https://doi.org/10.2352/ISSN.2470-1173.2021.16.COLOR-324 © 2021, Society for Imaging Science and Technology Optimization of monochromatic primaries in RGB system: on the specific question of purples Lionel Simonot1, Philippe Colantoni2, Mathieu Hébert2 1 Université de Poitiers, Institut Pprime UPR 3346 CNRS, Chasseneuil Futuroscope, France ; 2 Université de Lyon, UJM-Saint-Etienne, CNRS, Institut d Optique Graduate School, Laboratoire Hubert Curien UMR 5516, Saint-Etienne, France. The widest possible gamut is generally sought so that the Abstract maximum chroma can be achieved for each hue angle. For RGB In the CIE1931 xy chromaticity diagram, the set of visible systems, increasing the size of the triangular gamut can hardly be colors is delimited by the spectrum locus representing the done otherwise than by choosing three monochromatic primaries. monochromatic radiations and by the purple line, set of non- The choice of the spectral color green will strongly influence the spectral colors obtained by binary mixing between monochromatic system's ability to reproduce with a high chroma the colors of hue radiations at the two extremities of the visible range. In contrast ranging from orange to cyan through greens, favouring either with the spectrum locus, which represents, for most wavelengths, yellows or turquoises. The choice of the blue and red spectral bright and maximally saturated colors, the purple line rather colors will mainly affect the system's ability to reproduce blue, represents colors at the perception limit, corresponding to spectral purple, red and other shades with high chroma. To increase the powers with very low luminous efficacy. The notion of “practical” gamut coverage, one is tempted to take the red and blue primaries purple lines is discussed. It comes down to the definition of the at the extremes of the visible spectrum, but as the luminous blue and red monochromatic primaries of RGB light emitting efficacy is very low at these extreme wavelengths, some colors, systems. The choice of monochromatic primaries allowing the especially white, cannot be reproduced with sufficient luminous widest gamut while maintaining a good luminous efficacy over its efficacy. This is an obvious technical and energy issue for displays whole perimeter is still an open question: by choosing red and blue or projectors. A trade-off has therefore to be found between gamut primaries further in the extremes of the visible spectrum, the gamut size and luminous efficacy. In this paper, we detail the solutions size is increased but the luminous efficacy of the primaries, thereby that have been proposed and try to better describe the criteria for of all reproducible colors, is decreased. As optimal trade-offs, we suggest two RGB systems favoring either the gamut size, or the achieving an optimal solution. luminous efficacy. Enlarging the gamut is therefore equivalent to trying to achieve the highest chroma possible for each hue. It is worth considering the best way to quantify this color attribute. However, 1. Introduction even with the component Y representing luminance added to the Created in 1931 by the CIE, the XYZ color space is a 3D chromaticity diagram, CIE xyY color space is not a color space representing all perceptible colors. Simultaneously was appearance model, in contrast with CIELab or CIECAM02 spaces. created the xy chromaticity diagram, a 2D representation resulting The notions of hue, saturation and lightness are not directly from a projective transformation of the XYZ color space accessible. To overcome this difficulty, the concepts of dominant discarding the luminance component. This latter is suitable for wavelength (for hue) and excitation purity (for chroma) have been lighting systems for which lightness makes no sense. For example, defined. The dominant wavelength is the wavelength indicated by by decreasing the power of a white source, one still obtains a the meeting point S between the spectrum locus and the line source of white color not grey. Its well-known shape is delimited meeting the chromaticity points C and W representing respectively by the spectrum locus, line drawn by the chromaticity values the considered color and a white reference color selected attached to the visible monochromatic radiations, and by the purple beforehand. The excitation purity is then the ratio of Euclidian line, straight line joining the chromaticity values attached to the distances CW/SW in the diagram. Spectral colors therefore have an two extremities of the visible spectrum. Owing to its ingenious excitation purity unity and a dominant wavelength equal to that of mathematical construction, this diagram has the interesting their radiation. These notions make less sense for colors close to property to represent the chromaticities of light stimuli obtained by the purple line, whose hue does not benefit from a spectral color to additive mixing of two primary stimuli as a segment of straight define them. By convention, a negative dominant wavelength is line, whose extremities are the chromaticities of the two primary assigned corresponding to the complementary spectral color, i.e. stimuli, a linearity inherited from the linearity of the XYZ color on the same segment and opposite to the reference white. The space in respect to additive color mixing. These mathematical excitation purity is calculated in the same way, taking the purple properties probably explain the success, still well observable today, line as boundary with unit purity. This solution is not satisfactory that this diagram has met for the color characterization of displays, since colors on the purple line are practically imperceptible video projectors, and any other RGB system based on additive because it results from the mixture of two red and blue lights at the color mixing of three primary red, green and blue lights. Even limit of the locus spectrum, which are themselves almost though their color gamut is actually a 3D volume, more precisely imperceptible. This difference between purples and other hues runs an hexahedron, in the XYZ color space, its projection (a triangle) counter to the main ideas that have accompanied the evolution of in the xy chromaticity diagram is often preferred, probably because color representation systems since Newton, notably the idea of a a 2D diagram is more convenient to display than a 3D volume, and continuous color circle, where all hues are treated similarly. also because the triangle in the chromaticity diagram exhibits well the color reproduction quality in terms of chroma for each hue. IS&T International Symposium on Electronic Imaging 2021 Color Imaging XXVI: Displaying, Processing, Hardcopy, and Applications 324-1 y 0.9 (a) (b) (c) 0.8 546.1 nm 0.7 0.6 0.5 A 0.4 D65 0.3 700 nm 0.2 0.1 435.6 nm 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 x Figure 1. (a) Newton's chromatic disc [1]. The purples are on the OD segment that connects the two ends of the spectrum. (b) Maxwell's color triangle [3] with monochromatic primaries noted 24, 44 and 68. An angular sector is dedicated to purple between the two extreme wavelengths noted 20 and 80. (c) CIE xy chromaticity diagram. The purple line connects the extreme wavelengths of the visible: 380 nm and 780 nm. The monochromatic primaries of the CIE1931 RGB color space correspond to the wavelengths 700 nm, 546.1 nm and 435.8 nm. Color annotations have been added to the original documents to make them easier to read. We therefore provide a history of these ideas, starting in an example of mixture made of the seven colors according to the Section 2 with the place of non-spectral purple colors in color proportions indicated by the size of the small circles on the representation systems. We present in Section 3 the difficulty of periphery of the disc. The centre of gravity is obtained in Z. The determining the maximum chroma location for each hue, including line OZ cuts the disc periphery in Y: the hue of the mixture is an purples. In Section 4, we discuss the choice of monochromatic orange color that tends slightly towards red. The OZ distance gives primaries in existing RGB systems for which a practical purple line an indication of the saturation of the color: here, less than half is defined as the line joining the blue and red monochromatic compared to the corresponding spectral color (OY). Maximum primaries. In the trade-off between gamut coverage and luminous saturation is logically achieved by the spectral colors at the efficacy, we highlight two new RGB systems with monochromatic periphery of the disc. It should be noted that the non-spectral primaries. In Section 5, the proposed RGB system favours a high colors, finally called purples, are not represented on the luminous efficacy to obtain the reference white by ternary mixing circumference of the circle. However, Newton did not ignore them between the three primaries. In Section 6, we present an alternative completely and placed them on the OD segment as a result of that allows for a wider color gamut and a constant and not zero mixing violet and red. In contrast to Newton's disc, current color luminous efficacy on the line connecting the blue and red classification systems such as Munsell or NCS grant purples a primaries. large angular sector of between 25 and 30 %. In the 19th century, the English scientist Young suggests that 2. On purple in the History of color science our visual system should contain three types of particles, sensitive In 1665, the Great Plague epidemic in England forced the to the colors red, green or violet [2]. This trichromacy principle universities to close. Students had to confine themselves into their allowed to represent all colors perceptible in an equilateral triangle homes.