Page:Colorimetry104nime.djvu/22

ters Fig. 5.Points representing the colors of four printing ink specimens whose spectral reflectances are shown in figure 9.4.The colors of the ideal closed-cavity radiator are also shown, the temperatures of the radiators being indicated in degrees Kelvin. The smooth curve connecting these points is often called the Planckian locus. have been built and described by Allen [3], Donaldson [28], Guild [43], McAdam [96], Newhall [110], Stiles [145], Verbeek [154], and Wright [157]. The Wright instrument has spectrum primaries; the other four have primaries formed by combining a light source with glass filters. To the Guild and Wright instruments we owe our accurate information regarding the properties of the normal visual system which have been expressed in terms of the standard observer.

The foregoing instruments make up the comparison-field mixture by optical combination of light beams from different sources so that a sum of the separate effects is obtained. A similar optical effect is obtained if the beams are caused to fall upon the same portion of the retina in such rapid succession that a nonflickering spot of color is seen. The effect is that of a time-weighted average of the separate beams. A very simple and widely used tristimulus colorimeter is obtained by taking four disks that have been cut along a radius, interlocking them so as to expose a sector of each, and causing them to rotate on the spindle of a motor so rapidly that neither the separate sectors nor even flicker is perceived. Such an arrangement for combining colors by rotary mixture is called a Maxwell disk. The four disks provide the necessary three degrees of freedom in the adjustment for a match, and if the tristimulus values of the component disks be known ($X_{1},Y_{1},Z_{1};X_{2},Y_{2},Z_{2};X_{3},Y_{3},Z_{3};X_{4},Y_{4},Z_{4})$, the tristimulus values of the mixture can be computed from the fractions of the total area occupied by the respective sectors, $f_{1},f_{2},f_{3},f_{4}$:

${\begin{alignedat}{7}X&=f_{1}X_{1}&+&f_{2}X_{2}&+&f_{3}X_{3}&+&f_{4}X_{4}\\Y&=f_{1}Y_{1}&+&f_{2}Y_{2}&+&f_{3}Y_{3}&+&f_{4}Y_{4}\\Z&=f_{1}Z_{1}&+&f_{2}Z_{2}&+&f_{3}Z_{3}&+&f_{4}Z_{4}.\end{alignedat}}$

(4)

If the disks are chosen anew for each kind of unknown color to be measured so as to be all fairly similar in color to the unknown, the spectral composition of the mixture color is usually sufficiently nonmetameric that no restriction to the central 2 deg of the retina is required. Furthermore any two normal observers with some experience at making the adjustment can check each other closely. The chief drawback of this simple arrangement for product-control work in color is the time lost in adjustment of the sector disk areas. The motor must be turned off, brought to a stop, the disks loosened and readjusted, the motor turned on and allowed to resume speed several times to obtain a final setting of reasonably good, precision.

Nickerson has described a disk colorimeter [105] that avoids the difficulties of the elementary Maxwell disk. Light reflected from the unknown specimen fills one-half of a photometric field, and that from a stationary sector disk fills the other. By having the observer look at the sector disk through a rapidly rotating glass wedge, each sector is presented to view in sufficiently quick succession that no flicker is produced; and at the same time the sectors, since they are stationary, may be continuously adjusted until a color match is obtained. A further advantage is obtained by extending the rotary scanning to the unknown specimen. In this way the average color of a notably nonuniform specimen such as that made up of coarse salt crystals may be obtained. The disk, colorimeter has been extensively used by the United States Department of Agriculture for the color-grading of food products and is well adapted to product-control colorimetry of many kinds.

2.6. Dominant Wavelength and Purity

Another way to identify a combination of lights to specify a color, alternate to the tristimulus method, is to determine the luminance (photometric brightness) of one spot of light of fixed spectral composition (such as average daylight) and the luminance of a spot of light of continuously variable spectral composition separately identified (as by wavelength in the spectrum). In this way the requisite three degrees of freedom in adjustment to a color match are supplied. This form of identification leads naturally into a specification in which the luminance [20] of the unknown is given and the chromaticity is specified by two variables in polar coordinates. One of these variables is an angle, the other a radius, and both