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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 52, Iss. 6 — Jun. 1, 1962
  • pp: 685–691

Variability of Spectral Tristimulus Values


JOSA, Vol. 52, Issue 6, pp. 685-691 (1962)

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This paper describes a fundamental procedure for deriving “within” and “between” variances and co-variances in the spectral tristimulus values. The within variances are based on the replications of color-mixture data by an observer. The between variances are based on differences among the color-mixture data of individual observers. A statistical model for the system in which the experimental data are obtained is given, expected values (means), variances, and co-variances are developed, and the method by which these variances and co-variances may be distributed among the sources of uncertainties in the experimental data is presented. There is developed a procedure for determining the uncertainties in the constants of a linear transformation to a system analogous to the present CIE system. The formulas for variances and co-variances after linear transformation are given for an arbitrary choice of transformation constants. The complete set of variances and co-variances derived from an arbitrary transformation is listed for 20 mµ intervals. This set, together with the mean spectral tristimulus values, forms a complete standard observer system. The between-observer variabilities are found to be about 10% of the averages of the color-mixture data and the average ratio of the between-observer variabilities to the within-observer variabilities is found to be about 5.7.

I. NIMEROFF, JOAN R. ROSENBLATT, and MARY C. DANNEMILLER, "Variability of Spectral Tristimulus Values," J. Opt. Soc. Am. 52, 685-691 (1962)

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  1. I. Nimeroff, J. Opt. Soc. Am. 47, 697 (1957).
  2. W. S. Stiles and J. M. Burch, Optica Acta 6, 1 (1959).
  3. N. I. Speranskaya, CIE Committee Report, and in part, NPL Symposium 8 (Her Majesty's Stationery Office, London) 1, 317 (1958); also Optics and Spectroscopy VII, 429 (1959), (OSA translation).
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  5. D. B. Judd, Detailed Report of Progress (September, 1957, to April, 1959), CIE Working Committee W-1.3.1, Colorimetry.
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  9. G. Wyszecki, National Research Council of Canada Rept. APOI-907, June, 1959.
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