Abstract

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.

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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).
  4. I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Research Natl. Bur. Standards 65A, 475 (1961).
  5. D. B. Judd, Detailed Report of Progress (September, 1957, to April, 1959), CIE Working Committee W-1.3.1, Colorimetry.
  6. I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Opt. Soc. Am. 49, 1137 (1959).
  7. H. Hotelling, Ann. Math. Stat. 2, 360 (1931); J. E. Jackson, J. Opt. Soc. Am. 49, 585 (1959).
  8. D. B. Judd, J. Research Natl. Bur. Standards 43, 277 (1949).
  9. G. Wyszecki, National Research Council of Canada Rept. APOI-907, June, 1959.
  10. G. Wyszecki, J. Opt. Soc. Am. 49, 389 (1959).

Burch, J. M.

W. S. Stiles and J. M. Burch, Optica Acta 6, 1 (1959).

Dannemiller, M. C.

I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Opt. Soc. Am. 49, 1137 (1959).

I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Research Natl. Bur. Standards 65A, 475 (1961).

Hotelling, H.

H. Hotelling, Ann. Math. Stat. 2, 360 (1931); J. E. Jackson, J. Opt. Soc. Am. 49, 585 (1959).

Judd, D. B.

D. B. Judd, Detailed Report of Progress (September, 1957, to April, 1959), CIE Working Committee W-1.3.1, Colorimetry.

D. B. Judd, J. Research Natl. Bur. Standards 43, 277 (1949).

Nimeroff, I.

I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Research Natl. Bur. Standards 65A, 475 (1961).

I. Nimeroff, J. Opt. Soc. Am. 47, 697 (1957).

I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Opt. Soc. Am. 49, 1137 (1959).

Rosenblatt, J. R.

I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Opt. Soc. Am. 49, 1137 (1959).

I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Research Natl. Bur. Standards 65A, 475 (1961).

Speranskaya, N. I.

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).

Stiles, W. S.

W. S. Stiles and J. M. Burch, Optica Acta 6, 1 (1959).

Wyszecki, G.

G. Wyszecki, National Research Council of Canada Rept. APOI-907, June, 1959.

G. Wyszecki, J. Opt. Soc. Am. 49, 389 (1959).

Other (10)

I. Nimeroff, J. Opt. Soc. Am. 47, 697 (1957).

W. S. Stiles and J. M. Burch, Optica Acta 6, 1 (1959).

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).

I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Research Natl. Bur. Standards 65A, 475 (1961).

D. B. Judd, Detailed Report of Progress (September, 1957, to April, 1959), CIE Working Committee W-1.3.1, Colorimetry.

I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Opt. Soc. Am. 49, 1137 (1959).

H. Hotelling, Ann. Math. Stat. 2, 360 (1931); J. E. Jackson, J. Opt. Soc. Am. 49, 585 (1959).

D. B. Judd, J. Research Natl. Bur. Standards 43, 277 (1949).

G. Wyszecki, National Research Council of Canada Rept. APOI-907, June, 1959.

G. Wyszecki, J. Opt. Soc. Am. 49, 389 (1959).

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