Page:Colorimetry104nime.djvu/26

chromaticnss-scale Fig. 8.Uniform-chromaticity-scale triangle according to Judd [66].The length of the straight line connecting the points representing any two chromaticities on this triangle is approximately proportional to the perceptibility of the chromaticity difference. (UCS) System [66], from the CIE chromaticity coordinates, $x,y$, are

${\begin{aligned}r&={\frac {2.7760x;+2.1543y-0.1129}{-1.0000x;+6.3553y+1.5405}}\\\\g&={\frac {-2.9446x;+5.0323y+0.8283}{-1.0000x+6.3553y+1.5405}}\\\end{aligned}}$

(5)

The triangle resulting from this transformation is shown in figure 8.

In 1960 the CIE adopted a provisional recommendation that the transformation suggested by MacAdam in 1937 [89] be used whenever a spacing perceptually more uniform than that of the ($x,y$)-diagram is desired. This transformation is:

${\begin{aligned}u&={\frac {4x}{12y-2x+3}}\\\\v&={\frac {6y}{12y-2x+3}}\\\end{aligned}}$

(6)

Although the transformation coefficients are simple, the ($u,v$)-diagram (fig. 9) has a spacing that closely resembles the UCS diagram.

3.3. Visual Devices

a. Martens Photometer

One of the most useful visual devices for determining relative luminance is the Martens photometer. Figure 10 shows the Martens photometer combined with a diffuse illuminator to form the Priest-Lange reflectometer [134]. This reflectometer is intended for the measurement of luminous reflectance of opaque specimens relative to reflecting standards of similar spectral reflectance. The Priest-Lange instrument is also adaptable to the measurement of luminous transmittance of transparent plates relative to transmitting standards similar in spectral transmittance to the unknown. Finally, the Martens photometer, removed from the mounting, may be used for the determination of the luminance of an unknown self-luminous surface relative to a spectrally similar standard of known luminance. The superior usefulness of the Martens photometer arises from the convenience of the adjustment for equality of brightness between the two halves of the photometer field and from the fact that the dividing line between the half-fields is exceptionally narrow so that it is often invisible when a brightness match has been set.

b. Chromaticity-Difference Colorimeter

The determination of chromaticity coordinates, $x,y,$ by comparison of the unknown specimen with a working standard of similar spectral reflectance can be carried out visually with high precision by means of a colorimeter described by Judd [64]. The adjustment of the chromaticity of the comparison field to match the standard field is by two double wedges, one of greenish and the other of yellowish glass. Since the light from the comparison field must pass through both the yellow and the green wedge, some of the radiant energy being subtracted by each, it is sometimes called a subtractive colorimeter; see figure 11 which gives a schematic diagram. The standard and comparison fields are brought into juxtaposition by means of a Lummer-Brodhun cube having a double-trapezoid pattern subtending 9 × 13° at the observer's eye. The adjustment to near equality of brightness to facilitate detection of chromaticity differences is by movement of the projection lamp that illuminates both standard and comparison surfaces.

A substitution method is usually employed with this colorimeter, a match first being set up between the standard and comparison surfaces by adjustment of the wedges. Then the unknown specimen is substituted for the standard, and the wedges readjusted to restore the match. The differences in wedge settings can be calibrated in terms of differences in the chromaticity coordinates, $x,y,$ of the CIE standard coordinate system, provided the spectral reflectances of the comparison surface are known approximately, from the known spectral transmittances of the wedges. This calibration has been carried out for about 100 widely differing: comparison surfaces. It has been found that the calibration is chiefly a function of the chromaticity coordinates, $x,y,$ of the comparison surface; so calibrations for comparison surfaces intermediate in chromaticity to those already calibrated may usually be found satisfactorily by interpolation.

Because of the large patterned field of high luminance and the convenience of the brightness adjustment this instrument takes full advantage of the ability of the observer to detect small chromaticity difference. If specimen and comparison surfaces are similar in spectral composition, the settings for match may be repeated generally within 0.001 in chromaticity coordinates, $x,y$. The chromaticity-difference colorimeter has the disadvantage, how-