Spectral Ray-Tracing

Phyical models for color prediction

M. Theiss – Hard- and Software

Dr.-Bernhard-Klein-Str. 110, D-52078 Aachen, Germany

Phone: + 49 241 5661390     Fax:     + 49 241 9529100

e-mail: theiss@mtheiss.com     web: www.mtheiss.com

September 2002

This text shows how our SPRAY ray-tracing software can be used to predict colors of paints, digital prints or similar imaging techniques. Other SPRAY applications are described in www.mtheiss.com/spray_ex/index.html. The SPRAY technical manual is available in www.mtheiss.com/docs/spray/index.html, a tutorial for beginners can be found in www.mtheiss.com/sprayt1/index.html.

SPRAY history: Beyond Kubelka-Munk ...

In order to understand reflectance spectra of diffusely reflecting powders we started (many years ago) with the simple Kubelka-Munk two-flux concept. We computed the absorption and scattering coefficients from the optical constants and size parameters of our particles using the Mie theory (scattering of spherical particles). To be close to our experimental setup with a laser light source, we had to replace the diffuse illumination in the theory by a sharp illuminating beam. Then we wanted to describe the angle distribution of the emitted radiation for powders or arbibrary thickness. So we deleloped a multi-flux theory. Finally, in the attempt to analyze infrared diffuse reflectance spectra we found that we had to determine the intensity and angle distribution of the incoming radiation in our spectrometer. At this point we gave up extending the Kubelka-Munk concept, and developed the SPRAY software that computes optical spectra by ray-tracing.

SPRAY features

Like many ray-tracing products, SPRAY has light sources, mirrors, lenses and various basic shapes which can be used to build up the scenery. Very powerful optical constant models and almost arbitrary layer stacks covering the surface of the various geometric objects are highlights of the software.

Meanwhile SPRAY has a number of features that turn it into an excellent tool for color prediction. Based on physical modeling, the transfer of light from the light source through light scattering, absorbing and fluorescent media and across partially reflecting interfaces is simulated. SPRAY performs fully three-dimensional ray-tracing with almost no compromises.

Color prediction demo systems

In order to show you the possibilities of SPRAY with respect to color prediction this text discusses some simple demo systems in the next section.

Warning: We are no experts in paints and digital prints (yet)! However, having studied some pieces of literature, we have the feeling that SPRAY could be a useful tool for people composing images. If you agree, feel free to suggest more advanced setups. We will be happy to learn how paints and prints really work.

Paper: We discuss a simple model for paper based on scattering inclusions in a homogeneous host. You can tune the light propagation in the paper by the size distribution and the volume fraction of the inclusions, and the complex index of refraction of the host material.

Paints: Here we describe the optical performance of several pigment types in a homogeneous binder layer on paper. We show that SPRAY can be controlled as OLE automation server from Excel's VisualBasic (or any other OLE automation client)  in order to create automatically charts of spectra and color coordinates vs. pigment volume fractions.

Prints: The setup of a simple test system is explained which can be used to simulate light propagation through ink dots on paper.

Pigment research: This section gives a few examples of pigment investigations you can do with SPRAY. Size variation and coatings with single and multiple layers are treated.

Background information

The following background information is given, just in case you want to know some details.

Optical constants: The heart of any physical model for color prediction are the optical constants of the materials in the system. SPRAY has very powerful optical constant models and a large database. The section about optical constants discusses some typical materials, and gives the optical constants of all materials used in the examples above.

Light scattering: SPRAY has an integrated Mie program that computes the scattering and absorption characteristics of spherical particles. You can define a size distribution, and the particles may be coated with a thin film layer stack. The properties of all light scatterers used in the examples of this text are discussed in this section.

SPRAY features not covered by this text: