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We have used 13 experimental datasets (7420 colour pairs) to study the performance of the weighting function for lightness proposed by the CIEDE2000 colour-difference formula, because it has been suggested that this function can be improved by using the weighting function for lightness SL = 1 adopted by the CIE94 colour-difference formula. Using the standardised residual sum of squares (STRESS) index, it was found that: (i) replacing the SL in CIEDE2000 with SL = 1 improved the results for 7/13 datasets considered, but the improvement was statistically significant only for 1/13 datasets; (ii) a Whittle-type lightness-difference formula can be used to replace the term ∆L*/SL in CIEDE2000, which led to a new colour-difference formula with no statistically significant difference with respect to CIEDE2000 for any of the 13 experimental datasets. A modification of the CIEDE2000 formula using a Whittle-type lightness formula is proposed.

Their physical origin distinguishes chemical colors and structural colors, the latter being subdivided into prismatic colors and interference colors. Colors of optical coatings are interference colors. A short history of interference colors is given starting from Isaac Newton, and then continuing with Thomas Young (interference in optics), Leopoldo Nobili (electrochemical ‘metallocromia’), David Brewster, A. Michel-Levy (interference color chart), J. F. Gabriel Lippmann (interference color photography) and Dobrowolski (anticounterfeiting coatings). A concise review of standard colorimetry (psychophysical and psychometric colorimetry) is given with the aim of introducing the colorimetry of the optical coatings. Gonio-apparent color measurement technique is presented with the updated multi-angle spectrophotometers. As an example, classical computations of colors of optical coatings are shown.

Previous attempts to predict chromatic-adaptation correspondence have led to a sharpening dilemma—i.e., Von Kries primaries are chosen that do not include in the positive octant all the realizable (x,y) chromaticities. This leads to paradoxical adaptation predictions for the colors that have negative Von Kries coordinates. A solution is proposed here that expresses the asymmetric-matching relation of chromatic adaptation as the product of two matrix transformations, given source illuminant 1 and destination illuminant 2: from source tristimulus values via adaptation matrix 1 to the adapted state coordinates, and from the adapted state via the inverse of adaptation matrix 2 to the destination illuminant tristimulus values. To avoid the sharpening instability, the entire spectrum locus must lie within the positive octant of the adapted state tristimulus space. © 2013 Wiley Periodicals, Inc. Col Res Appl, 39, 275–278, 2014; Published Online 14 March 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/col.21799

Over time, much work has been carried out to ascertain the validity of Grassmann's laws, Abney's law, CIE standard color-matching functions and, up to now, no definitive answer has been given. Some of the phenomena subject of this debate are considered. An apparatus for color matching in 1.8° visual field has been realized with two sets of primary lights with broad spectral bands. This kind of primaries is the great difference with respect to other laboratories because it allows an indirect check of the Grassmann additivity law on the basis of the spectra and individual color-matching functions by evaluating: (1) the tristimulus values of the primary lights; (2) the transformation matrices between the two reference frames defined by the two primary sets; and (3) the tristimulus values associated to all the pairs of matching lights in the bipartite field produced in the evaluation of the two sets of color-matching function. The discrepancies of the data resulting in the check (1) and (2) are all compatible with the range defined by the uncertainty propagation of the individual color-matching functions. In the check (3) fifteen tristimulus values over 18 have a discrepancy lower than one standard uncertainty. Grassmann's proportionality law is checked directly by reducing the matching lights with a neutral filter and holds true. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 271–281, 2008.

General hypothesis for the definition of chromatic-opponency functions are given in a black-box approach to the problem. It is supposed that the color signals in the visual color processing can be factorized into the product of the lightness times a pair of chromatic opponency functions and the whole chromatic processing consists of three independent processes: a linear transformation, a logarithmic compression, and a chromatic opponency actuation. The main chromatic opponency functions, obtainable by very general hypothesis on the symmetry and on the homogeneity degree, are supposed equal to the logarithms of tristimulus-value ratios in a proper reference frame of the tristimulus space. The perceptual chromatic functions, individually with uniform scales, are a linear mixing of the main chromatic opponency functions. The Bezold–Brucke hue shift is not considered. A performance of these hypothesis is successfully realized on the OSA-UCS system, for extra macula vision, and on the chromatic discrimination ellipses, for macular vision. Unique hues are derived from the main chromatic opponency functions of spectral lights. © 2004 Wiley Periodicals, Inc. Col Res Appl, 30, 31–41, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20072

Today chromatic adaptation transforms (CATs) are reconsidered, since their mathematical inconsistency has been shown in Color Res. Appl.38, 188 (2013) and by the CIE technical committee TC 8-11: CIECAM02 Mathematics. In 2004-2005 the author proposed an adaptation transform based on the uniform color scale system of the Optical Society of America (OSA-UCS) [J. Opt. Soc. Am. A21, 677 (2004); Color Res. Appl. 30, 31 (2005)] that transforms the cone-activation stimuli into adapted stimuli. The present work considers all the 37 available corresponding color (CC) datasets selected by CIE and (1) shows that the adapted stimuli obtained from CC data are defined up to an unknown transformation, and an unambiguous definition of the adapted stimuli requires additional hypotheses or suitable experimental data (as it is in the OSA-UCS system); (2) produces a CAT, represented by a linear transformation between CCs, associated with any CC dataset, whose high quality measured in ΔE units discards the possibility of nonlinear transformations; (3) analyzes these color-conversion matrices in a heuristic way with a reference adaptation that is approximately that of the OSA-UCS adapted colors for the D65 illuminant and particularly shows accordance with the Hunt effect and the Bezold-Brucke hue shift; (4) proposes the measurements of CC stimuli with a reference adaptation equal to that of the visual situation of the OSA-UCS system for defining adapted colors for any considered illumination adaptation and therefore for defining a general CAT formula.

Color-space metrics are considered and three main aspects are analyzed: (1) the distinction between small and large color differences; (2) the relation between space metrics and color-difference formulae; (3) the color-scale comparison between CIE 1931 and CIE 1964 observers.The analysis, based on daylight adaptation, is made for the 2° visual field on a chromaticity diagram with uniform scales according with the MacAdam ellipses1 and, for the 10° visual field, on the OSA-UCS.2,3 The conclusions are: (i) the main difference between 2° and 10° observers is a proper dilation of the chromaticity scales; (ii) the chroma scale of the Munsell system is uniform for the 10° visual field; (iii) the scales of the Munsell system are in good agreement with those of OSA-UCS; (iv) the usual color-difference formulae (CMC, CIE94) represented on the OSA-UCS space show a distortion that seems due to their definition in the CIELAB space; the BFD formula shows a lower distortion. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 351–361, 2001

The colorimetric difference between pairs of observers is simulated by a proper filtering of the stimulating radiation, and their comparison is made on properly defined Common Reference Frames in the tristimulus space. As examples, two comparisons are proposed: (1) Comparison between the Vos modification of the CIE 1931 Standard Colorimetric Observer and the CIE 1964 Supplementary Standard Observer: in this case, it is supposed that the difference between these two color-vision systems is due to the macula lutea only, which with a spectral selective absorbance alters the power spectral distribution of the color stimuli. The optical density of the macular pigment is well reproduced. (2) Comparison between the Vos modification of the CIE 1931 Standard Colorimetric Observer and the CIE 1931 Standard Colorimetric Observer: in this case, the difference between these two observers could be simulated by different calibration of the photodetectors. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 177–184, 1999

Chromatic-response functions and a uniform-scale chromaticity diagram are derived by assuming that normal trichromatic vision is obtained by combining tritanopic and deuteranopic vision. Two different opponent-chromatic mechanisms can be related to these two dichromatic visions. The chromatic-response functions obtained are the logarithms of proper cone-activation ratios (CAR). Each opponent-chromatic mechanism consists of two parts separated by a properly defined neutral point that depends on the surround chromaticity. The Abney-hue shift, the wavelength discrimination for trichomats, deuteranopes, and tritanopes, and the threshold purity are well reproduced. © 1998 John Wiley & Sons, Inc. Col Res Appl, 23, 27–38, 1998

Recent literature suggests that individuals may consume less food when this is served on red plates. We explored this intriguing effect in three experiments. Independent groups of participants were presented with constant amounts of popcorns, chocolate chips, or moisturizing cream, on red, blue, or white plates. They were asked to sample the foods (by tasting them) or the cream (by rubbing it on the hand and forearm) as they wished and to complete mock "sensory analysis" questionnaires. Results confirmed that red plates reduce taste-related consumption and extended this effect to the touch-related consumption of moisturizing cream. Suggesting that the effect was not due to a decrease in the consciously experienced appeal of products on red plates, overall appreciation of the foods or cream did not differ according to plate color. After careful photometric measures of the materials used for each food-plate pairing, we determined that food and cream consumption was not predicted by Michelson (achromatic) contrast. Although the origin of the intriguing effect of the color red on consumption remains unclear, our results may prove useful to future potential explanations.

A Chromatic Adaptation based on the OSA-UCS system makes a Color Conversion between different illuminations and defines adapted coordinates with uniform perceived scales, whose digitalization has a color independent color degradation.

In digital image capture, the camera signals produced by the D65 illuminant, once translated into tristimulus values of the CIE 1931 standard colorimetric observer (assuming the Maxwell-Ives-Luther criterion is satisfied), are considered good to produce accurate color rendering. An image obtained under any illuminant other than D65 does not appear realistic and the tristimulus values of the camera must be transformed into the corresponding ones produced by the D65 illuminant. This transformation must satisfy color constancy. In this work, the transformation is obtained by a color-vision model based on the Optical Society of America-Uniform Color Scales system [Color Res Appl 2005; 30: 31–41] and is represented by a matrix dependent on the adaptation illuminant. This matrix is obtained by minimizing the distance between the pairs of the uniform scale chromatic responses related to the tristimulus values of the 99 different color samples of the SG Gretag-Macbeth ColorChecker measured under a pair of different illuminants, one of which is the D65. Then any picture captured under a given light source can be translated into the picture of the same scene under the D65 illuminant. Metameric reason allows only approximate solutions. The transformations from Daylight and Planckian illuminants to the D65 illuminant have a very regular dependence on the color temperature, that appears to be the typical parameter for the color conversion. © 2012 Wiley Periodicals, Inc. Col Res Appl, 38, 412–422, 2013

The design of a compact spectrometer for analysis of artworks is presented. Its operation is based on the use of a variable transmission filter associated with an array detector. The instrument allows the measurement of the spectral reflectance factor and combines the acquisition of data in a continuous spectrum with the small dimension that is of primary importance for in-situ spectral imaging.

The non-uniformity of scale in the usual chromaticity diagrams is a very old problem in colour measurements. This program computes the transformation from the CIE 1931 (x, y) chromaticity diagram to the recent uniform scale (θ, δ) diagram and vice-versa. Moreover the program evaluates the most important colorimetric quantities for a comparison with the experimental data. Finally the chromatic gamut needed for TV applications is shown.

An investigation of the color metrics and the complexity of the CIEDE2000 formula shows that CIELAB space is inadequate to represent small-medium color differences. The OSA-UCS (Uniform Color Space) Committee has shown that no space with uniform scale for large color differences exists. Therefore the practical way for color-difference specification is a color-difference formula in a nonuniform space. First, the BFD (Bradford University) ellipses are considered in the OSA-UCS space, and their very high regularity suggests a new and very simple color-difference formula at constant luminance. Then the COM (combined) data set used for the development of the CIEDE2000 formula is considered in the OSA-UCS space, and the color-difference formula is extended to sample pairs with a different luminance factor. The value of the performance factor PF/3 for the proposed OSA-UCS-based formula shows that the formula performs like the more complex CIEDE2000 formula for small-medium color differences.

Generally, the colour of the non-luminous objects in nature is due to absorption, diffusion and refraction of light. Thecolour of the optical coatings, as that of some kind of bird feathers, soap bubbles, butterfly wings, some insects, etc. isdue to interference and therefore is named interference colour. This kind of colour belongs to the gonio-apparent orspecial-effect colours . Generally, industrial colorimetry does not deal with interference colour and the usual colorimetricinstruments are inadequate to measure it. Only recently, with the new mica-pigme nt coatings, colorime try is consideringthe measurement of the interference colour and new multiangle spectrophotometers are produced.This work is a general introduction to the ground of colo rimetry and, at the end, deals with interference colours.A short overview is given of the Physiological Optics and of the Colorimetric Standards of the “CommissionInternational de l’Eclairage” (CIE): particularly, Psychophysical Colorimetry, Psychometrical Colorimetry andMeasurement Geometries are summarised.The colorimetry of gonio-apparent colours is considered. For a complete and detailed optical characterisation ofinterference colour the measurement of bidirectional transmittance and reflectance is needed. Particularly, basic elementsfor the colorimetric analysis of the interface between isotr opic non-absorbing media and for thin monolayers are given.Keywords: Colorimetry, CIE, interference colour, gonio-apparent colour

Many problems regarding color opponency are still unsolved. In this study the system of the uniform color scales of the Optical Society of America (OSA-UCS) is analyzed with the aim of obtaining answers to very general questions on color opponency. The perceptual color opponencies in the OSA-UCS system, represented by its coordinates (j, g), appear to work in a mutually interacting way. On the hypothesis that such an interaction is due to a linear mixing of a pair of independent opponent mechanisms with scales satisfying a proper Weber fraction, three chromatic opponency functions are derived, whose sum is equal to zero. These functions are the logarithms of the ratios of two tristimulus values in a proper reference frame (called the “main reference frame”) and therefore are antisymmetric and zero-degree homogeneous functions of these tristimulus values. Any pair of these three functions is a set of two independent functions. A new formula for color opponency in the OSA-UCS system is derived in which the perceptual color opponencies (j, g) are written as products of the lightness by a proper linear mixing of any pair of the three chromatic opponency functions. All this is possible because the lattice of the OSA-UCS system is composed of geodesic lines.

Two different transformations between the (X 10 , Y 10 , Z 10 ) coordinates and the (L OSA , g, j) ones of the Uniform Color System of the Optical Society of America (OSA- UCS) are given related to two possible different geometrical structures. Both transformations are logarithmic functions obtained by integration of Weber fractions of ratios of suitable color stimuli. The first structure is related to the color opponency proper of the (g, j) coordinates of the OSA-UCS) system and the second one to a mixing of the (g, j) coordinates. The second transformation has a simpler and highly symmetrical structure, and the regularity of the OSA- UCS lattice is higher.

Recently, chromatic-response function with uniform scales are obtained as logarithms of proper cone activation ratios (CAR hypothesis) and can be considered as Cartesian coordinates for equiluminant-color palettes. Particularly, a properly combined choice of the 'fundamental' primaries, that are at the basis of these functions, and of the RGB primaries of the display give equiluminant-chromatic 'rectangular' palettes, that with the Weberian-lightness define a color space with good scale uniformity and suitable for the color-signal coding. All the transformations are logarithmic. The couple of 'fundamental' primaries laying on the alychne and a third one of pure luminance are considered for trichromatic cameras.

In this paper, two types of weighting tables are derived by applying the local power expansion method proposed by Oleari [Color Res. Appl.25, 176 (2000)CREADU0361-231710.1002/(SICI)1520-6378(200006)25:3 3.0.CO;2-Z]. Both tables at two different levels consider the deconvolution of the spectrophotometric data for monochromator triangular transmittance. The first one, named zero-order weighting table, is similar to weighting table 5 of American Society for Testing and Materials (ASTM) used with the measured spectral reflectance factors (SRFs) corrected by the Stearns and Stearns formula. The second one, named second-order weighting table, is similar to weighting table 6 of ASTM and must be used with the undeconvoluted SRFs. It is hoped that the results of this paper will aid the International Commission on Illumination TC 1-71 on tristimulus integration in focusing on ongoing methods, testing, and recommendations.

The most widely used color-difference formulas are based on color-difference data obtained under D65 illumination or similar and for a 10° visual field; i.e., these formulas hold true for the CIE 1964 observer adapted to D65 illuminant. This work considers the psychometric color-vision model based on the Optical Society of America–Uniform Color Scales (OSA-UCS) system previously published by the first author [J. Opt. Soc. Am. A21, 677 (2004)JOAOD60740-323210.1364/JOSAA.21.000677; Color Res. Appl.30, 31 (2005)CREADU0361-231710.1002/col.20072] with the additional hypothesis that complete illuminant adaptation with perfect color constancy exists in the visual evaluation of color differences. In this way a computational procedure is defined for color conversion between different illuminant adaptations, which is an alternative to the current chromatic adaptation transforms. This color conversion allows the passage between different observers, e.g., CIE 1964 and CIE 1931. An application of this color conversion is here made in the color-difference evaluation for any observer and in any illuminant adaptation: these transformations convert tristimulus values related to any observer and illuminant adaptation to those related to the observer and illuminant adaptation of the definition of the color-difference formulas, i.e., to the CIE 1964 observer adapted to the D65 illuminant, and then the known color-difference formulas can be applied. The adaptations to the illuminants A, C, F11, D50, Planckian and daylight at any color temperature and for CIE 1931 and CIE 1964 observers are considered as examples, and all the corresponding transformations are given for practical use.

A uniform-color-scale diagram for a 10° visual field is derived from the Optical Society of America Uniform Color Scales lattice. The 100 diagram is obtained from the 1964 CIE (x10, y10) chromaticity diagram by the application of two successive transformations: the first is a transformation of appropriate angle variables defined in the CIE (x10, y10) chromaticity diagram and related to two opponent processes; the second is a dilatation that mixes the opponent processes linearly.

Dichromats have angular color discrimination in the usual chromaticity diagrams. Normal trichromatic vision is obtained by combining tritanopic and deuteranopic vision. In this paper, a new pair of angular variables is introduced from which, by a suitable transformation, a uniform-scale chromaticity diagram in zero-curvature space is obtained.