From macroscopic point of view it can be said that, when light meets paper material it:
- reflects away from top surface of paper material and - refracts inward from top surface of paper material.
Part of inward refracted light is absorbed by paper material and energy of light is converted into heat energy. Absorption depends on material and wavelength of light (Lindholm et al., 1983). The non-absorbed remaining of light transmits through paper material and interacts with lower surface of paper material and refracts in this boundary. This is shown in figure 3.1 (Pauler, 2002).
Figure 3.1. Interaction of light and paper material in macroscopic scale (Pauler, 2002).
3.2 Light scattering
From microscopic point of view it can be said that, 3D network of wood fibres make the light material interaction much more complicated. Figure 3.2 illustrates this complexity of interaction.
When light interacts with paper material, it reflects horizontally, vertically and outbound from surfaces of the fibres and pigments particles (figure 3.2a). Light also refracts so that it changes its path (figure 3.2b). When light hits particles and pores which have the same or smaller dimensions as the wavelength of incoming light, it diffracts the light (figure 3.2c) (Pauler, 2002).
a) b)
c) d)
Figure 3.2. Interaction of light and paper material in microscopic scale (Pauler, 2002).
In figure 3.2c diffraction happens, when light meets a round particle that has diameter equal or smaller than the hitting wavelength; that is why it is directed to all directions. This diffraction and scattering phenomena are discussed further in this literature review. Light penetrates into pigment particles and fibres and absorbs into them (figure 3.2d). Because fibres are hollow, they contain many optical boundaries and optical interactions (described earlier) happens also inside fibres (Pauler, 2002; Lindholm et al., 1983). Usually one concept that is used to describe reflection, refraction and diffraction is light scattering (Pauler, 2002; Aaltonen, 1983).
When considering paper materials, light scattering is depending on (Lindholm et al., 1983):
- amount of optical boundaries to reflect the light,
- refractive index of compounds in paper material (fibres, filler/coating pigments, etc.) and - amount, size, shape and distribution of particles that have same size as wavelength of light
(remarkable particle size range is 0.25 – 1 µm).
3.3 Diffuse reflection
All optical phenomena described earlier (reflection, refraction, diffraction and absorption) can multiply themselves inside paper material. This process cannot be observed from outside. Only thing to observe is that paper material has smooth, white and matt-like surface. i.e. diffuse reflection is visually observed (Pauler, 2002; Lindholm et al., 1983). This is illustrated in figure 3.3 (Aaltonen, 1983).
Figure 3.3. Diffuse reflection (io = intensity of incoming light, ih=intensity of reflected light, ia=intensity of absorbed light, it=intensity of transmitted light and is=intensity of scattered light) (Aaltonen, 1983).
3.4 Reflectance
Reflectance of paper materials is relation between intensity of light reflected from top surface of material and intensity of incoming light that has interacted with top surface of material. Reflectance can be calculated as equation 3.1 (Fresnel equation) shows. This case is for light incoming to top surface of paper material perpendicularly.
2
0
% 0
100
n n
n - n
R (3.1)
where R reflectance of material, % n refractive index of material, - n0 refractive index of air, -
Refractive index of air is 1.0 and refractive index of celluloid materials is 1.5, which gives reflectance of 4 % for paper materials. This means that 96 % of incoming light penetrates into paper material and 4 % is reflected away. Paper materials have never really smooth surface in practice and this is why part of light is in practice scattered away with large angle (Pauler, 2002).
3.5 Directed reflection
Top surface of paper material can be processed such that reflection is directed. These processes can be for example calendaring (process which smoothens paper surface via compressing paper between cylinders) or coating (applying a layer of pigment on top surface of paper to enhance printing properties of paper). Such processes make paper top surface more even; so all of reflection from paper top surface is not diffuse. This kind of directed reflection is called gloss in paper technology.
Gloss is a desired property of paper materials, because this enhances the shine and fullness of printed colours (Niskanen, 1998; Pauler, 2002; Aaltonen, 1983). Figure 3.4 represents reflection values of paper materials that are processed different ways and the angle of incoming light varies from 50 to 70 (Pauler, 2002).
Figure 3.4. Directed reflection for different paper materials (Pauler, 2002).
As it can be noticed from figure 3.4, glossy art paper gives narrow and high peak where untreated, matt paper gives wide and low peak. Figure 3.4 shows that processing of paper materials causes the angle of reflected light to be almost the same with angle of incoming light. When top surface of paper material become rougher and coarser (matt paper in figure 3.4) the angle of reflected light is larger; rough and coarse paper surface causes diffuse reflection. On the contrary, smoother paper surface (art print in figure 3.4) causes directed reflection and this way gloss of paper material is increased (Pauler, 2002).
3.6 Polarized light
If random polarized light, see appendix 2 (Steen, 1991), is directed to top surface of paper material perpendicularly, four percent of incoming light is reflected. When angle of incoming light is decreased, reflection of polarization plane parallel to top surface (RII) is decreased. When angle of incoming light is decreasing, reflection of polarization plane that oscillates perpendicularly to top surface of paper material (R) is strongly decreased and reaches value of zero. After this so called Brewster angle this reflection (R) is increased, when angle of incoming light is decreased. In case of paper material Brewster angle depends on wavelength of incoming light and refractive index of paper material (Pauler, 2002).
Figure 3.5 shows value of reflectance in function of reflectance angle, when random polarized light (reflectance R), polarized visible light that oscillates parallel to top surface (reflectance RII) and polarised light that oscillates perpendicularly to top surface (reflectance R) hits to surface that has a refractive index of 1.5 (Pauler, 2002).
Figure 3.5. Effect of random polarised and polarised visible light, when angle of incoming light is changed and refractive index of surface is 1.5 (Pauler, 2002).
4 Parameters that describe optical properties of paper materials
4.1 Reflectance factor
Reflectance factor R0 means reflectivity of one single paper material sheet, when background is absolute black (Niskanen, 1998; Pauler, 2002). Figure 4.1 represents definition of reflectance factor (Pauler, 2002).