Basis Functions of the Total Radiance Factor of Fluorescent Whitening Agents

Abstract

This paper describes the representation of the total radiance factor of fluorescent whitening agents by up to three basis components. Applying the dimensionality reduction technique to the total radiance factor of 84 cotton samples treated with different fluorescent whitening agents, it was possible to reconstruct the spectral behavior of specimens by using a very small number of basis functions, accurately. In order to study the properties of the basis function, a three-dimensional Euclidean spectral space was implemented to represent the samples. The orientation of the samples that confirmed the whiteness index limitations of CIE1982 were along a line in this space, as expected from a set of white specimens. The perfect correlation was also found between the CIE1982 whiteness index, W, and the first derived principal component coordinates of the samples.

Keywords

principal component analysis fluorescent whitening agent total radiance factor dimensionality reduction spectral space whiteness index

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References

Cohen, J. B. , Dependency of the Spectral Reflectance Curves of the Munsell Color Chips , Psychon. Sci. 1, 369–370 (1964).

Fairman, H. S. , and Brill, M. H. , The Principal Components of Reflectances , Color Res. Appl. 29, 104–110 (2004).

Garcia-Beltran, A. , Nieves, J. L. , Hernandez-Andres. J. , and Romero, J. , Linear Bases for Spectral Reflectance Functions of Acrylic Paints , Color Res. Appl. 23, 39–45 (1998).

Maloney, L. T. , Evaluation of Linear Models of Surface Spectral Reflectance with Small Number of Parameters , J. Opt. Soc. Am. A. 3, 29–33 (1986).

Marimont, D. H. , and Wandell, B. A. , Linear Models of Surface and Illuminant Spectra , J. Opt. Soc. Am. A. 9, 1905–1913 (1992).

Tzeng, D. , and Berns, R. S. , A Review of Principal Component Analysis and Its Applications to Color Technology , Color Res. Appl. 30, 84–98 (2005).

Worthey, J. A. , and Brill, M. H. , Principal Components Applied to Modeling: Dealing with the Mean Vector , Color Res. Appl. 29, 261–266 (2004).

Romney, A. K. , and Indow, T. , Munsell Reflectance Spectra Represented in Three Dimensional Euclidean Space , Color Res. Appl. 28, 182–196 (2003).

Ramanath, R. , Kuehni, R. G. , Snyder, W. E. , and Hinks, D. , Spectral Spaces and Color Spaces , Color Res. Appl. 29, 29–37 (2004).

10.

Grum, F. , Colorimetry of Fluorescent Materials, in “Optical Radiation Measurements”, F. Grum and C. J. Bartleson , Eds, Academic Press, New York , pp. 238–239, 1980.

11.

Smith, K. J. , Colour-order Systems, Colour Spaces, Colour Difference and Colour Scales, in “Colour Physics for Industry”, R. McDonald , Ed., Society of Dyers and Colourists, Bradford , pp. 195–204, 1997,

12.

Uchida, H. , A New Whiteness Formula , Color Res. Appl. 23, 202–209 (1998).