Relative wavelength metric for the complete hue cycle: Derivation from complementary wavelengths

Abstract

In recent research, it has been increasingly necessary to employ an extended wavelength metric to cover the complete hue cycle so as to research or represent data as a function of relative wavelength rather than psychological scales such as CIELAB or Munsell hue angle. This article describes such a relative wavelength metric and its derivation from complementary wavelength functions. The metric provides a useful psychophysical, wavelength-based, ratio scale for the hue cycle allowing nonspectrals to be treated in the same coherent scale as spectral hues. Several indicators, e.g., color order hue cycles, infer the (optimally efficient) spectral hues comprise about 71% and the nonspectrals about 29%, of the hue cycle interval. This gives a hue cycle whose relative wavelength interval is about 240 nm for illuminant D65. To relate to CIE colorimetry, spectral complementary wavelengths to the nonspectrals' relative wavelengths are identified for seven illuminants including D65, D50, C, and A. Data are given for CIE 1931, and briefly 1964, colorimetry.

Complementary colors: The structure of wavelength discrimination, uniform hue, spectral sensitivity, saturation, chromatic adaptation, and chromatic induction

“…21 The MCI pair varies between illuminants, but for illuminant D65 it is 578.2 and 479.8 nm (each with CI ratio 1: 1), and the mean (termed hue cycle midpoint) is 529 nm. 20,21 Note that 529 nm agrees closely with the 530 nm peak (in G) of the dashed gray line in Fig. 3, that it is located in mid-spectrum, and that its complementary (529 c) is located in Fig.…”

“…These details enable a reasonably accurate estimate 20 of the CI ratios of the green and nonspectral curves, shown in Fig. 3 (black solid line).…”

“…In this uniform scale, the only diametrically opposite pairs that are complementary are those with a half-cycle complementary interval (120 nm), i.e., 448 and 568 nm, 491.5 and 611.5 nm (both pairs are from CIE data), and 529 nm and 409/ 649 e. Figure 4(B) illustrates the complementary wavelength scale, where every diametrically opposite pair is a complementary wavelength pair; the distribution of complementary wavelength pairs around the circle is not arbitrary but deduced by methods described in Ref. 20 and incorporating the CI ratios listed in Table I and graphed in In summary, Fig. 4 shows two wavelength scales: a uniform wavelength scale (constant angles give constant wavelength intervals, i.e., 18 ¼ 1.5 nm) for general use, and a complementary wavelength scale (constant angles give varying wavelength intervals) for special purposes.…”

“…1 at about the middle of the nonspectral range, where one would expect to locate the hue cycle ends. In the relative wavelength metric, 20 the hue cycle midpoint is also the mean of the cycle ends, so these are each a half-cycle from the midpoint, i.e., 120 nm, given the cycle interval of 240 nm/e (Appendix).…”

“…To identify the equivalent wavelengths colorimetrically, their (spectral) complementary wavelengths must be specified, as described in Ref. 20 and listed in Table I [see also Figs. 1 and 4(B)].…”