Paper is the basis of many prints. Its large diffuse reflectance is almost independent of wavelength. Hence it is used as a white background, onto which pigments with strongly wavelength-dependent absorption are deposited where color is wanted.

The propagation of light through paper is very important for the color of a printed area. For a successful color prediction a correct description of the underlying paper is required. A physical model should reproduce available measured optical properties of the relevant types of paper in a quantitative way.

In this SPRAY demo, we use a simple paper model which is able to reproduce some basic features of paper. Instead of taking into account all the specific paper ingredients and their microstructure, we describe paper as a two-phase composite: Spherical air inclusions are embedded in a host material with optical constants similar to those of glass (see details below in the section of optical constants). Here is a sketch of the setup:

The size distribution of the voids determines the angle-dependence of the average single scattering event (which is computed by the Mie program integrated into SPRAY), whereas the volume fraction of the voids controls the strengths of the scattering, i.e. the scattering coefficient. The host material weakly absorbs  in the UV which is controlled by an oscillator term in the optical constant model.

In the following the properties of two types of (model) paper are compared: One with large inclusions and another one with small ones.

The graph below shows a SPRAY visualization of some test rays for the case of large inclusions. A collimated incident beam is directed onto the paper from the top (normal incidence of light). The path of 20 test rays is displayed in the following graph for a volume fraction of 0.3:

Starting many rays and placing large detectors above and below the paper one can compute the diffuse reflectance and transmittance of the model paper:

In order to visualize intensity distributions one can place screens (virtual CCD cameras, represented by the two blue bars in the sketch below) where detailed information is wanted:

The top screen looks like this

whereas the bottom screen shows a broader distribution:

The intensity distributions as well as the diffuse reflectance and transmittance spectra could be compared to measured data in order to estimate how good the model describes the real paper.

The smaller spheres with the same volume fraction have a larger scattering coefficient and a broader scattering distribution. This leads to a more concentrated radiation distribution:

The diffuse reflectance is significantly higher compared to that of the larger inclusions:

The distribution 'measured' with the top screen shows a more pronounced confinement of the rays:

This paper type (small inclusions) is used for the following simulations of paints and prints.