# Colorimetry/Chapter 5

There are many tests analogous to the comparison of a solution of an unknown amount of a constituent with a series of suitably prepared standard solutions to find the concentration of the specimen. In these tests the colors of the unknowns exhibit a one-dimensional change with concentration; and, although this change may be complicated in terms of luminous transmittance and chromaticity coordinates [102], a suitably spaced series of standards over this range of colors will yield the desired concentration either by actual match with one of the standards, or by visual interpolation among them, Such a series of standards is said to constitute a color scale. The ideal material from which to make the standards is the constituent of the unknown itself; in this way there is guaranteed not only a perfect color match at some point along the scaled but also a perfectly nonmetameric match so that variation of the illuminant or individual-observer variations are generally unimportant.
However, if the unknown is impermanent, it may become necessary to try to duplicate the desired ​colors in a more nearly permanent medium. Glass is a frequent choice because of its generally supeprior permanence. Some degree of metamerism has then to be tolerated because the standards have I coloring constituents not a perfect spectral match for the unknown. It is also rare that a perfect job of color matching for any standard illuminant and observer is done. The observer is then faced with what is often a difficult, and sometimes an impossible, task. He must estimate the position of the unknown color on the scale, and often it will seem to him that the unknown color is not equal to any of the standard colors, nor intermediate between any two of them. The concepts in terms of which the observer perceives these color differences then come into play. If he judges the color difference between the two luminous areas presented to him in terms of hue, brightness, and saturation, as is fairly common, he could estimate the position of the unknown color on the color scale as the point on the scale yielding the same hue, or as that yielding the same brightness or the same saturation; or he could try to estimate the point on the scale yielding the closest color match; or he could disregard brightness differences and try to estimate the point on the scale yielding the closest chromaticity match. The determination becomes an estimate based on what criterion of equivalence is used by the observer, and it depends upon his mental capability in an essentially indescribable way. In spite of these drawbacks, a good color scale is a useful time-saver, as long as it is not used in attempts to provide a one-dimensional solution to what is essentially a multidimensional problem.
Judgments of position on the color scale according to equality of brightness can be expected to correspond to luminous transmittance. Judgments according to equality of hue agree well with the Munsell renotation hue; loci of constant hue for ordinary conditions of observation are indicated on the (x,y) diagram by the curved lines of figure 3 separating the areas corresponding to the various hue luimes. Judgments according to equality of saturation agree well with Munsell renotation chroma (see fig. 22). If there is only secondary brightness variation along the scale, judgments of nearest chromaticity match may be found approximately by taking the shortest distance on a uniform-chromaticity-scale diagram [14, 23, 55, 66, 141, 142]. Figure 8 shows the uniform-chromaticity-scale triangle according to Judd [66]. If the chromaticity coordinates of a color are (x,y) in the standard CIE system, the color would have chromaticity coordinates (r,g) in this uniform-chromaticity-scale triangle in accord with eq (5). On this diagram the ellipses of figure 7 would be equal 3 tangent circles. If there is primary variation of J both luminance and chromaticity, no reliable way of estimating the nearest color match has yet been developed. According to the OSA Colorimetry Committee [24] , "The complete experimental clarification of this problem is one of the major programs yet to be undertaken in the field of colorimetric research."
Perhaps the most widely used one-dimensional color scale is that of color temperature for classifying light sources. The color temperature of a light source is the temperature at which the walls of a furnace must be maintained so that light from a small hole in it will yield the chromaticity of the source to be specified. The color scale thus consists of the series of lights producible by closed-cavity radiation and is specified by temperature on the absolute scale (degrees Kelvin). Working standards of color temperature may consist of an incandescent lamp operating at a fixed voltage combined with a series of amber or blue glasses, like the Lovibond blue glasses; but by far the most common way of producing these chromaticities over moderate ranges of color temperature is by variation of the voltage applied to an incandescent lamp. The locus of these chromaticities (the so-called Planckian locus) is shown on figures 7 and 8. If the chromaticity of the light source is close to, but not exactly equal to, any of the Planckian chromaticities, still it is possible to correlate a color temperature with the source by taking the nearest chromaticity match. Figure 25 shows this correlation [67, 81]. The isotemperature lines, which cut the Planckian locus at varying angles, are all such as to be perpendicular to this curve on figure 26. The x,y and u,v chromaticity coordinates of a number of Planckian radiators ($c_{2}$ = 14,380) and standard sources in the 2° and 10° observer systems have been computed by Nimeroff [123]. These are listed in table 12. Since color temperature specifies only the chromaticity of a light, there are many spectral compositions corresponding to the same color temperature. Color temperature of a source is therefore an incomplete and unreliable indication of the rendering of the colors of objects illuminated by it or of the photographic effect of the source. To make color temperature a meaningful and useful basis for comparing two lights it must also be known that they are spectrally similar. Thus, incandescent lamps may be usefully intercompared by means of color temperature, and fluorescent lamps with about the same admixture of mercury spectrum may also be so intercompared, but incandescent lamps may not be intercompared with fluorescent.
When the degree of refinement and quality of such products as oils, rosin, and sugars may be characterized on similar one-dimensional color scales which range from dark red through yellow to perfectly colorless, the development of a complex color specification for these products is redundant. These perceived color changes correlate ​Fig. 27.Chromaticities of some standards for grading petroleum products (solid circles), rosin (crosses), and honey (squares).The solid curve is generated by an ideal absorption-band sweeping across the spectrum from the short-wave to the long-wave band [40]. The standards have broad absorption bands of different sharpness. with a shift in the wide absorption band toward the ultraviolet as brown pigments are removed on refining. The differences in scales among these products correspond to differences in sharpness of the absorption band, with oils possessing the sharpest bands, rosins next, and sugars least sharp. Figure 27 compares, on the 1960 CIE-UCS [80] chromaticity diagram, the chromaticity locus generated by varying an ideal absorption band (40) with a few color standards used for petroleum solid dots), rosin (crosses), and sugar (squares) products.
It is sometimes convenient to state the color of a product in terms of its equivalent on another scale and modified by an adjective that describes the off-locus position. Thus U. S. Rosin Standard X (extra water white), which is equivalent to ASTM petroleum color 1.4 but slightly on the purple side, will be designated 1.4p. The letter g will be used to designate departures toward green.
For more than 30 years the color of lubricating oils and petrolatum has been graded by comparison with the colors of 12 glass standards [7]. The petroleum product in a 33-mm layer and the standard are illuminated by artificial daylight produced by combining an incandescent lamp of color temperature approximately 2750 °K with a filter of Corning Daylite glass specially selected to have spectral transmittances within specified tolerances and further to have for standard source A luminous transmittance, $\phi _{v}$, and chromaticity coordinates, within the limits:
| $\tau _{v}$ | 0.107 to 0.160 |
| $x$ | .314 to  .330 |
| $y$ | .337 to  .341 |
| $z$ | .349 to  .329 |
The specimen holder, the magazine containing the glass color standards, the artificial daylight assembly, and a viewing diaphragm defining the direction of view are mounted together to form a portable instrument known as the Union colorimeter.
Table 13 gives the Lovibond analysis of the glass color standards (6), the luminous transmittance, $\tau _{v}$, and chromaticity cordinates, for source C [141], the color names used by the International Petroleum Association, and the nearest chromaticity match on the new ASTM color scale, which was adopted in 1957. This new scale consists of a set of glasses which define a scale that is closer to the range of petroleum colors and with improved step uniformity [48,72].
Table 14 gives for these glasses the luminous transmittances and chromaticity coordinates for source C in the defining UCS (r,g -system as well as in the standard CIE (x,y) -system. Also listed re the luminous transmittance tolerances for the glass standards and their equivalents on three other scales.
The grading of naphthas, kerosines, and so on, has for many years been carried out by comparison of the color of rather thick layers (up to 20 in) of the refined oil with the colors of a set of three color standards made of yellowish glass. The Saybolt ​
chromometer is a device for carrying out this comparison. It consists of an artificial daylight lamp meeting the same requirements as given above for the ASTM Union colorimeter, a graduated tube for the oil specimen, a holder for the glass color standards, and a prism eyepiece to bring into juxtaposition the two fields to be compared. There is an open ungraduated tube beneath the holder for the glass standards that serves to duplicate to a degree on the standard side of the instrument the effect of light multiply reflected within the specimen tube. The glass standards consist of two whole disks and one "one-half" disk; these standards must have luminous transmittances, $\sigma _{v}$, and chromaticity coordinates, $x,y$, for source C, as follows:
Oils having colors closely resembling that of distilled water are graded on the Saybolt chromometer by comparison with the half disk; more yellowish oils by one or two whole disks. The depth of oil yielding the closest color match with the glass disk is found by a prescribed procedure [5], ​and the color of the oil specimen is designated by a number defined from the disc used and the required depth of oil. Table 15 gives this definition [5] in terms of Saybolt number, Union color, u, land ASTM color, a.
In spite of the fact that the prism eyepiece brings the fields to be compared into juxtaposition and so facilitates the detection of differences in brightness, the change in luminous transmittance with thickness of these refined oils is so slight that it is much less easily detected than the corresponding chromaticity change. The settings of the Saybolt chromometer therefore probably depend essentially on nearest chromaticity match. If the oil sample is turbid, however, not even an approximate match can be obtained, and the method may be inapplicable. In these cases a thickness of the specimen yielding a chromaticity match is much darker than the standard, and no reliable setting of depth of sample yielding nearest match can be found.
Figure 28 shows a portion of the (x,y) chromatcity diagram on which have been plotted the rectangles corresponding to the chromaticity tolerances for Saybolt half disks and whole disks (see above). It will be noted that the tolerances are fairly wide so that variations of ±10 percent of the chromaticity change caused by introduction of the disk into the daylight beam are permissible. The relation between the Union color numbers, u, and the Saybolt color expressed in terms of number of whole disks, n, and depth, D, in inches,
$u={\frac {1.182n}{D}}$
may be derived by reference to figure 28. Two vectors, each corresponding to 300 wedge units define the steps from source C to Saybolt ½ disk to Saybolt whole disk, or 600 wedge units in all. The chromaticity point representing Union Color No. 1 does not fall exactly on the extended line. The intersection of the dotted line and the extended line gives the closest chromaticity match, and shows that the chromaticity of Union Color No. 1 approximates 1.10 Saybolt disk. An oil of Union Color No. 1 will therefore match 1.00 Saybolt disk in a thickness of 33.0/1.10 or 30.0 mm (1.182 in) and will match two whole disks in a thickness of 60.0mm (2.365 in).
The corresponding relation for ASTM color number, a, is
$a=0.607n/D$
based on the facts that the glass that defines ASTM color number 0.5 is closely equivalent to 1.03 Saybolt disk (as shown on fig. 28) and that thickness on the ASTM scale has been changed to 1.25 in from 33.0 mm [7].
In addition to the brown pigments found in petroleum products, edible vegetable oils (corn, cottonseed, olive, peanut, rapeseed, sesame, soy-bean) usually contain some chlorophyll. Although metamerism exists between the oils and Lovibond glasses [100], the oils are graded, for commercial purposes, by the number (N) of Lovibond red units, added to Lovibond 35-yellow, that are required to match a 5.25-in layer of the oil. Table 16 shows for values of N from 0 to 100 on the $35Y+NR$ scale the CIE source C chromaticity coordinates, $x,y$, and the nearest chromaticity match on the ASTM scale and on the Gardner scale (the Gardner scale is described in the next section).
Thomson [50] showed that spectral transmittance of oil at wavelengths 460, 550, 620, and 670 nm $r_{460}$, $r_{550}$, $r_{620}$, and $r_{670}$) can be expressed in an index that gives excellent correlation with color grading by the Lovibond red units. This index,
${\begin{aligned}1.29\log(1/r_{460})&+69.7\log(1/r_{550})\\+41.2\log(1/r_{620})&-56.4\log(1/r_{670})\\\end{aligned}}$
has been found useful for commercial grading of vegetable oils.
Gum rosin has been graded by color for more than 50 years. Up to 1914 the color standards were made of rosin itself in spite of the relative impermanence of its color, and from 1914 to 1936 standards composed of combinations of Lovibond glasses were used. Brice [15] has described the selection of the present twelve official standards composed of two components of colored glass combined with one component of clear glass, all three cemented together with Canada balsam. The various combinations are given letter designations denoting the grades of rosin delimited by them and have legal status under the Naval Stores Act. The cemented face of the clear glass in each combination is fine ground so as to duplicate the slight turbidity characteristic of molded samples of rosin, which commonly contain traces of fine dirt. The chromaticity spacing was adjusted by means of the uniform-chromaticity-scale triangle of figure 8 so as to progress regularly from small steps for yellow rosins to steps of about four times the initial size for reddish orange rosins. Osborn and Kenyon have studied rosin colors spectrophotometrically [124]. Table 17 gives the names associated with letter designations, luminous transmittance, $T$, and chromaticity coordinates, $x,y$, for CIE source C, together with the nearest chromaticity match on the ASTM, $35Y+NR$, and Gardner color scales.
Many special color scales have been set up for the specification of paint vehicles (varnishes, linseed oil, tung oil, etc.). A solution of nickel sulfate and iodine [16] is used to define the darkest color permissible for spar varnish. A color comparator having eighteen glass color standards made by Hellige, Inc., has been used for similar purposes. The Pfund color grader compares a variable thickness of the unknown specimen with a variable thickness of an amber colored glass [131]. The standard is wedge shaped, and the cell for the specimen is likewise wedge shaped. The Parlin (or Cargille) color standards consist of a set of thirty-five solutions. The first ten are Hazen platinum-cobalt solutions, [52], developed originally to measure the color of natural water and still used for that purpose under the name of APHA (American Public Health Association) standards [4]. The remainder of the Parlin color standards are caramel solutions. They have been adopted by the ASTM (Designation D365–39) for testing the color of soluble nitro-cellulose base solutions. The Pratt and Lambert color standards are varnish mixtures calibrated against the Pfund color grader. The Du Pont, colorimeter employs six plates as color standards, together with a wedge of the same glass permitting a continuous variation of color between the standards. The Gardner color standards consist of eighteen combinations of the red and yellow Arny solutions. Gardner has determined the Arny and ​Lovibond specification for the nearest matches for all the above-mentioned sets of color standards and has also obtained the nearest equivalents in terms of potassium dichromate solutions [31]. From these nearest equivalents it is possible to express color specifications given by any of these means in terms of any other of them, as shown in Table 18 which gives the chromaticity coordinates, x,y, of each of the eighteen Gardner standards for CIE source C, nearest chromaticity match on the Lovibond 35Y + NR scale, the ASTM scale and the Union color scale, together with the nearest lightness match on the Union scale. The Gardner standards define a locus of chromaticities that agrees closely with that of the ASTM standards with only 6 of the 18 standards departing by more than 0.001 as indicated by the letters "p" and "g".
The British Paint Research Station has recommended [151] combinations of Lovibond glasses for color-grading oils and varnishes. Some of the combinations involve colorless or blue glasses to be combined with the oil to match red and yellow glasses, and a device facilitating the setting up of such combinations is also recommended. The Lovibond glasses are mounted in a slide, and the two photometric fields to be compared are brought into juxtaposition by mirrors.
For regulatory purposes, the classification of sugar products (honey, maple syrup, molasses, sugarcane) is conducted visually by comparison with glass chromaticity standards. The source C chromaticity coordinates, x,y, are listed in table 19 ​for the glasses developed by Brice [15] and adopted by the U. S. Department of Agriculture for this purpose. The nearest chromaticity matches on three one-dimensional color scales (ASTM, 35Y+NR, and Gardner) are also given for each standard.
Increasing use is being made of one-dimensional photometric methods [86, 37, 162, 16,3] for more precise designation of sugar colors. Deitz [26] has developed a one-dimensional specification that is defined as the color difference between the solvent and the sugar solution. The color difference is evaluated in Adams chromatic-value space [2] and is expressed in terms of a so-called NBS unit of sugar color. Measurements of the attenuancy at two wavelengths (420 nm and 560 nm) are used in this evaluation to a good approximation. Brice [16] developed a similar one-dimensional specification that is based on chromaticity differences expressed in MacAdam units [19].
* ↑ Tolerances on chromaticity coordinates, r,g,h (b = 1-r-g), are ±0.006.
* ↑ Same as Sugarcane Sirup No. 1.
* ↑ Same as Sugarcane Sirup No. 2.
* ↑ Same as Sugarcane Sirup No. 3.