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Fig. 1.Horizontal cross-section of the normal human eye. a selective filter interposed between the vitreous humor C and the retina i. Metamers set up for one normal observer usually fail to hold strictly for anyone else. This failure is ascribable to variations in amount of pigmentation of the eye media (cornea, lens, humors, macula), the macular pigment being one of the chief variables. The properties of the normal eye derived from a small-field study of these extreme metamers therefore refer only to the central 2 deg of the retina, and they refer to an hypothetical average eye. Nobody has been found whose eye differs so little from this average eye that the differences could not be detected. Practically speaking, therefore, nobody has an eye that is colorimetrically normal.

1.5. Grassman's Law

From a knowledge of spectral metamers, it has been possible to summarize concisely the properties of the average normal eye. This summary is made in accord with the principle known as Grassman's law [42] foreshadowed by Newton's laws of color mixture. If a light composed of known amounts of three components (called primaries) is equivalent in color to an unknown light, the three known amounts may be used as a color specification for this light. These amounts are called the tristimulus values of the color. Grassman's law states that, when equivalent lights are added to equivalent lights, the sums are equivalent. Thus, if an unknown spot of color were matched by shining on the same spot of a white screen two component spotlights of tristimulus values, $X_{1}$, $Y_{1}$, $Z_{1}$, and $X_{2}$, $Y_{2}$, $Z_{2}$, respectively, by Grassman's law, the tristimulus values, $X$, $Y$, $Z$, of the unknown spot of color would be simply:

${\begin{alignedat}{5}X&=&X_{1}&+&X_{2}\\Y&=&Y_{1}&+&Y_{2}\\Z&=&Z_{1}&+&Z_{2}\\\end{alignedat}}$

(1)

Any beam of light, whether it originates from a self-luminous body or comes, by transmission, scattering, or reflection, from a nonself-luminous object, may be considered as made up of a large number of portions of the spectrum. The amounts of these various portions may be determined by spectrophotometry. The spectral values, ${\overline {x}}(\lambda )$, ${\overline {y}}(\lambda )$,${\overline {z}}(\lambda )$, of each of these portions have been determined for a number of normal observers, and average values are given in table 1 in arbitrary units for a spectrum of unit spectral irradiance.

The principle expressed in Grassman's law has been established by repeated experiment over a wide middle range of retinal illuminances. It breaks down for very high retinal illuminances [159] that begin to approach those sufficient to do the eye permanent harm, and it breaks down if the illumination of the whole retina continues for several minutes to be so slight that vision by the retinal rods (twilight vision) intrudes significantly [84]. Between these two extremes, however, Grassman's law holds independently of the adaptive state of the eye. Thus, if two stimuli of different wavelength distributions of energy be found that are once responded to alike by the eye, they will be seen alike even after exposure of the eye to another stimulus sufficient to change considerably the appearance of the two equivalent stimuli. For example, if a portion of the spectrum near 640 nm (red) be superposed on a portion near 550 nm (yellowish green), it will be found possible to obtain the color of this combination from an intermediate portion of the spectrum, say, 590 nm (orange). If the retina of the eye be highly illuminated by light of wavelength near 640 nm, and its sensitivity to radiant flux of this wavelength region considerably reduced in this way, it is found that, although neither of the equivalent stimuli any longer appears orange, they still give identical colors; for example, they may yield identical yellows or identical greenish yellows. The eye thus cannot be trusted to yield the same color perception from a given stimulus; simultaneous and successive contrast affect it profoundly. But the eye is still a satisfactory null instrument and obeys Grassman's law.

By Grassman's law it is possible to test whether any two beams of light of differing spectral composition form a metameric pair. The condition for metamerism of two beams of light of spectral irradiance. $E_{1}$ and $E_{2}$, is that simultaneously:

${\begin{aligned}\sum _{0}^{\infty }(E_{1})_{\lambda }{\overline {x}}(\lambda )\Delta \lambda &=\sum _{0}^{\infty }(E_{2})_{\lambda }{\overline {x}}(\lambda )\Delta \lambda \\\sum _{0}^{\infty }(E_{1})_{\lambda }{\overline {y}}(\lambda )\Delta \lambda &=\sum _{0}^{\infty }(E_{2})_{\lambda }{\overline {y}}(\lambda )\Delta \lambda \\\sum _{0}^{\infty }(E_{1})_{\lambda }{\overline {z}}(\lambda )\Delta \lambda &=\sum _{0}^{\infty }(E_{2})_{\lambda }{\overline {z}}(\lambda )\Delta \lambda \\\end{aligned}}$

(2)

where ${\overline {x}}(\lambda )$, ${\overline {y}}(\lambda )$ and ${\overline {z}}(\lambda )$ characterize the observers' spectral responses. (These equations are written in accord with the CIE notation adopted in 1963. Symbols with subscripted $\lambda )$, as $E_{(}\lambda )$, indicate spectral concentration, while symbols with parenthetical $\lambda$, as ${\overline {x}}(\lambda )$, indicate other spectral relationships not critically dependent on choice of wavelength interval.) The wavelength interval,