The Rd,a,b scale is an industry specific color scale that was developed as early version of the Hunter L, a, b scale. Rd is used to designate lightness and is the same as the CIE Y Brightness/ Luminosity value. Sometimes the Rd, a, b is expressed as LRd, aRd, bRd. This application note represents the history and calculation of the Hunter Rd, a, b color scale.
History of HunterLab Rd, a, b Color Scale
Color metrics and color science have developed since the early 1900s with two overall themes, to quantify color based on human perception and to represent those color values in a form similar to the words used by humans to communicate color and color differences.
By 1931, the CIE tristimulus values X, Y, Z based on reflectance or transmission spectral data were used to quantify the human perception of color of an object. However X, Y, Z does not correspond well to lightness, saturation and hue typically used by humans to describe color.
Between 1943 and 1967 Richard Hunter made his best attempts to change the CIE X, Y, Z color scale into a form that facilitated better communication while incorporating the human vision concept of opponency. His efforts came in three stages starting with the Rd, a, b scale developed for C/2 conditions in 1943. Rd is identical to Y Brightness/Luminance which corresponds to average reflectance or transmittance of the material. The higher the reflectance or transmittance of an object, the higher the Rd value. The “aRd” and “bRd” values quantify redness-greenness and blueness-yellowness, but are not the same mathematical formula as the current Hunter a and b, or CIE a* and b* color values. The calculations are shown below in Figure 1.
• X, Y, Z are measured CIE tristimulus values for the sample
• Xn, Yn, Z are the CIE White Point tristimulus values in Tables 1 & 2 below for the chosen measurement illuminant/observer combination
• f(Y) = 0.51à (21 + 0.2 à Y) / (1 + 0.21à Y) (see note #1)
• Ka and Kb coefficients are given in the tables
Another key feature of this scale was that it could be automatically computed by analog devices such as the tristimulus colorimeters of the time.
The Limestone Application
The Rd value of this scale used most often as a single-value overall brightness or reflectance for loose, neutral-color limestone-based powders. The Y-value is equivalent to the Rd but some industries become familiar with particular metrics and retain them to report the color quality of their products. In addition, bRd is sometimes used as a companion metric with Rd to quantify yellowness associated with trace metal contamination of limestone based powders.
In general, a limestone powder of the best color quality is associated with a higher Rd value and bRd value close to 0.
Limestone is typically prepared for analysis by pressing into a plaque as shown in Figure 2.
Further History The Hunter L, a, b color scale for C/2 illuminant/observer conditions was developed in 1958 and found popular acceptance which continues to this day.
In 1967 the Hunter L, a, b color scale was adapted to additional illuminant and observer combinations through the use of Ka and Kb coefficients. In 1976, the Hunter L, a, b color space was further mathematically optimized by the CIE to become the rectangular CIE L*, a*, b* color scale - lightness, redness-greenness and blueness-yellowness, and its polar equivalent, CIE L*, C*, h color scale - lightness, saturation and hue.
Today most of the color scale development has been done in terms of color differences, with a particular focus on elliptical scales. Elliptical differences correlate well to visual perception meaning that one unit of difference in an elliptical scale equals a visual unit of color change.
While still in use by the limestone industry, the Hunter Rd, a, b color scale has been supplanted over time by the Hunter L, a, b and CIE L*, a*, b* color scales.
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