Predicting the spectral reflectance factor of translucent paints using Kubelka‐Munk turbid media theory: Review and evaluation

The use of Kubelka‐Munk (K‐M) turbid media theory in predicting the spectral reflectance factor of an opaque specimen from the specimen's constituent optical constants is well established in practice and well described in the literature. For translucent samples, there is a paucity of published results and the approaches are disparate. Accordingly, a review of K‐M theory and its application for predicting the spectral reflectance factor of translucent samples is presented and tested. Four methods for determining the absorption and scattering coefficients with respect to a certain film thickness are described: the black‐white method, the infinite method, the masstone‐tint method, and the two‐region method. The black‐white and infinite methods use the general form of the K‐M equation. The masstone‐tint method can be used for both the general form and the opaque simplification. The two‐region method, combining opaque and translucent approaches, was enhanced in this research and included an opacity calculation to automatically differentiate opaque and translucent spectral regions and a smoothing technique to combine both spectral regions. The two‐region method was tested using a set of acrylic‐emulsion artist paints and glazes spanning a range of opacities from opaque to nearly transparent. The results were reasonable and provided statistically significant improvement compared with the opaque simplification, commonly used in art conservation science and industrial color matching. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 417–431, 2009     

Digital color reconstructions of cultural heritage using color‐managed imaging and small‐aperture spectrophotometry

There are many examples of cultural heritage having optical properties that have changed with the passage of time. Examples include the yellowing, darkening, and fading of paints and varnishes caused by light exposure and atmospheric pollution. When it is infeasible to treat an object, an image simulation can provide a view to the past, known as a color reconstruction. A technique is described that relies on a color‐managed image, spectral reflectance factor measurements of the object, an optical model of colorant mixing, an optical database of artist materials, spreadsheet software, and image editing software. Spectral calculations are used to create adjustment curves where segmented portions of an object's image are translated in color. This approach has been used to produce color reconstructions of paintings by Vincent van Gogh and Georges Seurat. This colorimetric translation methodology is described and an example shown for the Chicago version of Vincent van Gogh's Bedroom. The methodology is compared with pixel‐based processing.     

About the theoretical aspect of multiple light scattering: Silvy's theory

The general problem of light scattering in turbid media has been studied often. Compared to the exact solution for plane‐parallel diffusers, the Kubelka and Munk solution appears as an approximation. The photon diffusion model is also an approximate solution restricted to the case of low light absorption, for which the prior work of Silvy has been ignored. It gives interesting relations between Kubelka‐Munk conventional parameters and the more intrinsic quantities related to the properties of the media introduced by the photon model. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 227–228, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10149     

电脑测配色系统在实色涂料中的应用

简要介绍电脑测配色系统中的硬件和软件系统中的概念,详细阐述了应用于atacolor电脑测配色系统建立配色数据库的过程,及影响电脑测配色系统在实色涂料中颜色精度的因素。     

Optimization of quinacridone magenta,Cu-phthalocyanine cyan,and arylide yellow ink films formulated for maximum color gamut

Investigation of ink formulation options with the purpose to obtain color-gamut-optimal set of Cyan Magenta and Yellow CMY inks is reported. Implementation of the thickness dependent Kubelka-Munk model on multiple ink layers having different and well-defined thicknesses, provides characteristic absorption and scattering (K, S ) spectra of the ink ingredients. These data enable accurate computation of the reflectance spectrum and thus the L*a*b* color coordinates for any given ink thickness or substrate. Pigment materials investigated are quinacridone as magenta, copper-phthalocyanine as cyan, and arylide yellow. Scaling the peak of the absorption band to the number of molecules per unit area for the specific pigments studied in this article provides the molar extinction coefficients, 1.21 × 10⁴ , 4.7 × 10⁴ , and 3.3 × 10⁴ cm²/millimole respectively, regardless of the different ink formulations used, in accord with Avogadro's principle. Having a set of three pairs of K, S spectra is used to compute the color gamut of any CMY color combination in the L*a*b* space as a function of ink layer thickness and formulation. Using an iterative algorithm, a color-gamut-optimal set of CMY inks is obtained.     

建筑涂料领域中影响电脑配色准确性的因素

电脑配色在涂料行业是一门新兴技术,颜色配方的准确性一直是配色师关注的问题。从色浆数据库的建立、基漆数据库的建立、颜色配方的设计、色浆与基漆的匹配、色浆/基漆批次稳定性等方面来阐述影响电脑配色精度的因素。     

Impact of matching field size on color matching (functions) accuracy

Accurate colorimetry starts with accurate color matching functions (CMFs). Due to changes in the macular pigment and cone pigment optical densities at different retinal locations, different CMFs are required for different stimulus field sizes. To characterize the accuracy of the CIE recommendation for the use of 2° and 10° standard CMFs and the field-size dependent CIEPO06 model, in this study, a series of achromatic matching experiments were performed with 2°, 4°, 6°, 8°, and 10° bipartite fields using spectrally narrowband primaries. Using the CIEPO06 model, optimal field sizes were estimated that minimize the chromaticity differences between the spectrally narrowband observer matches and the spectrally broadband achromatic target. It was found that the optimal field size estimated using the CIEPO06 model is close to half the actual bipartite field size in most cases, except for the 2° field. The discrepancy between the 10° bipartite field in Stiles & Burch's experiments and our optimal field size (6.54°) was assumed to be due to different individual color comparison strategies. However, the results of experiments requiring specific observer gaze positions did not support this assumption and the reason for the discrepancy remains unclear. Confirming our earlier results, the primary set (636, 521, 447 nm) was again found to be largely insensitive to changes in CMFs and to provide the most accurate matches under various fields of view. The inter- and intra-observer variability ellipses for 2° matches are larger than those for 10°, consistent with Brown's finding for color discrimination ellipses. The magnitude of the intraobserver variability was similar for all field sizes, except for 2° field size, where matching errors were larger for some primary sets.     

Theoretical considerations on small color differences ascribed to the standard observer made on the basis of individual color‐matching functions

An analytical method to determine how color‐matching functions influence the perception of chromaticity differences is proposed. We show that, as a consequence of the observer metamerism, a metameric color‐match perceived by one observer may appear to be a significant mismatch to a different observer. It is also shown that, on average, the differences between the color‐matchings made by two different observers can be estimated to be in the order of 2 CIELAB units. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 194–200, 2009     

The total colorant sensitivity of a color matching recipe: An approach to colorant weighting and tinctorial strength errors

The repeatability of the recipe color can be affected by several different types of inevitable inaccuracies in the coloration process. Two of the major causes of poor target‐color reproducibility are the (random) weighing and (proportional) strength errors. This article describes alternative definitions of colorant strength sensitivity and total colorant sensitivity of a dyeing recipe. The influences of the maximal colorant weighing and strength errors are taken into account in order to bring the magnitudes of the two treated types of sensitivity into a mutually realistic balance between each other. The quantifications of precision and accuracy of a color matching recipe are also developed and combined into a single‐number measure of recipe quality. The listed quantities are expected to be useful in selecting the most reliable one(s) among the different formulations for the same standard color. The methods are presented for calculating numerical estimates of the newly introduced quantities. The precision and accuracy of the coloration process are investigated in laboratory experiments involving repeated dyeings. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 300–306, 2008.     

Grassmann's laws and individual color‐matching functions for non‐spectral primaries evaluated by maximum saturation technique in foveal vision

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.     

Application of the nondestructive second derivative spectrophotometry to eliminate the effect of substrate in identification of madder used in Persian carpets

The handmade Persian carpet is famous worldwide not only for its elegant design and artistic structure, but also for its brilliant color harmony and incomparable raw materials. Various natural dyes accompanied by different mordants are used on various woolen yarns to obtain a wide range of unrepeatable shades for carpet. In this article, as a first step, the diversity of the undyed woolen yarns used in Persian carpets was statistically investigated by implementation of the Principle Component Analysis. Then the second derivative of Kubelka‐Munk function of samples dyed with madder was considered to reach a pattern for identifying madder. The results show that, although the spectral reflectance of different selected woolen yarns has at least 3 dimensions, all derivative curves are qualitatively very similar with the same minimum and maximum peaks at 510 and 605 nm, respectively. The findings are confirmed when various types of madder were used in the dyeing process. As a result, it is shown that the nondestructive derivative spectrophotometry is able to identify madder on alum mordanted woolen yarns used in Persian carpets and to eliminate the effect of substrate. It is a useful technique for preservation, conservation, and dissemination of the Persian carpet.     

Single‐constant simplification of Kubelka‐Munk turbid‐media theory for paint systems—A review

For opaque coloration systems, Kubelka‐Munk turbid media theory is used commonly to model optical mixing behavior. Most educational publications on the subject use opaque paint systems when describing the two‐constant approach and textile systems when describing the single‐constant simplification. Because of the differences in defining concentration for these systems and the corresponding degrees of freedom, the single‐constant simplification for paint and textile systems are not identical. The second edition of “Principles of Color Technology” showed a numerical example for an opaque paint system modeled using the textile equations. The third edition used the same example but modified the degrees of freedom, a hybrid of the paint and textile approaches. Recent research by Berns and Mohammadi has evaluated the single‐constant simplification for modeling artist paints; they have used both the hybrid and paint approaches. Thus, it was of interest to review these different approaches and determine whether these differences have practical importance and whether future printings and editions of Principles of Color Technology should be modified. The three approaches were tested for tints made from a mixture of cobalt blue and titanium white acrylic emulsion artist paints. The differences between the textile and hybrid approaches were inconsequential. The paint approach was superior and its use is recommended for opaque paint systems. The differences in the numerical example from Principles of Color Technology were very small. For future printings of the third edition, the example will remain unchanged. For future editions, including the numerical example remains an open question. © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 201–207, 2007     

Optical implementation of spectral filtering for the enhancement of skin color discrimination

Light reflected from an object contains a range of information about its physical and chemical properties. Changes in the physical properties of an object can sometimes be evident as barely detectable changes of color. Our earlier study (Proceedings of the 15th Color Imaging Conference, Albuquerque, New Mexico, 2007. p 195–200) proposed a method for designing a spectral filter to enhance visual discrimination. Two filters were designed: one to discriminate skin and vein colors on human arms, and other to discriminate human facial colors in the presence and absence of cosmetics. In this study, the filters with theoretically designed spectral transmittances were implemented as real optical filters. Visual inspection of RGB color images taken with a digital camera through the developed optical filters showed clear enhancement of discrimination of two preselected colors. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2012     

Mathematical determination of the numerical data corresponding to the color‐matching functions of three real observers using the RGB CIE‐1931 primary system and a new system of unreal primaries X′Y′Z′

In this work, we determine the numerical data of the experimental color‐matching functions (cmf's) of three real observers (JAM, MM, and CF) for two small fields (2°). In previous works, these cmf's have been shown generically and expressed only in a new system of unreal X′Y′Z′ primaries. Here, we show results found with these cmf's for the visible spectrum in intervals of 10 nm, from 400 to 700 nm. The data refer to both the RGB CIE‐1931 system and a new system of unreal primaries X′Y′Z′, established by a procedure similar to that of the XYZ CIE‐1931 system. This transformation was needed, because negative values appeared in various cmf's when they were referred to the XYZ CIE‐1931 system. Recently, we have called this new system G94 (Granada ‘94). Here, we also describe the method and calculation of the matrix that enables this transformation; in testing six real observers with new cmf’s, we found positive results. We have used these new and experimental cmf's in several preceding works, as have other authors as well, to whom J. A. Martínez privately communicated the corresponding numerical data. The use of these cmf's by all the authors has led to noteworthy results. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 89–95, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10127     

Color mixing and color separation of pigments with concentration prediction

In this study, we propose a color mixing and color separation method for opaque surface made of the pigments dispersed in filling materials. The method is based on Kubelka–Munk model. Eleven different pigments with seven different concentrations have been used as training sets. The amount of concentration of each pigment in the mixture is estimated from the training sets by using the least‐square pseudo‐inverse calculation. The result depends on the number and type of pigments selected for calculation. At most we can select all pigments. The combinations resulted with negative concentrations or unusual high concentrations are discarded from the list of candidate combination. The optimal pigment's set and its concentrations are estimated by minimizing the reflectance difference of given reflectance and predicted reflectance. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 461–469, 2008     

Geodesic calculation of color difference formulas and comparison with the munsell color order system

Riemannian metric tensors of color difference formulas are derived from the line elements in a color space. The shortest curve between two points in a color space can be calculated from the metric tensors. This shortest curve is called a geodesic. In this article, the authors present computed geodesic curves and corresponding contours of the CIELAB ( ), the CIELUV ( ), the OSA‐UCS (ΔE_E) and an infinitesimal approximation of the CIEDE2000 (ΔE₀₀) color difference metrics in the CIELAB color space. At a fixed value of lightness L*, geodesic curves originating from the achromatic point and their corresponding contours of the above four formulas in the CIELAB color space can be described as hue geodesics and chroma contours. The Munsell chromas and hue circles at the Munsell values 3, 5, and 7 are compared with computed hue geodesics and chroma contours of these formulas at three different fixed lightness values. It is found that the Munsell chromas and hue circles do not the match the computed hue geodesics and chroma contours of above mentioned formulas at different Munsell values. The results also show that the distribution of color stimuli predicted by the infinitesimal approximation of CIEDE2000 (ΔE₀₀) and the OSA‐UCS (ΔE_E) in the CIELAB color space are in general not better than the conventional CIELAB (ΔE) and CIELUV (ΔE) formulas. © 2012 Wiley Periodicals, Inc. Col Res Appl, 38, 259–266, 2013     

The effect of gloss on color

A model was developed for the effect of gloss on reflected color, taking the measurement geometry of the color measuring device into account. It considers the total front surface reflectance of a given sample to be independent of gloss and determined only by its refractive index and the angle of the incident beam. Although the total front surface reflectance is fixed, its specular component increases (and the diffuse component decreases) with increasing sample gloss. Therefore, the diffuse reflectance factor measured by a spectrophotometer decreases with sample gloss. In this article, a defined curve was fitted to the measured reflectance factor of black xerographic print samples having a range of gloss values for the 0/45 and diffuse spectrophotometer geometries, and this curve was used to predict the CIELAB color values for samples of the other colors at various gloss levels. The predicted color was compared to the measured color for cyan, magenta, yellow, red, green, and blue images that spanned a wide range of gloss. The RMS color error between the predicted and measured color of all of these images was found to be about 3 CIELAB ΔE* units. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 369–376, 1999     

Theoretical analysis of subtractive color mixture characteristics IV—Theorems on ideal color and tristimulus dimension

Giving a continuation to our work to understand the characteristics of the tristimulus values in colors obtained by subtractive color mixture, we extend several theorems provided in our previous articles. Previously, we started proving theorems for a single dimension, considering only individual tristimulus values. In the present article, the one‐dimensional discussion is extended to the three‐dimensional discussions of the tristimulus space. These theorems establish the absolute lower and upper bounds for tristimulus values of subtractive color mixtures of the ideal color. The results contribute toward a comprehensive modeling of subtractive color mixture. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 427–437, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.     

Effect of luminance of samples on color discrimination ellipses: Analysis and prediction of data

Four data sets are analyzed to quantify three effects of luminance of samples on chromaticity discrimination: on ellipse area, axis dimensions (a and b), and a/b ratio. Ellipses for aperture, surface, and simulated surface colors in CIE 1931 and 1964 x, y, Y color spaces are shown to reduce axis dimensions with higher luminance by different functions for the major and minor axes. Reduction is greater for major than minor axes, thus improving ellipse circularity. The functions plot straight lines in log‐log scale as power law equations, except luminances below 3 cd/m². We give formulae to predict a and b axes, a/b ratio, and ellipse area for almost any luminance in x, y, Y spaces. Effect of luminance is remarkable on ellipse area, which on average halves with every 3.5 times higher luminance. To illustrate the substantial effects of luminance, RIT‐DuPont ellipses are predicted for three levels of equal luminance at 42, 212, and 2120 cd/m². In the latter, ellipses are much smaller and are nearer circular than in the former. Higher luminance is known to improve color discrimination, so reduced ellipse area is to be expected but does not occur in CIELAB and DIN99 spaces because of lack of luminance‐level dependency. We discuss our results' implications on uniform color space. Weber fraction ΔY/Y indicates brightness discrimination decreases with increasing luminance and is thus independent of chromaticity discrimination. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 186–197, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20107     

颜填料体积浓度的用量对涂料保色性的研究

阐述了配色原理,分析了不同PVC用量对涂膜的附着力、硬度、耐水、耐酸等性能的影响,得到PVC的用量在48%时,涂料的各种性能达到最佳,同时还给出了用来配深、中、浅各种颜色的白色涂料PVC的范围及相应的色浆用量,采用控制颜填料体积浓度的用量,解决了涂料保色性的问题;通过扫描电镜分析、粒度分析对比,观察了涂料的外貌和平均粒径,结果表明,在PVC为48%时,涂料的分散效果及稳定性均好。