Encyclopedia of Color Science and Technology

Living Edition
| Editors: Ronnier Luo

Clapper-Yule Model

  • Mathieu Hébert
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27851-8_49-6


The Clapper-Yule model is a physically based model describing the reflection of spectral light fluxes by a printed surface and enabling the prediction of halftone prints on diffusing substrates [1]. The model relies on a closed-form equation obtained by describing the multiple transfers of light between the substrate and the print-air interface through the inks. Physical parameters are attached to the inks, the diffusing support, and the surface. The model assumes that the lateral propagation distance of light within the substrate, due to scattering, is much larger than the halftone screen period. Most photons therefore cross different ink dots while traveling in the print. The reflections and transmissions of light at the surface are explicitly taken into account depending on the print’s refractive index, as well as the considered illumination and measuring geometries.

The Clapper-Yule Equation

The Clapper-Yule equation derives from the description of multiple reflections...


Surface Coverage Spectral Reflectance Measuring Geometry Halftone Pattern White Primary 
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  1. 1.
    Clapper, F.R., Yule, J.A.C.: The effect of multiple internal reflections on the densities of halftone prints on paper. J. Opt. Soc. Am. 43, 600–603 (1953)CrossRefADSGoogle Scholar
  2. 2.
    Judd, D.B.: Fresnel reflection of diffusely incident light. J. Res. Natl. Bur. Stand. 29, 329–332 (1942)CrossRefGoogle Scholar
  3. 3.
    Rossier, R., Bugnon, T., Hersch, R.D.: Introducing ink spreading within the cellular Yule-Nielsen modified Neugebauer model. In: IS&T 18th Color Imaging Conference, San Antonio, TX, USA, pp. 295–300 (2010)Google Scholar
  4. 4.
    Hersch, R.D., Emmel, P., Crété, F., Collaud, F.: Spectral reflection and dot surface prediction models for color halftone prints. J. Electron. Imaging 14, 33001–33012 (2005)CrossRefGoogle Scholar
  5. 5.
    Hersch, R.D., Brichon, M., Bugnon, T., Amrhyn, P., Crété, F., Mourad, S., Janser, H., Jiang, Y., Riepenhoff, M.: Deducing ink thickness variations by a spectral prediction model. Color. Res. Appl. 34, 432–442 (2009)CrossRefGoogle Scholar
  6. 6.
    Hébert, M., Hersch, R.D.: Reflectance and transmittance model for recto-verso halftone prints: spectral predictions with multi-ink halftones. J. Opt. Soc. Am. A 26, 356–364 (2009)CrossRefADSGoogle Scholar
  7. 7.
    Mazauric, S., Hébert, M., Simonot, L., Fournel, T.: Two-flux transfer matrix model for predicting the reflectance and transmittance of duplex halftone prints. J. Opt. Soc. Am. A 31, 2775–2788 (2014)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.ERIS Group, CNRS, UMR 5516, Laboratoire Hubert CurienUniversité de Lyon, Université Jean Monnet de Saint-EtienneSaint-EtienneFrance