help to organize my workplace.

Finally, I want to express my gratitude to Jan Voracek for the opportunity to study in LUT.

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1 Introduction

1.1 Goals

Producing paper of the same color is an important issue for paper mills. Nowadays the color of paper can vary from one roll to another, which causes dissatisfaction among customers. For example, it is the topical question for printing houses, which require a paper of the same color for printing books, magazines and other press of fine quality. Nowadays, the color of paper is estimated based on L*a*b* values (L*a*b* is perceptually uniform color description model). This approach is not enough accurate, which results in the slightly different color of produced paper. Some time ago, multispectral approach was proposed to apply to color estimation. However, research in this field failed since there was no appropriate background at that moment.

The goal of this thesis is to investigate multispectral approach in color estimation. This approach is more accurate than L*a*b* one, since L*a*b* values are calculated from the spectral curve. One way to estimate color of paper is to measure its deviation from the standardized spectral reflectance curve. The degree of similarity is determined through metrics. Study included examination of 12 metrics from literature [27] and 1 metric, which was constructed by our group, for ability to recognize differences in hue, saturation and brightness. After analysis of experimental results, the best metrics were chosen.

1.2 Thesis structure

Origin of color is described in Chapter 2. This chapter is concentrated on sources of light, properties of matter and physiology of human vision, which influence on color together.

Chapter 3 describes some of color models, which are used for color classification and description. It presents following models: RGB, CMY, HSI, XYZ, L*a*b*. In Chapter 4, methods of determination of perceptual difference between colors are considered.

Experimental part is presented in Chapter 5. It describes task, experiment, and results.

Finally, chapter 6 contains conclusion and suggestions for further research.

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2 Color appearance

The color of objects appears in the presence of three components, which are the light source, the object, and the observer. Color appearance of object is preceded by the series of events. Light source emits light, which is incident on the object. The object reflects a part of light, which is received by receptors of the observer.

2.1 Physical nature of light

Light appears to be dualistic in nature [29, p. 3]. It possesses properties of both particles and waves. Particle of light called photon propagates through the space with the constant speed of 3*10 m/sec. Wave of light has electromagnetic nature, and it is characterized by ⁸ the wavelength, which is the distance between two adjacent wave crests, and the amplitude, which is the height of the wave [3]. Light behaves as electromagnetic waves in reflection, refraction, diffraction phenomena, but it shows properties of particle in emission, absorption, and interaction with matter [29, p. 3]. There are different types of light with respect to their wavelengths: gamma rays, x-rays, ultraviolet, visible, infrared, short radio waves, etc. Longest waves (radio waves) are more than 10 nanometers (nm) length. ⁶ Shortest waves (gamma rays) are less than 0.1 nm [29, p. 20]. Visible light is electromagnetic radiation from the range between 380 and 780 nm (Fig. 1). Thus, human eye responds to light of wavelengths greater than extreme violet and less than extreme red.

These limits are not strict: most individuals respond to light of wavelength to about 3*10 nm (ultraviolet light) [30, 202]. ²

Figure 1. Visible part of electromagnetic spectrum [3].

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Wavelength of light defines its color. Monochromatic light is that of a single wavelength.

Polychromatic light is a mixture of waves of different wavelengths [29, p. 49]. A classic example of polychromatic light is white light. Although there is no unique definition of white light, it is considered as light that contains waves of all wavelengths in approximately equal proportions [29, p. 360].

2.2 Sources of light 2.2.1 Types of light sources

Light is emitted by various natural and artificial sources. Examples of natural light sources are the sun, stars, and lightning. Examples of artificial light sources are candles, lamps, and lasers. Artificial sources differ from each other by the way of producing energy [2]. In temperature light sources energy is obtained by heating. An increased temperature forces atoms to move faster, which makes them to collide together and pass energy to electrons.

As a result, electrons jump to higher energy levels. This is unstable state for atom, which causes electrons give off their energy by emitting photons [2]. An example of temperature light source is candle [2]. In luminescent light sources, the energy is obtained from chemical reaction or under the influence of electricity. A luminescent light source, which uses phosphors (chemical substances that absorb and re-emit light), is called photoluminescent [2]. When the re-emission takes place concurrent with the absorption, the source is called fluorescent; when the re-emission continues after the light is no longer being absorbed, it is called phosphorescent. The example of a photoluminescent source is a fluorescent lighting tube, which is actually a mercury lamp coated inside with phosphor [3].

Another group of light sources produces light energy using atom-smasher or lasers. They are very high-focused, controllable and powerful [2].

2.2.2 Illuminants

Light source is a physical emitter of radiation, while illuminant is a specification for a potential light source [5]. Not every illuminant represents the light source because of

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technical complications with the construction. Theoretical sources are called blackbodies or Planckian radiators (after great German physicist Max Planck) [3].

Both actual light sources and illuminants are primarily characterized by their color temperature and spectral power distribution [3].

2.2.3 Color temperature

Color temperature is the temperature of “blackbody”. Blackbody radiator can be specified through Planck’s Equation as a function of single variable that is absolute temperature [15, p. 68]. Thus, color temperature of a blackbody radiator uniquely defines its spectral power distribution. Correlated color temperature (CCT) is the term used for description of actual light sources. It refers to the color temperature of a blackbody radiator that has the most near spectral power distribution as the source in point [15, p. 68].

Standard unit of color temperature is Kelvin. Kelvin is equivalent to Celsius in magnitude [3]. Conversion from Kelvin to Celsius is accomplished as follows:

t/°C = T/K - 273.15

2.2.4 Spectral power distribution

Spectral power distribution of the light source characterizes composition of the emitted light from a source or illuminant at a particular color temperature. It is a plot, or a table, of a radiometric quantity as a function of wavelength [15, p. 67]. For light sources, it can be measured by a spectrophotometer.

Blackbodies with cool color temperatures emit light of longer wavelengths (from red to yellow) in large quantities than shorter wavelengths (from blue to violet). Hotter blackbodies emit light of all wavelengths in approximately equal proportions, with tendency to shorter wavelengths [3]. Examples of spectral power distributions are represented in Fig. 2.

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“Multispectral Analysis of Paper Production Phases ”, Irina Mironova, 2002 Figure 2. Examples of Spectral Power Distributions [3].

2.3 Interaction of light and matter

Another important factor, which influences on color we see, is the interaction between light and matter [3]. When light is incident on surface, all or some of the following physical phenomena occur:

• Reflection

• Transmission

• Absorption

2.3.1 Reflection

In general case, when light beam is incident on boundary between two media, one part of incident light is reflected (Fig. 3), another part is transmitted, and the remainder is absorbed [15, p.73]. The amount of reflected light depends on nature of the surface and the angle of incidence. The amount of reflected light increases as the angle of incidence increases [1].

6500 K CIE Illuminant D₆₅

Wavelength, nm

Relative Spectral Power

400 700

0 200 150 100 50 2854 K

CIE Source A

Wavelength, nm

400 700

0 200 150 100 50

Average Daylight

Wavelength, nm

400 700

0 200 150 100 50

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“Multispectral Analysis of Paper Production Phases ”, Irina Mironova, 2002 Figure 3. Reflection.

Scattering is another aspect of reflection. Scattering occurs when the frequency of the light wave transmitted through a substance is not equal to natural frequencies of the molecules of a substance [30, p. 460]. It is the phenomenon of reradiation of absorbed energy by the molecules [29, p. 197] (Fig. 4). The classic example of scattering is a scattering of sunlight by the air molecules, which causes blue color of sky [3]. The intensity of scattering depends on two factors:

The size of a particle (Fig. 5)

The difference between refractive indexes of the medium and of the particles (Fig.

6).

Figure 4. Scattering.

When scattering intensity depends on wavelength of the light, scattering is called selective.

For example, air molecules scatter short waves more intense than long waves [3], which causes blue color of the sky.

Incident beam Reflected beam

Angle of incidence

Incident beam

Scattering by molecules

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Figure 5. Scattering intensity is a function of a relative refractive index [4].

Figure 6. Scattering intensity is a function of a particle diameter for a typical pigment [4].

2.3.2 Transmission

Another phenomenon that can take place when light is incident on surface is transmission.

When light is transmitted from one medium to another, in which the velocity of light is different, refraction occurs [30, p. 4]. The velocity in vacuum is equal to 3×10⁸m/sec. The velocity in the material is smaller. The ration of the velocity of light in a vacuum (c) to the

Particle diameter

Scattering intensity

Different Identical Different Relative refractive index

Scattering intensity

High Medium Low Zero

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velocity of light in the material (v) is called index of refraction (n) of the material for the particular wavelength (Eq. 1):

cν

n= (1)

Moreover, the velocity in the material, and the index of refraction respectively, is different for waves of different wavelengths (this effect is called dispersion). For all cases, the index of refraction is larger for short waves. [29, p. 17]. The change in the velocity causes light to change direction. The angle between the refracted wave and the normal to the surface is calculated from Snell's Law (Fig. 7) (Eq. 2):

β α sin sin

1 2 = n

n (2)

Figure 7. Snell's Law.

2.3.3 Absorption

When light passes through a matter in the solid, liquid, or gaseous state, it can be absorbed by it [30, p. 446]. The phenomenon is accompanied with heating of the material [4].

General absorption occurs when a substance absorbs light of all wavelengths in approximately equal quantities. Such substances appear to be grey. However, no substance is known which absorbs light of all wavelengths equally; some of substances absorb light of wide range of wavelengths. Selective absorption is absorption of light of certain wavelengths. A substance appears to be color due to selective absorption.

α

n1

n2

β Angle of refraction

Angle of incidence

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“Multispectral Analysis of Paper Production Phases ”, Irina Mironova, 2002 There are two laws of absorption:

1. Materials of equal thickness absorb equal quantities of light [Lambert’s law] (Fig. 8) 2. Materials of equal concentration of a dye absorb equal quantities of light [Beer’s law]

(Fig. 9).

The laws should be applied to each wavelength separately because they operate with colorants that absorb only certain wavelengths. Moreover, the laws are not universal.

Lambert’s law is always true in the absence of scattering, whereas Beer’s law is appropriate for certain materials [4].

Figure 8. Lambert’s law. It states that materials of equal thickness absorb equal amounts of light.

Figure 9. Beer’s law. It states that materials with equal amount of colorant absorb equal amounts of light.

2 units of thick

1 ^1/2 ^1/4

1 ^1/4

1 unit of thick 1 unit of thick

1

1 ^1/2 _1/4

1 unit of colorant

2 units of colorant 1 unit of colorant

1/4

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“Multispectral Analysis of Paper Production Phases ”, Irina Mironova, 2002 2.3.4 Spectral characteristics of materials

Reflection, transmission, and absorption are the phenomena, which take place when light interacts with matter. Reflectance, transmittance, and absorptance are used to define portions of the reflected, refracted, and absorbed light to the incident light beam [15, p. 73].

Thus, reflectance is defined as the ratio of the reflected light to the incident light at each wavelength. Transmittance is defined as the ratio of the transmitted light to the incident light at each wavelength, and absorptance is defined as the ratio of the absorbed light to the incident light at each wavelength. The quantities are determined by measurement, which is the subject of spectrophotometry. In describing color, these quantities are of great importance. Color of the object appears to be saturated, if the material of the object reflects light of certain wavelengths and absorbs the rest. Color of the object appears to be dark (subdued), if the material of the object absorbs almost all light and reflects small amount of light of the certain wavelength. When the material of the object reflects almost all light and absorbs small amount of it, the object looks light (pale) [4].

Examples of reflectance curves are represented on Fig. 10.

Figure 10. Examples of Reflectance curves.

YELLOW

Wavelength, nm

Reflectance, %

400 700

0 100

RED

Wavelength, nm

Reflectance, %

400 700

0 100 BLUE

Wavelength, nm

Reflectance, %

400 700

0 100

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2.4 Human vision

Physiology of human vision is the third important factor in color appearance. Human vision is often referred to be trichromatic by the nature since the color is formed by the combination of three stimuli of the retina for the red, green and blue colours. By firing these receptors in different combinations and proportions all palette of visible lights is produced [3].

The cause of the man’s trichromatic vision is in the anatomy of a human eye.

2.4.1 Human visual system

Human eye is an optical system with a great number of elements, the most significant of which are shown in Fig. 11.

Figure 11. Anatomy of an eye [15].

Cornea is an image-forming element of an eye. Due to its curved surface, there is the largest change in the index of refraction at the air interface [15, p. 4]. Light passes through the cornea and is focused on the lens, which adjusts to the distance. Power of the incident light is controlled by the pupil [3]. It narrows or widens depending on brightness of the

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surrounding light by the action of the iris (the colored part of the eye). The pupil is also responsible for filtering of the light. It hinders the penetration of ultraviolet radiation, which is dangerous for retina. Then light passes through a transparent gel called the vitreous humor and is focused an inverted image of the object being viewed on the retina [3].

The retina consists of photoreceptors: rods and cones. The photoreceptors are neurons, which are part of the central nervous system [15, p. 6]. Rods serve vision at low luminance (in the dark), while cones serve vision at high luminance (daylight). The rod is mostly cylindrical along its length, while the cone is tapered. Each rod or cone is roughly 0.002 millimetre (mm) in diameter and 0.04 mm in length. The most of rods and cones is in the area of the retina called the fovea. In the very centre of the fovea is an area called the foveola composed entirely of cones [3]. There are three different types of cones, which are referred to as long-wavelength, middle-wavelength, short-wavelength. Since the perception of color depends on the firing of these three types of nerve cells, it follows that visible color can be mapped in terms of three numbers called tristimulus values [7]. The receptors transform light to nerve impulses, which are passed to the visual zone of the cortex, where impulses are interpreted as pictorial representation [3].

2.4.2 Spectral sensitivity

Spectral sensitivity represents the response of the human eye to different wavelengths. The cones are mostly sensitive to a red, green, and blue light. However, the sensitivities do not actually peak at these wavelengths, but in the reddish, greenish, and bluish parts of the spectrum [3] (Fig. 12). Vision served only by rods is called scotopic vision. Vision served only by cones is called photopic vision. Vision by means of both rods and cones is called mesopic vision.

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Figure 12. Spectral sensitivities of cones in the human eye [3].

In the daytime (high luminance) and in the twilight (low luminance), human eye perceives the same colors differently, since different receptors are active (Fig. 13).

Figure 13. Spectral sensitivity of cones in the human eye in the daytime and in the twilight.

Scotopic vision is mostly black-and-white (rods are fired), while photopic vision is color (cones are fired) [6].

Sensitivity S Cones

Wavelength, nm

Relative sensivity

400 700

0 100

Sensitivity M Cones

Wavelength, nm

Relative sensivity

400 700

0 100

Sensitivity L Cones

Wavelength, nm

Relative sensivity

400 700

0 100

Scotopic vision Rods

Wavelength, nm

Relative sensivity

400 700

0 100

Photopic Vision Scotopic Vision

Relative sensitivity

0 400 0.4 0.6 0.2 1.2 1.0 0.8

Wavelength, nm 700

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“Multispectral Analysis of Paper Production Phases ”, Irina Mironova, 2002 2.4.3 Stimulus

The stimulus is the signal received by the brain. It represents the color that we actually see.

Stimulus is formed by multiplying of the spectral power distribution of the light source by the spectral reflectance of the colored object by the spectral sensitivity of the cones in the human eye [3] (Fig. 14).

Figure 14. Example of the stimulus curve. It is formed from the spectral power distribution of the light source, the spectral reflectance of the colored object and the spectral sensitivity of the human eye.

2.4.4 Color perception

Since physiological factor is an important for color perception, different observers can see the same color differently. There are also people who have abnormal trichromatic vision.

Moreover, the same observer can see the same color differently depending on surroundings and viewing conditions.

2.4.4.1 Adaptation mechanisms

Dark adaptation is the change in visual sensitivity that occurs when the level of illumination is decreases. Human eye responds to the lack of illumination in the following way. The cones become more sensitive in a couple of minutes. Then, visual sensitivity is about constant for about 10 minutes. By then, the cones become inactive, while the rods

Spectral Power Distribution

Spectral Reflectance

Spectral

Sensitivity STIMULUS

× × =

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begin to control the sensitivity. Rod sensitivity continues to increase for about 30 minutes until it becomes approximately constant.

Light adaptation is the change in visual sensitivity that occurs when the level of illumination is increases. Human eye responds by initiating the same physiological mechanisms as when dark adaptation. However, in this case visual system becomes less sensitive, since illumination intensity is higher.

Chromatic adaptation is the change in visual sensitivity under different illumination conditions. Chromatic adaptation is illustrated in Fig. 15, in which the same object is observed under various types of illumination (daylight, incandescent and fluorescent). The blue color of the object looks slightly different because of the different sensitivity of the human eye. S-cones of the human eye become less sensitive under daylight than under fluorescent light to compensate short waves energy (daylight contains more short waves energy than fluorescent light). L-cones of the human eye become relatively less sensitive under incandescent light than under fluorescent light to compensate long waves energy (incandescent light contains more long waves energy than fluorescent light) [15, p. 27]

Figure 15. Color object under different light sources [3].

2.4.4.2 Metamerism

Metamerism is a phenomenon exhibited by the two colors of objects, which match under one illumination conditions and look different under another illumination conditions (Fig.

16) [3]. These colors called metamers have different spectral reflectance, but evoke the same stimulus in the L, M, and S cones of the human eye under particular illumination conditions [3].

Incandescent Fluorescent Daylight

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“Multispectral Analysis of Paper Production Phases ”, Irina Mironova, 2002 Figure 16. Metamerism [3].

2.4.4.3 Simultaneous contrast

Simultaneous contrast causes the color to be changed when the color of the background is changed. [3]. The green color in Fig. 17 looks “greener” on the violet background than on the yellow background.

Figure 17. Simultaneous contrast.

Source 1 Source 2

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3 Color description

Color models are used for the color classification and description using certain attributes such as hue, saturation, intensity, chroma, lightness, or brightness [9]. Color model denotes a coordinate system, in which color is represented by the single point. There are two types of the models: device-independent and device-dependent. The most known device- dependent models are RGB (Red, Green, Blue) used in color monitors and broad class of video cameras, and CMYK (Cyan, Magenda, Yellow, Black) used in color printing. The most known device-independent models are XYZ and L*a*b*, which are appropriate for color interpretation and processing [9].

3.1 Color terminology

Before describing color models, principal terms have to be clarified. Careful description of terms is of importance in order to ensure all terms are presented and interpreted consistently. The definitions presented in 3.1.1-3.1.5 are from [15, p. 99-106].

3.1.1 Color

“Color: Attribute of visual perception consisting of any combination of chromatic and achromatic content. This attribute can be described by chromatic color names such as yellow, orange, brown, red, pink, green, blue, purple, etc., or by achromatic color names such as white, grey, black, etc., and qualified by bright, dim, light, dark, etc., or by combinations of such names”.

“Note: Perceived color depends on the spectral distribution of the color stimulus, on the size, shape, structure and surround of the stimulus area, on the state of adaptation of the observer’s visual system and on the observer’s experience of the prevailing and similar situations of the observations”.

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“Multispectral Analysis of Paper Production Phases ”, Irina Mironova, 2002 3.1.2 Hue

“Hue: Attribute of visual sensation according to which an area appears to be similar to one of the perceived colors: red, yellow, green, blue, or to a combination of two of them”.

“Achromatic color: Perceived color devoid of hue”.

“Chromatic color: Perceived color possessing of hue”.

Hue is associated with the dominant wavelength in the mixture of light waves. In fact, when people describe the color, they usually use the attribute of hue. Although, the attribute is natural for us, it is difficult to define it. Traditionally, hue is illustrated on the “hue circle” (Fig. 18).

Figure 18. “Hue circle” [9, p. 297].

3.1.3 Brightness and lightness

“Brightness: Attribute of a visual sensation according to which an area appears to emit more or less light”.

“Lightness: The brightness of an area judged relative to the brightness of a similarity illuminated area that appears to be white or highly transmitted”.

S H

Yellow

Magenta Blue

Cyan Red

Green

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According to the definition, brightness refers to the absolute level of human perception, while lightness is the measure of relative brightness, normalized for changes in the illumination and viewing conditions [15, p. 102].

The difference between terms of brightness and lightness can be explained by the example of the illuminated cube (Fig. 19). Lateral and top cube sides are illuminated differently and reflected different amounts of light accordingly, which results in different brightness.

However, the lightness is the same due to its interpretation as brightness relative to the brightness of a similarly illuminated white object.

Figure 19. The cube presented for illustration of different color attributes [15, p. 102].

3.1.4 Colorfulness and Chroma

“Colorfulness: Attribute of a visual sensation according to which the perceived color of an area appears to be more or less chromatic.

Note: For a color stimulus of a given chromaticity and, in the case of related colors, of a given luminance factor, this attribute usually increases as the luminance is raised, except when the brightness is very high.”

“Chroma: Colorfulness, chromaticness, of an area judged as a proportion of the brightness of a similarly illuminated area that appears white or highly transmitting.

Note: For given viewing conditions and at luminance levels within the range of photopic vision, a color stimulus perceived as a related color, of a given chromaticity and from a

Sides, which have different brightness, colorfulness and identical lightness, chroma, saturation

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surface having a given luminance factor, exhibits approximately constant chroma for all levels of illuminance except when the brightness is very high. In the same circumstances, at a given level of illuminance, if the luminance factor is increased, the chroma usually increases.”

Colorfulness describes the amount of the color content, which is defined by hue. The achromatic color has zero colorfulness and chroma, and the amount of color content increases as colorfulness/ chroma increase. Colorfulness is related to chroma as brightness is related to lightness. In other words, chroma is relative colorfulness. Like lightness, chroma is approximately constant across changes in the luminance level [15, p. 104].

Colorfulness increases as the luminance level increases, since it is an absolute perceptual property [15, p. 104]. The difference between colorfulness and chroma can also be illustrated by the example of the illuminated cube (Fig. 21). In this case, lateral and top cube sides are different in colorfulness since they are illuminated with different amounts of the light of the identical structure [15, p. 104]. However, they have the same values of chroma due to the interpretation as colorfulness to brightness of similarly illuminated area.

3.1.5 Saturation

“Saturation: Colorfulness of an area judged in proportion to its brightness.”

“Note: For given viewing conditions and at luminance levels within the range of photopic vision, a color stimulus of a given chromaticity exhibits approximately constant saturation for all luminance levels, except when brightness is very high.”

The definition of saturation is near to the definition of chroma; the only difference is that saturation is colorfulness of the stimulus relative to its own brightness, while chroma is colorfulness of the stimulus relative to brightness of the similarly illuminated area. An example, when the stimulus exhibits saturation, but not chroma, is traffic signals viewed in isolation in the dark [15, p. 104]. Saturation of the color on lateral and top cube sides (Fig.

21) is approximately identical [15, p. 105].

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“Multispectral Analysis of Paper Production Phases ”, Irina Mironova, 2002 3.1.6 Definitions in Equations

Different terms are used to describe a color. One can confuse their definitions and relations.

The one way to simplify understanding of the terms is to represent them in simple equations. While, the equations are not mathematically strict, they “provide a first-order description of the relationships between the various color percepts” [15, p. 106].

Chroma can be described as colorfulness relative to the brightness of a similarly illuminated white [15, p. 106]:

(White) Brightness

ss Colorfulne

= Chroma

Saturation can be expressed through colorfulness and brightness or chroma and lightness [15, p. 106]:

Brightness ss Colorfulne

= Saturation

Lightness Chroma

= Saturation

Finally, lightness can be described as brightness of the stimulus to the brightness of a similarly illuminated white stimulus [15, p. 106]:

(White) Brightness

Brightness

= Lightness

3.1.7 Brightness-Colorfulness Versus Brightness-Chroma

One way to describe a color is through the above-listed color attributes. Typically, three of five attributes are used, which are hue, lightness, and chroma. The reason is to avoid redundancy. However, the complete color specification requires all five attributes:

• Brightness

• Chroma

• Colorfulness

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• Chroma

• Hue

Let’s consider an example. Imagine a yellow school bus being outside in a sunny day. The yellow color of the bus has certain values of hue, colorfulness, chroma, brightness, and lightness [15, p. 108]. Then imagine the printed photographic reproduction of the bus under the subdued lighting in an office or at home. Colors of the actual bus and bus on the reproduction have identical hue, chroma and lightness, but different colorfulness and brightness. Only if the photographic reproduction will be viewed under the same lighting, all five attributes will be identical [15, p. 108]. When specifying color through three attributes, it is usually used related ones (lightness and chroma) instead of absolute ones (brightness and colorfulness). However, it depends on the application. For example, if taking the photograph of the bus from the previous example under the lighting of the candle and reproducing the brightness and colorfulness of the original scene, the print would be extremely dark. In this case quality of reproduction will be low [15, p. 108]. There are also several situations, where brightness and colorfulness is of more importance than lightness and chroma. One situation is specification of color-rendering properties of light sources, when the colored object is viewed under different light sources [15, p. 108]. Another application is estimation of image quality for certain types of reproduction. For example, if the estimation of the quality of the reproduction is carried out in a darkened room, the observer can be interested in brightness and colorfulness than in lightness and chroma [15, p. 108]. Thus, the selection of the attributes to describe the color should be done carefully according to a given application.

3.2 RGB

RGB represents color through three primary spectral components: red, green, and blue. The model is based on the Cartesian coordinate system [9]. The color subspace is the cube where red is usually on the x-axis, green is on the y-axis, and blue is on the z-axis (Fig. 20).

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“Multispectral Analysis of Paper Production Phases ”, Irina Mironova, 2002 Figure 20. The RGB color cube [9].

Secondary colours of the RGB model are cyan, magenta, and yellow, which are at three another corners of the cube. Grey scale of the model is along the line connecting to white and black points. All colour values are restricted to the range from zero to one [9]. Number of possible colours depends on the number of bits representing each color in RGB space. If the number of bits is 24, then total number of colours is

( )

²⁸ ³ ⁼¹⁶^,⁷⁷⁷^,²¹⁶ [9]. The RGB model is valuable since it relates closely to the way we perceive color with the L, M, S receptors in our retinas [10]. It is used in display devices, such as monitors and TV sets.

3.3 CMY

Cyan, magenta, and yellow are the basic colours of CMY model, which subtracts primary colours from the white color (Eq. 3).

















−

















=

















B G R Y

M C

1 1 1

(3)

Although primary colours of the CMY model are secondary ones of RGB and vice versa, the CMY model produces dirty colours, which are unlike to bright colours in the RGB

B

(1,0,0) Red

(0,0,1) Blue

(0,1,0) Green

R

G

Yellow Cyan

Magenda

Grey scale

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model [10]. There is another difference between these two models: the CMY gamut is smaller than the RGB gamut (Fig. 21).

Figure 21. CMYK gamut in compare with RGB gamut [10].

There is also modified model of CMY, which is called CMYK. It includes the forth component K denoting the black color. Since the model is used in printing devices, there is a necessity of pure black color (black color derived from the mixture of cyan magenta and yellow gives dirty black) [9].

3.4 HSI

The RGB and CMY models are ideally suited for hardware implementations. Moreover, the RGB system is close to the human perception of color through red, green and blue primaries [9]. Unfortunately, the RGB, CMY, and similar color systems do not interpret color from the human point of view, since people describe color through such attributes as hue, saturation, brightness, lightness, etc [9]. In addition, RGB and CMY color models reproduce less colours than human eye actually perceives. It can create a problem in color production in monitors, printers, scanners, and similar devices [9]. HSI model represents a color using names, which is more clear and understandable for user and can be employed in user interface design [12]. The model describes a color by hue, saturation and intensity attributes. Hue means the color itself (pure color) (See 3.1.2), saturation shows amount of white color mixed with that pure color (See 3.1.5). Intensity gives knowledge about color brightness, what is the same as grey-level for monochromatic images [9]. The gamut of the HSI model is represented in cylindrical coordinates (Fig. 22). The hue (H) is represented as the angle in the range from 0° to 360°. Saturation (S) corresponds to a radius from 0 to 1.

Intensity (I) varies along the z-axis with 0 (black) and 1 (white) [13].

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“Multispectral Analysis of Paper Production Phases ”, Irina Mironova, 2002 The HSI color space is a simple transformation of the RGB cube (Eq. 4-7).





>

−

<=

= 360 , B G G B ,

if H if

ϑ

ϑ (4)

, where

[ ]

[

⁽ ⁾ ⁽ ⁾⁽ ⁾

]

^}

) ( ) 2 (

1 { cos

12 2

1

B G B R G

R

B R G R

−

− +

−

− +

= ⁻ −

ϑ (5)

[

min( , , )

]

) (

1 3 R G B

B G S R

+

− +

= (6)

) 3(

1 R G B

I = + + (7)

Figure 22. The cone model of the HSI color space [13].

The HSI model is an ideal development tool for image-processing applications because it separates the intensity component from color- carrying components of hue and saturation [9]. For example, some machine vision applications such as histogram operations, convolution, and intensity transformations operate only on image intensities. Thus, it is easier to perform them using HSI space [13]. The disadvantage of the HSI model is the dependency from the actual device and lack of correlation with visual perception [12].

S H Yellow 120°

Green

240°

Blue

0,0 Black 1,0 White

Magenda Red Cyan 0°

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3.5 XYZ

3.5.1 XYZ color-matching function

In 1931, the Commission Internationale de l'Eclairage (CIE) developed a device- independent color model based on human perception. The color model called XYZ represents a color through three primaries, which are similar to red, green, and blue [15, p.

84]. The transformation to XYZ primaries was made to eliminate negative values of RGB color-matching functions (Fig. 23). The XYZ primaries can produce all physically realizable color stimuli [15, p. 84], which was achieved with fictitious primaries that are more saturated than monochromatic lights. Although color primaries are fictitious, color- matching functions produced by them are real [15, p. 84].

a) b)

Figure 23. a) The XYZ color-matching function b) The RGB color-matching function [31].

The XYZ tristimulus values are defined in a similar fashion as the RGB primaries (Eq. 8 - 10):

∑

^Φ

= ⁷⁰⁰

400

) ( ) (λ x λ K

X (8)

∑

^Φ

= ⁷⁰⁰

400

) ( ) (λ y λ K

Y (9)

∑

^Φ

= ⁷⁰⁰

400

) ( ) (λ z λ K

Z (10)

0 350 1.0 0.5 2.5 2.0 1.5

Wavelength, nm 850

-0.5 350 1.5 0.5 3.5 2.5

Wavelength, nm 850

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“Multispectral Analysis of Paper Production Phases ”, Irina Mironova, 2002 )

(λ

Φ is defined differently for different types of stimulus. For self-luminous stimuli Φ(λ) is the relative spectral power distribution; for the reflective materials Φ(λ) is the product of spectral reflectance of the material R(λ)and spectral power distribution of the light source or illuminant of interest, S(λ). For transmitting materials Φ(λ) is defined as the product of the spectral transmittance of the material, T(λ) and spectral power distribution of the light source or illuminant of interest, S(λ) [15, p. 85]. The normalization constant K (Eq. 11) is defined differently for relative and absolute colorimetry. In absolute colorimetry, k is equal to the 683 lumens/watt to make the system of colorimetry compatible with the system of photometry [15, p. 85]. For relative colorimetry k is defined by equation:

λ λ

λS λ y d

K ⁼

∫

⁽ ⁾ ⁽ ⁾

100 (11)

In the relative colorimetry, the tristimulus values are normalized to values from zero to approximately 100 for different materials [15, p. 88].

3.5.2 Chromaticity diagrams

Chromaticity diagram was introduced to project the tristimulus values to the two- dimensional unit plane (x+y+z=1) [17]. The transformation of tristimulus values to chromaticity coordinates is accomplished by normalization, which removes information about luminance [15, p. 90]:

Z Y X x X

+

= + (12)

Z Y X y Y

+

= + (13)

Z Y X z Z

+

= + (14)

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The color in the plane is defined by (x, y) coordinates. Since the plane is unitary, z coordinate is simply calculated from the equation:

y x

z=1.0− − (15)

The transformation from the three-dimensional to the two-dimensional representation inevitably leads to losses of color information. Therefore, to specify the color stimulus fully, one of the tristimulus values should be added to the two chromaticity coordinates.

3.6 L*a*b*

The L*a*b* color model was developed to be an approximately uniform color space. The uniformity was achieved by incorporating features to account for chromatic adaptation and non-linear visual responses [17, p. 92]. In L*a*b*, “L” is the luminance, “a*” is a value for which “-a*” is green, and “+a*” is red, “b*” is a value for which “-b*” is blue, and “+b*” is yellow (Fig. 24). It is important that non-linear relationships for L*, a* and b* mimic logarithmic response of the human eye [11]. Moreover, L*a*b* is approximately uniform color system: equal distances between colors in the L*a*b* space correspond to equal perceptual difference. This property allows L*a*b* space to be used in scientific imaging and colorimetry as a tool to measure perceptual difference between two colors [11].

Figure 24. Three-dimensional representation of CIELAB color space.

light

yellow

green red

blue

dark L*

a*

b*

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CIELUV is another uniform color space, which together with CIELAB was recommended to be used for the color-difference specification of reflecting samples. But, due to the popularity of CIELAB, it is not used widely [15,p. 94].

3.7 Multispectral images

A multispectral image is a data set with two spatial dimensions and the spectral dimension.

In such an image, every pixel is represented by a large number of spectral components. The number of components can vary from 4 to about 100, but usually it is in the range from 20 to 40. The spectral range of images is not limited by the visual part of electromagnetic spectrum, which provides more accurate color information. The spectral range can be extended from the 300 nm to approximately 14000 nm including the UV, visible, near-IR and mid-IR ranges [22, p. 309]. However, increase number of spectral components has disadvantage, which is images have increased size from tens of megabytes to hundreds of megabytes and in image libraries, there can be hundreds of images [20]. The size of multispectral images in comparison with grey-level and RGB images is much larger (Table 1).

Table 1. Memory requirements for images [21].

Image size 256x256 512x512

Grey-level 65 kB 262 kB

RGB 196 kB 786 kB

Multispectral 20 nm resol. 1 MB 4 MB Multispectral 5 nm resol. 3 MB 15 MB

Due to their advantages, multispectral images have a variety of special applications such as global environmental monitoring, mapping, natural resource management, land use planning and telemedicine.

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4 Color difference models

4.1 Color difference equations

Color difference in the CIELAB space is measured as the Euclidean distance between the two stimuli in the L*a*b* coordinates. The difference can be calculated through luminance and two chroma coordinates (Eq. 16) or lightness, chroma and hue (Eq. 17). Equation (17) is derived from equations (16) and (18) [15, p. 94].

[

^* ² ^* ² ^* ²

]

¹^/²

* = (∆ ) +(∆ ) +(∆ ) ⁻

∆E_ab L a b (16)

[

^* ² ^* ² ^* ²

]

¹^/²

* = (∆ ) +(∆ ) +(∆ ) ⁻

∆E_ab L C_ab H_ab (17)

[

^* ² ^* ² ^* ²

]

¹^/²

* = (∆ ) +(∆ ) +(∆ ) ⁻

∆H_ab E_ab a C_ab (18)

, where ∆C_ab^* is the chroma difference in CIELAB color space and ∆H_ab^*is the hue difference in CIELAB color space.

Unfortunately, color difference evaluations of CIELAB are not a good measure of the magnitude of the perceptual color difference between two stimuli. This was the reason to improve the measure. One of the most widely used modifications of CIELAB color difference equations is CMC equation (Eq. 19) [15, p. 94].

( )

² ²

( )

² ²

( )

² ²



 

 + ∆



 

 + ∆



 



=  ∆

H C

L S

H cS

C lS

CMC L (19)

where l and c are acceptability/perceptibility terms (l=1 and c=1 means perceptibility, and l=2 and c=1 means acceptability),

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(

^L^L

)

S_L

01765 . 0 1

040975 .

0

= + ,

(

1 0.0131

)

⁰^,⁶³⁸

0638 .

0 +

= +

C

S_C C ,

) 1

(fT f

S

S_H = _C + − ,

1900 )

(

) ) ((

4 4

= +

ab ab

C

f C ,

) 35 cos(

4 . 0 36 ,

0 + +

= H

T ,

) 168 cos(

2 . 0 56 ,

0 + +

= H

T , if (H> 164 and H <345)

The CMC colour difference formula is similar to the CIE versions but includes weighting functions for different areas of the colour space [14]. It is based on a visual experiment on color-difference perception in textiles.

CIE evaluated the CMC equation and modified the CIELAB equation for industrial use.

The color difference measurement is called CIE94 (∆L*,∆C_ab*,∆H_ab* with the symbol

*

E94

∆ ) (Eq. 20) [15,p. 94]

( )

² ²

( )

² ²

( )

² ²

*

94 



 

 + ∆



 

 + ∆



 



=  ∆

∆

H H C

C L

L k S

H S

k C S

k

E L (20)

, where S_L =1, S_C =1+0.045C^*_ab, S_H =1+0.015C_ab^* .

The coefficients k_L, k_C, k_Hare used to adjust relative weighting of the lightness, chroma and hue components, respectively, of color difference for various viewing conditions and applications apart from the CIE94 reference conditions [15, p. 95]. CIE94 color differences are averaged across the color space, which resulted in significantly smaller values of CIE94 color differences in comparison with those of CIELAB [15, p. 95]. The CIE reference conditions for the use of the CIE94 color-difference equations are as follows [15, p. 95]:

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“Multispectral Analysis of Paper Production Phases ”, Irina Mironova, 2002 Illumination: CIE illuminant D65 simulator

Illuminance: 1000 lux

Observer: Normal color vision

Background: Uniform, achromatic, L^* =50 Viewing mode: Object

Sample size: Greater than 4° visual angle Sample separation: Direct edge contrast

Sample color-difference magnitude: 0 to 5 CIELAB units

Sample structure: No visually apparent pattern or nonuniformity

Due to the reference conditions, CIE94 color difference equation cannot be used for any application.

4.2 MacAdam Ellipses

MacAdam ellipses were invented by MacAdam in 1943 to determine imperceptible variations of the color to the human eye. The research was based on series of experiments, where trained observers tried to distinguish 100 color targets among 25,000 matches [18].

Starting points for color matching were varied. The experiments were carried out both at constant and various luminance [18]. The results of experiment are ellipses on the CIE (x, y) chromaticity diagram. At the centre of ellipses are target colors. For the observer, colors inside the ellipse are equal to the target color and slightly different on the boundaries [19].

The ellipses on the top turned out larger than those on the bottom. Moreover, ellipses rotate when moving up, which demonstrates non-uniform representation of colors on the CIE (x, y) chromaticity diagram (Fig. 25 a) [19].

The improved chromaticity diagram was proposed by CIE in 1976 (Fig. 25 b). It was defined in the (u’ v’) coordinates, which are as follows (Eq. 21):

Z Y X u X

3 15 ' 4

+

= +

Z Y X v Y

3 15 ' 9

+

= + (21)

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a) b)

Figure 25. a) CIE 1931(x, y) chromaticity diagram, b) CIE 1976(u', v') chromaticity diagram [31].

The 1976 (u’, v’) chromaticity diagram is more uniform in representation of colors, but still not perfect [17].

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5 Experiment

5.1 ABC of Paper Production Process

The color of paper is affected by chemical matters involved in paper production process. To gain understanding of reasons of the variation of the color of paper, paper production process is considered.

Paper is made from various raw materials that can be taken from wood, straw, cotton, flax, grass, spoilt sheets, etc. As a matter of fact, paper can be produced from any plant material;

the only one essential component is cellulose fiber [24, p. 20]. Usually, main raw materials are hardwood, such as birch, beech or chestnut, and softwood, such as fir and pine-tree.

Softwood has long fibers, which make paper strong, while hardwood has short fibers, which improve paper quality parameters. For producing high-grade paper, cotton and linen is used. The best properties of their fibers, such as strength, durability, permanence and fine character are inherited by the paper; which allows it to be used for printing legal documents, drawing, special editions of books [24, p. 24].

Paper production process consists of following phases (Fig. 26):

1. Debarking

Since the bark is of no value for papermaking [24, p. 34], it is removed firstly by a large, spinning and rotating drum that makes the logs move around. The bark comes off because of the rub between logs. [23].

2. Chipping

To make grind easier, logs are cut into chips by a large circulated knife [23].

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“Multispectral Analysis of Paper Production Phases ”, Irina Mironova, 2002 3. Pulping

At the pulping phase, the cellulose and hemi-cellulose are separated from the lignin and other tree oils and resins. There are kinds of pulping: mechanical and chemical [23]. When mechanical pulping, logs are grinded in the rotated millstone, which processes most of wood into the fiber (about 90-95 percents). The process produces pulp of low quality since grinding breaks the cellulose fibers, which decreases pulp strength. As a result, the paper has a weak fiber network and a high lignin content, which causes it to darken under sunlight. Due to the listed disadvantages, finished paper can be used for newsprint, telephone books and similar applications that do not need the paper of the high quality [23].

There is a modification of mechanical pulping, which is called thermo-mechanical pulping.

When the thermo-mechanical pulping, chips are treated with the steam before pulping, which allows to reduce energy costs. Furthermore, there is chemo-thermo mechanical pulping (CTMP) that is the process in which wood chips are chemically treated before steaming. This allows the lignin and resin to be extracted from the wood resulted in stronger pulp. Pulp produced by CTMP can be used for production of coated papers [23].

The chemical pulping is the process of cooking in some chemical liquid under the pressure.

It produces very pure cellulose fibers, but the output pulp is about 55 percents. [24, p. 37].

4. Bleaching

The cooked pulp is of brown color and contains pieces of wood, uncooked bark and knots [2, p. 38]. Thus screening and bleaching are required. At bleaching process, lignin, which affects the purity of fibers, is removed from a pulp. Firstly, the pulp is treated by oxygen resulted in light-brown color of fibers. Then, the pulp is bleached by chlorine gas or chlorine dioxide or peroxide or similar matter [23].

5. Paper Machine

A paper machine consists of four sections. In the first section, a pulp is mixed with the water and minerals in the ratio of 1 percent to 99 percents. After that, the water is removed step by step in such a way that intermeshed fibers form a dry, compact, solid, continuous web [24, p. 69]. At the press section, the paper is squeezed between rollers and a felt (a large mat of nylon and polyester filaments). The process removes 10-15 percents of the water from the paper. Then, the paper goes to the drier section, after which only 2-6 percents of water is remained in it. The drier section consists of row of heated rolls,

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between which paper goes. Finally, the paper is sized to make it smother and stronger.

Moreover, in this stage it is coated with starch and minerals. Finally, the paper is dried again in the after-dryer section [23].

6. Coating

The purpose of coating is to make paper surface even by burying imperfections under a layer of very fine mineral pigments [24, p. 116]. At the coating process, gliding paper is coated by the rotated brush. Coated paper acquires good properties, which allows it to be used in printing [23].

7. Supercalendering

This is a process to make paper glossy and smooth. The section of supercalendering consists of several large heated rolls, which press the paper. After supercalendering, the paper is cut into smaller rolls and delivered to customer [23].

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Figure 26. Paper Production Phases. [from UPM-kymmene]

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5.2 Spectrum measurement

Spectral measurements of paper samples were the part of the experiment. Spectral measurements were carried out by one-pixel Minolta Spectrophotometer CM-2002.

Spectrophotometer represents the present-day device, which allows measurements in the laboratory conditions.

5.2.1 Measurement Principles

The spectrophotometer uses a double-beam feedback system for measurement. The specimen is illuminated diffusely and viewed at 8 angle to the normal to the specimen surface, the width of the viewing beam is 7.4 . The geometry satisfies the specification described in CIE publication 15.2, ISO 7724/1 and DIN 5033 teil ² 7 [25, p. 139]. ²

When user presses “Measurement” button, following operations in the viewing system are initiated [25, p. 139] (Fig 27):

1. Light from the pulsed xenon arc lamp is thoroughly diffused inside the integrating sphere and provides even illumination over the area of the specimen surface to be measured.

For the SCE (specular component excluded) measurements, the light trap is opened.

Then the light, which would have been reflected by the surface on the integrating sphere at the light trap position enters the light trap and is absorbed.

2. Light reflected from the specimen surface at an angel of 8 to the normal enters the optical fiber cable for taking measurements and is transmitted to the spectral sensor 2.

3. The light from each optical fiber cable is divided by wavelength (from 400 to 700 nm) at 10 nm pitch before striking the segments of the silicon photodiode array of the spectral sensor. The segments of the spectral sensor convert received light into electrical currents proportional to an intensity of light. These electrical currents are then passed to analog control circuits.

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Two spectral camera sensors allow take into account both light, which illuminates the specimen surface, and light reflected by the specimen surface. Such double-beam feedback system eliminates effects of variations in spectral characteristics or intensity of the illumination [25, p.140].

Figure 27. Geometry of Spectrophotometer CM-2002 [25, p. 142].

5.2.2 SCE/SCI modes

The CM-2002’s geometry allows switching between two modes: SCI/SCE. The difference between two modes is that for SCI mode measuring, light includes both diffusely reflected light and specularly reflected light, while for the SCE mode, measuring light includes only light reflected diffusely from the specimen surface. User can easily switch from one mode to another by opening and closing a trap. When the trap is opened, specularly reflected light is released, while, when it is closed, specularly reflected light is ensnared (Fig. 27) [25, p.

142].

Multispectral Analysis of Paper Production Phases