On the theory of compound colours, and the relations of the colours of the spectrum

摘要

AbstractEven though the theory of trichromacy is sometimes referred to as the Young‐Helmholtz theory, arguably the most important person in its development was James Clerk Maxwell (1831–1878). It seems appropriate to initiate this series of classical articles with Maxwell's (1860) “On the Theory of Compound Colours, and the Relations of the Colours of the Spectrum.” This article, which is a paragon of imaginative, precise, and analytic research, made a number of seminal contributions to the study of color, some of which I have listed below. The list is ordered in the same sequence as topics are treated in the article. All unattributed quotes are from the paper.Aims of color research: Maxwell shifted the direction of color research from issues of subjective appearance to the scientifically more profitable study of color mechanisms, by aiming “to determine the laws of the composition of colors in general, to reduce the number of standard colours to the smallest possible, to discover, if we can, what they are, and to ascertain the relation which the homogeneous light of different parts of the spectrum bears to the standard colours.”Young's trichromatic theory: Helmholtz wrote, “Young's theory of the color sensations… remained unnoticed until Maxwell directed attention to it.” Maxwell identified the fundamental aspect of the theory as the projective transformation of the infinite‐dimensional space of spectral distributions to a color space of smaller dimensions. He tested the dimensionality of color space with his novel experiment of metameric color matching, i.e., by finding sets of physically distinct lights that have identical color appearance.Linking proposition: Maxweell recognized thut colorspace would be three dimensional if Young's three classes of transducers had the property that “each nuve acts, not us some have thought, by conveying to the mind the knowledge of the length ofcin undulation of light, or of its periodic time, but simply by being more or less affected by the rays which fall on it. The sensation of each elementary nerve is cupable only of increase or diminution, but no other change.” The Principle of Univariance gave this statement the physical interpretation that a photopigment can signal the number but not the wavelengths of the quanta absorbed.Representation of colors: As one of the first instanticitions of the linear algebru thut he had invented, Grassmann explicated the postulates necessary for Newtion theory of color mixture. Maxwell adapted the properties of a linear space to write explicitic for equations. All metameric lights were assigned to the same eyuivulence class, and each class was represented by a unique threedimensioncil vector. For gruphicul clarity, colors were shown on a planar chromaticity lriangle whose vrrtices corresponded to the vectors representing the standard colors.Psychophysical method: By using a method when the observer was required only to make judgments of identity versus nonidentity, Maxwell did not have to be concerned with the subjective aspects of possible differences. This may have been the first instance of what Brindley later culled Class A psychophysical experiments.An interesting aspect oj Maxwell's method was that all matches were made to the same standard white, thus “all the observations were of the same kind.” A number of studie8‐10have documented that Maxwell and maximum saturution matches give similar results except for test lights in the short‐wave part of the spectrum, where Max‐well matches give superior results.Trichromators: Maxwell's trichromator, which functioned like a reversed spectroscope, enabled him to independently control the intensity of four lights‐a standard white in one field, and three spectrally narrow lights in the other. By this means he was able to measure what we now call color‐matching jknctions (CMFs) and chromaticity coordinates. It is worth remembering that prior to this experiment, Helmholz's determination of complementury colors was the most extensive series of measurements on color mixture, and the circular form of the color field proposed by Newton had not been tested.One shortcoming o f Maxwell's trichromutor was that intensity could only be adjusted by means of slit width, which also altered the spectral composition of the light. Despite this limitation, by choosing the standard colors astutely, Maxwell was able to measure CMFs that are in substantial agreement with the CIE functions.Maxwellian view: In the trichromator, the lens was placed so that the source was imaged in the plane of the eye's pupil. The observer saw neither an erect nor an inverted image of the source, but rather afield of uniform illumination. Advantages ofwhut is now termed the Max‐wellian view have been described by Westheimer.Chromatic versus brightness sensitivity: There has been much recent debate on the relative sensitivities of the chromatic und luminance systems Cfor references, see Suchtler and Zaidi). The first quantitative treatment of this issue may have been Muxwell's determinution from an unulyvJis of errors, that in his experimental conditions, “the eye appears to be a more accurate judge of the identity of colour of two parts of the field than of their equal illumination.”Maxwell spot: The Maxwell spot was first described in this article as best seen on a blue background that replaces a yellow buckground. Maxwell identiJied the appearance of the spot with what is now called the macular pigment, which is confined to the foveal region, and indicated that Haidinger's brushes were phenomenal manifestations of the same cause.Individual differences in color vision: By comparing CMFs of two observers, Maxwell identiJied differences in preretinal ubsorption in the short wavelengths as the main cause of individual differences in color matching. By correlating the relative intensities of different primaries with the visibility of the Maxwell spot, he attributed this absorption to the macular pigment. More recent analyses15‐16have shown that interobserver variubility in color matches is due mainly to individual differences in optical density of lenticular pigment as well as macular pigment, both of which absorb maximally at short wavelengths.Dichromatic vision as a reduced form: Maxwell defined dichromatic vision as a reduced form of trichromatic vision, i.e., ifthe effects ofpreretinal absorption were equal, a dichromat would accept as metamers all matches made by a trichromat. Traditionally, dichromatic vision is defined in terms of copunctul points in u two‐dimensional trichromatic chromaticity diagram. The copunctal point is the point of intersection of lines through pairs of chromaticities that are indistinguishable to the dichromat. Maxwell's scheme is more elegant. In a three‐dimensional color space, the vector differences ofpairs of colors indistinguishable to a reduction‐type dichromat will all be parallel. The three types of dichromatic vision can thus be characterized completely by one confusion vector each, or in Maxwell's terms: “that colour, the absence of the sensation of which constitutes the defect of the dichromic eye.”Derivation of cone spectral sensitivities: When the three‐dimensional color space is affinely transformed to the three dichromatic confusion vectors as axes, each coordinate is proportional to the excitation of a corresponding independent cone class, and the CMFs are transformed to cone spectral sensitivities. Explicit derivations of Maxwell's procedure can be found in Nuberg and Yustova Judd and Zaidi.There is, of course, much more to this article than just these highlights. Maxw