Applications of the Kubelka-Munk Color Model Kristen Hoffman  Dr. Edul N. Dalal   RIT Center for Imaging Science  Xerox Corporation, Wilson Center for Research and Technology

Introduction - Goals and Accomplishments Goal: Ability to model the reflectance of a color xerographic sample Developed: Predictive color model based on Kubelka-Munk theory Model extended to – Bidirectional Measurement Geometry – MultiLayer Images – Xerographic Print Samples

Background: Kubelka-Munk Theory Color reflection depends on – Material properties - the absorption and scattering spectra, K( ) and S( ) – Sample thickness, X – Substrate reflectance spectrum, Rp ( ) Model applies to – Uniform thickness samples with complete substrate coverage – Single color images

Background: Saunderson Correction Parameters Two parameters – k 1 and k 2 - corrections are made for reflections at the sample surface – Derived for integrating sphere measurement geometry – Applied to reflectance spectrum before the Kubelka-Munk model

Developed Color Model

Correction Equations

Introduction of k 0 Correction Parameter k 0 – Describes front surface reflection reaching detector of measurement device – Correlation exists for 45/0 measurement geometry as a function of 75  image gloss – Depends on refractive index ratio at the air-image boundary

Derived Correction Equations for Bidirectional Geometry Systems Link to Derivation:

Multi-Layer Images

Examples of Image Layer Structure (a) Single colorant layer considered in the original Kubelka-Munk model (b) Multiple colorant layers generally encountered in process color xerographic prints

R p ( ) R p ( ) corr R 1 ( ) corr R 2 ( ) corr R n ( ) corr R( ) k 0, k 1, k 2 for substrate k 0, k 1, k 2 for toner K, S for layer n K, S for layer 2 K, S for layer 1 Saunderson Correction Kubelka- Munk Kubelka- Munk Kubelka- Munk Inverse Saunderson Substrate Bottom-most toner layer Second toner layer Top-most toner layer Calculated Sample Reflectance

Non Planar Toner Layers

Image Photomicrographs

Toner Layer Thickness Measurements Layer structure digitized electronically – Measurements made at every 0.5  m – Small interval divides print into planar sections K/M applied to each small planar interval

Results

Fitted Absorption Spectra for Xerox 5760 CMY Toners

Fitted Scattering Spectra for Xerox 5760 CMY Toners

Results - Toner Layer Thickness Probability Distribution Example

Results - Single Layer, 45/0 dE* CIELAB Average C = 1.83 M = 1.77, Y = 1.26

Results - Multi-Layer Image RGBRGB

Results - Multilayer Non Planar Print dE* CIELAB Average 5.1, RMS = 5.5

Conclusions Benefits of K/M Color Model – Based on physical parameters of toner set – No print samples needed – Good predictions (low color error)