Abstract

The loci in CIE space of colors with a given difference from a standard are calculated from the Adams-Nickerson equation. The calculation is carried out by means of a point-by-point transformation from an intermediate chromatic value space to CIE space. Digital computers are used for the entire calculation and transformation. The calculated quasi-ellipsoids may be compared with those observed by Brown and MacAdam. For routine decision work, an approximation involving the intersection of three right cylinders based on projections of the original ellipsoid is employed.

© 1957 Optical Society of America

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References

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  1. D. Nickerson, Am. Dyestuff Reptr. 39, 541 (1950).
  2. L. G. Glasser and D. J. Troy, J. Opt. Soc. Am. 42, 652 (1952).
    [Crossref]
  3. D. DeJager, paper presented at the Spring, 1956Meeting of the Optical Society of America.
  4. Opler, Meikle, and Charlesworth, J. Opt. Soc. Am. 43, 550 (1953).
    [Crossref] [PubMed]
  5. E. Allen and W. M. Chow, J. Opt. Soc. Am. 44, 349 (1954).
  6. W. J. R. Brown and D. L. MacAdam, J. Opt. Soc. Am. 39, 808 (1949).
    [Crossref] [PubMed]
  7. G. W. Ingle and L. Rudick, Instruments 26, 400 (1953).
  8. H. R. Davidson and J. J. Hanlon, J. Opt. Soc. Am. 45, 617 (1955).
    [Crossref]

1955 (1)

1954 (1)

E. Allen and W. M. Chow, J. Opt. Soc. Am. 44, 349 (1954).

1953 (2)

1952 (1)

1950 (1)

D. Nickerson, Am. Dyestuff Reptr. 39, 541 (1950).

1949 (1)

Allen, E.

E. Allen and W. M. Chow, J. Opt. Soc. Am. 44, 349 (1954).

Brown, W. J. R.

Charlesworth,

Chow, W. M.

E. Allen and W. M. Chow, J. Opt. Soc. Am. 44, 349 (1954).

Davidson, H. R.

DeJager, D.

D. DeJager, paper presented at the Spring, 1956Meeting of the Optical Society of America.

Glasser, L. G.

Hanlon, J. J.

Ingle, G. W.

G. W. Ingle and L. Rudick, Instruments 26, 400 (1953).

MacAdam, D. L.

Meikle,

Nickerson, D.

D. Nickerson, Am. Dyestuff Reptr. 39, 541 (1950).

Opler,

Rudick, L.

G. W. Ingle and L. Rudick, Instruments 26, 400 (1953).

Troy, D. J.

Am. Dyestuff Reptr. (1)

D. Nickerson, Am. Dyestuff Reptr. 39, 541 (1950).

Instruments (1)

G. W. Ingle and L. Rudick, Instruments 26, 400 (1953).

J. Opt. Soc. Am. (5)

Other (1)

D. DeJager, paper presented at the Spring, 1956Meeting of the Optical Society of America.

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Figures (2)

Fig. 1
Fig. 1

The three projections of the intermediate ellipsoid (right) and the corresponding quasi-ellipses (left) when ΔE=3.0 and (X,Y,Z)=(40.46, 39.57, 92.78).

Fig. 2
Fig. 2

Projections of the quasi-ellipsoids (a) onto the x, y plane for several indicated values of ΔE and Y. The ellipses in (b) are constant Y sections of the observational limits of Brown and MacAdam. (ΔE=10.) The absolute magnitudes are not directly comparable but the figures are supplied to show their relative size, shape, and orientation. Figure b is taken directly from reference 6. See also the color plate in that reference.

Equations (8)

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Δ E = 42 { ( 0.23 Δ V Y ) 2 + [ Δ ( V X - V Y ) ] 2 + [ 0.40 Δ ( V Z - V Y ) ] 2 } 1 2 .
1764 ( Δ V X ) 2 - 3528 ( Δ V X ) ( Δ V Y ) + 2139.7 ( Δ V Y ) 2 - 564.4 ( Δ V Y ) ( Δ V Z ) + 282.2 ( Δ V z ) 2 = 1.
V Q = K Q ( 1.2219 V Q - 0.23111 V Q 2 + 0.23951 V Q 3 - 0.021009 V Q 4 + 0.0008404 V Q 5 ) ,
1764 ( Δ V X ) 2 - 3528 ( Δ V X ) ( Δ V Y ) + 1857.5 ( Δ V Y ) 2 = 1 ,
375.7 ( Δ V Y ) 2 - 564.4 ( Δ V Y ) ( Δ V Z ) + 282.2 ( Δ V Z ) 2 = 1 ,
309.7 ( Δ V X ) 2 - 465.7 ( Δ V X ) ( Δ V Z ) + 245.2 ( Δ V Z ) 2 = 1.
Δ E = { 0.5 [ ( Δ e ) X Y 2 + ( Δ e ) X Z 2 + ( Δ e ) Y Z 2 ] } 1 2 .
[ i . e . K ( Δ e ) max Δ E ] .