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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 20 — Sep. 26, 2011
  • pp: 19199–19211

Principal components analysis on the spectral bidirectional reflectance distribution function of ceramic colour standards

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns  »View Author Affiliations

Optics Express, Vol. 19, Issue 20, pp. 19199-19211 (2011)

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The Bidirectional Reflectance Distribution Function (BRDF) is essential to characterize an object’s reflectance properties. This function depends both on the various illumination-observation geometries as well as on the wavelength. As a result, the comprehensive interpretation of the data becomes rather complex. In this work we assess the use of the multivariable analysis technique of Principal Components Analysis (PCA) applied to the experimental BRDF data of a ceramic colour standard. It will be shown that the result may be linked to the various reflection processes occurring on the surface, assuming that the incoming spectral distribution is affected by each one of these processes in a specific manner. Moreover, this procedure facilitates the task of interpolating a series of BRDF measurements obtained for a particular sample.

© 2011 OSA

OCIS Codes
(030.5630) Coherence and statistical optics : Radiometry
(120.5820) Instrumentation, measurement, and metrology : Scattering measurements
(290.1483) Scattering : BSDF, BRDF, and BTDF

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: June 27, 2011
Revised Manuscript: August 19, 2011
Manuscript Accepted: August 23, 2011
Published: September 19, 2011

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, "Principal components analysis on the spectral bidirectional reflectance distribution function of ceramic colour standards," Opt. Express 19, 19199-19211 (2011)

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  1. F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” National Bureau of Standards Monograph (National Bureau of Standards, 1977), Vol. 160.
  2. C. Bordier, C. Andraud, and J. Lafait, “Model of light scattering that includes polarization effects by multilayered media,” J. Opt. Soc. Am. A 25, 1406–1419 (2008). [CrossRef]
  3. L. Simonot, “Photometric model of diffuse surfaces described as a distribution of interfaced Lambertian facets,” Appl. Opt. 48, 5793–5801 (2009). [CrossRef] [PubMed]
  4. R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” Technical report, Computer Graphics (ACM, 1981), Vol.  15, No. 3.
  5. B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18(6), 311–317 (1975). [CrossRef]
  6. G. J. Ward, “Measuring and modelling anisotropic reflection,” Comput. Graphics 26, 265–272 (1992). [CrossRef]
  7. X. D. He, K. E. Torrance, F. X. Sillion, and D. P. Greenberg, “A comprehensive physical model for light reflection,” Technical report, Computer Graphics (1991), Vol.  25, No. 4.
  8. J. F. Blinn, “Models of light reflection for computer synthesized pictures,” Comput. Graphics 11, 192–198 (1977). [CrossRef]
  9. E. P. F. Lafortune, S. C. Foo, K. E. Torrance, and D. P. Greenberg, “Non-linear approximation of reflectance functions,” Technical report (Cornell University, 1997).
  10. S. H. Westin, H. Li, and K. E. Torrance, “A comparison of four BRDF models,” Technical report PCG-04-02, Program of Computer Graphics (Cornell University, April2004).
  11. A. Ngan, F. Durand, and W. Matusik, “Experimental analysis of BRDF models,” Eurographics Symposium on Rendering, K. Bala and P. Dutre, eds. (2005).
  12. I. G. E. Renhorn and G. D. Boreman, “Analytical fitting model for rough-surface BRDF,” Opt. Express 16(17), 12892–12898 (2008). [CrossRef] [PubMed]
  13. J. L. Simonds, “Application of characteristic vector analysis to photographic and optical response data,” J. Opt. Soc. Am. 53, 968–971 (1963). [CrossRef]
  14. J. M. López-Alonso, J. Alda, and E. Bernabéu, “Principal-component characterization of noise for infrared images,” Appl. Opt.41, 320–331 (2002). [CrossRef] [PubMed]
  15. A. Ferrero, J. Alda, J. Campos, J. M. López-Alonso, and A. Pons, “Principal components analysis of the photoresponse nonuniformity of a matrix detector,” Appl. Opt. 46, 9–17 (2007). [CrossRef]
  16. A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, A. Corróns, and A. M. Rubio, “Gonio-spectrophotometer for low-uncertainty measurements of bidirectional scattering distribution function (BSDF),” Proceedings of CIE Expert Symposium on “Spectral and Imaging Methods for Photometry and Radiometry,” Publication CIE x036:2010 (CIE, Vienna, Austria, 2010), pp. 79–84.
  17. T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999). [CrossRef]
  18. D. Hünerhoff, U. Grusemann, and A Höpe, “New robot-based gonioreflectometer for measuring spectral diffuse reflection.” Metrologia 43, S11–S16 (2006). [CrossRef]
  19. F. B. Leloup, S. Forment, P. Dutré, M. R. Pointer, and P. Hanselaer, “Design of an instrument for measuring the spectral bidirectional scatter distribution function,” Appl. Opt. 47(29), 5454–5467 (2008). [PubMed]
  20. R. Corey, M. Kissner, and P. Saulnier, “Coherent backscattering of light,” Am. J. Phys. 63, 561–564 (1995). [CrossRef]
  21. T. J. Papetti, W. E. Walker, C. E. Keffer, and B. E. Johnson, “Coherent backscatter: measurement of the retroreflective BRDF peak exhibited by several surfaces relevant to ladar applications,” Proc. SPIE6682, 66820E (2007). [CrossRef]

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