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APPENDIX UNDERSTANDING TEST DESIGN In order to understand how a color test is designed and why it works, it is helpful to understand how normal color vision is represented by color mixture. Normal color mixture data allow specification of color surfaces according to an important visual property: the condition under which two color samples will appear identical to a normal observer. COLOR MATCH TNG As described in Chapter 2, in a color-matching experiment an arbitrary color is matched in visual appearance to a mixture of primary colors. When identical in visual appearance, the two color fields that have dissimilar spectral distribution are called metamers. A fundamental property of normal human color vision is that it is possible to find a metamer for any spectral hue by variation of only three primary colors. The terms trichromat (a three-color mixer) and trichromacy (the property of being a three-color mixer) come from this property of normal vision. For spectral lights, the primaries and the spectral light are , arranged In pairs so that the spectral light and one primary match the remaining two primaries. Thus, except at the primaries themselves, the appearance of the mixture fields will not be like the spectral hue or any of the primaries. The importance of the experiment relates not to the appearance of the hue but to the equivalence of hue. One way of presenting the results of color mixture experiments is in a chromaticity diagram. A diagram called the x,y chromaticity diagram was devised by the Commission Internationale of Eclairage (CIE) based on the average color matches of many color-normal observers. Figure A-1 shows the x,y chromaticity chart for the ~standard. 1931 CIE observer. An isosceles triangle completely encloses the experimentally determined chromaticity diagram. The spectral wavelengths are represented around the perimeter of the chromaticity diagram, which is called the spectrum locus, and equal energy Awaited occurs in the center. Since the chromaticity diagram represents only color matches and not hues, the hue names added to the chart in Figure A-1 are provided for the convenience of those who are not familiar with the appearance of different wavelength regions of the spectrum. Saturation 97 t

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y 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 02 0.1 o CYA N ~ 500 1 520` GREEN ~ ~~S30 510 '/ ~0 YELLOW-GREEN 4 basso ~60 Y E LLOW ED RIO 49d ~ W/ ' ~ ,80 ~ z 1 470~.5 _ _ _ VIOLET 400 1 ~ ~ ~ 1 ~ 1 ~ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 ~~ ' X FIGURE A-1 The CIE (x,y) chromaticity diagram. Source: Pokorny et al. (1979, by permission. is not specified by the chromaticity chart, but in general it can be said that saturation along any line from the center to the spectrum locus increases with the distance from the center. The line connecting the coordinates for 380 nm and 700 nm is identified as the line of nonspectral purples. All real colors may be represented within the boundaries formed by the spectrum focus and the purples. Mixtures of any two chromaticities can be represented by ~ straight line joining the pair of mixture lights on the diagram. Each mixture is a point on the line specified by the relative amounts of the two components of the mixture.

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99 REPRESENTATION OF DEFECTIVE COLOR VISION IN THE CHROMATICITY DIAGRAM The dichromat is an observer who requires only two primaries for spectral color matching. For example, the dichromat can match any spectral color to a mixture of a blue primary (e.g., 450 nm) and a red primary (650 nary). The color-matching data of protanopes and deuteranopes can be plotted on the normal chromaticity diagram. The procedure, however, is theoretically correct only if dichromacy is a reduced form of normal trichromacy; that is, if the dichromat is simply lacking one of the normal discriminative mechanisms. For dichromats, some mixture lines on the x,y chromaticity diagram represent a series of colors that cannot be discriminated from one another (so-called isochromatic or confusion lines). Sets of such isochromatic lines are shown in Figure A-2: the upper panel gives isochromatic lines of protanopes; the lower panel gives those of deuteranopes. By associating the coordinates in the x,y chromaticity diagram with their usual series of color appearances to normal trichromats, we can describe approximately which colors are confused by the two types of dichromats. For both protanopes and deuteranopes, one isochromatic line lies on the spectrum locus from 540 nm to 700 nm; protanopes and deuteranopes are said to confuse spectral yellow-greens, yellows, oranges, and reds. From other data we know that, as a general rule, protanopes confuse reds with dark browns; pale blues with purples and magentas; blue-greens, whites, and reds; light greens with light browns (fawn). Deuteranopes confuse red, orange, and light browns; blues, violets, and blue-purples; blue-greens, whites, and purples; light greens, magentas, and purple-reds. One confusion line passes through equal energy white. It indicates precisely which chromaticities and in particular which monochromatic light (neutral point) can be completely matched with the equal energy white. Chromaticities represented above this line are said to appear "yellow" with increasing saturation; those below the line are ~blue, n also with increasing saturation. Accordingly, the visible spectrum is said to appear as shades of yellows and blues to observers with protanopia or deuteranopia. A word of caution is in order. The CIE standard observer represents a person with average visual photopigments, lens, and macular pigment absorptions. The isochromatic lines are thus similarly indicative of those expected for an average group of dichromats whose ocular media have characteristics similar to those of normal trichromats. For a single dichromatic observer, the "isochromatic" contours may look quite different from those of Figure A-2, just as a single normal observer will make color matches that differ from the group average. Neverthe- less the isochromatic lines are useful in the design and evaluation of screening tests for color defects and in indicating what kinds of colors will be confused by protanopes, deuteranopes, and tritanopes. Protano- malous and deuteranomalous trichromats are said to make color confusions that are qualitatively similar to, although of less severity than, the corresponding dichromat (Farnsworth, 1943~. This similarity forms the basis for many tests for color defect. Farnsworth also introduced the - t

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oB 0.6 0.2 100 09 1 1 1 1 1 [--- 1 ~ I 520 ~,`30 5'0 ~ \~540 0.7 _ 05 500 it\ Y 0.4 _ 0.3 _ _ _ 1 _ 0.1 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 \ O _ \ \\~570 4------~20 480\~ 470 an/ 460 ~ _ L , 40O, , , ~ , , , O 01 02 0.3 0.4 0.5 06 0.7 08 X : O _ -0.1 -0.2 -0.3 -0.4 boo ~ i . . O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 O.9 1.0 1.1 1.2 1.3 1.4 X FIGURE A-2 Confusion lines for protanopes (upper panel) and deuteranopes (lower panel). Source: Pokorny et al. {1979), by permission. 1 e

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101 term protan to characterize protanopes and protanomals and the term deutan to characterize deuteranopes and deuteranomals. The data of tritanopes may also be plotted on the CIE (1931) x,y chromaticity diagram; their isochromatic lines converge on the "blue" corner of the diagram. THEORY OF TEST CONSTRUCTI ON Pseudoisochromatic Plate Tests Most pseudoisochromatic plate tests are constructed empirically. The colors are selected on a trial-and-error basis, and only those plates shown to have high diagnostic efficiency are retained. The trial-and- error procedure is necessary because the surface mode of presentation complicates plate design. Factors such as form, size, glossiness, texture, and glitter will affect the readability of the plates. Stilling (1873) designed the first plates, using great ingenuity and finesse. Applying information obtained from two color-defective assistants (one red-green blind, the other blue-yellow blind) and following Hering's color theory (see Hering, 1964) of opposing pairs, he succeeded in constructing a series of plates in which figures composed of one set of variegated color dots appeared on a background of corresponding confusion colors. For instance, he used red-orange dots on a dull yellow background and yellow-green dots on an orange- brown background to detect red-green deficiencies, and pale blue dots on a pale yellow-green background to detect yellow-blue deficiencies. Since Stilling's time, various types of plate tests have been constructed. Although some tests are better than others, all make use of four basic plate designs. The first, a vanishing test plate, is the simplest and most frequently used. The colors of the figure and background are confused by certain types of dichromats (i.e., the colors will fall on a given confusion line). A defective observer fails to read the figures that are clearly discerned by normal observers. The figure is said to have ~vanished. for the defective observer. In modern tests (such as the Tokyo Medical College test), the color distance between the colors of f igure and background is varied; these tests are designed both to screen and to quantify the defect. An observer cannot recognize any of the plates, no matter how great the color distance between the figure and background, is assumed to have a severe color defect. If the plates with the greatest distance between figure and background can be read but those with intermediate and small color difference cannot be read, the defect may be designated as medium; and if only the plates with the smallest color difference are confused, the defect is mild. This principle is illustrated in Figure A-3 with reference to the screening and quanti- tative red-green plates of the Tokyo Medical College. However, the ability of a given color-defective observer to read a set of plates depends not only on the observer's chromatic discriminative ability but also on how appropriate the selected confusion colors are for that observer. 1 r

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102 be\ 4 y - 3 ~0 FIGURE A-3 Construction of "vanishing types plate as applied to the Tokyo Medical College Test. Based on data from Lakowski (1969 ~ . The second type of plate design is the qualitatively diagnostic type. It is an extension of the vanishing type, except that two clusters of colored dots are used to print two digits or symbols against a common background. For a red-green plate, one of the digits or symbols should be visible to the deuteranope and the other visible to the protanope. The inclusion of these plates theoretically allows the examiner to distinguish the different types of dichromats, but in practice this idea is not well realized. Figure A-4 illustrates this design with respect to plate number 13 of the diagnostic series in the AD ERR test. The third type of plate design is the transformation plate. This is perhaps the most interesting and cleverly designed of the pseudoiso- chromatic plates. Both normal and defective observers can see a figure in the plate, but each identifies a different one. For example, on plate 5 of the Ishihara test (5th edition), the normal observer sees a .5" composed of yellow-green and light green dots on a background of light and dark orange and pink dots, whereas the red-green dichromat reports seeing a rather neutral .2. on a ~warm. background of colored

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103 .4 .3 \ Figt: Wit \ .C \ .2 .3 FIGURE A-4 Design of quantitatively diagnostic plate from AD H-R-R test (plate 13~. Source: Lakowski internal communication, Visual Lab., U.B.C., (1976~. dots. The design is accomplished by the strategic placement of colored dots that cluster in four locations on the chromaticity diagram, as shown in Figure A-S. For a normal observer, whose reference point for color is the position of Illuminant C, two of the clusters constitute the green figure and two constitute the orange background. The con- fusion lines for red-green dichromats, however, indicate that their reference point for color appears to be in the red-purple areas of the chromaticity diagram. The positions of the four clusters relative to the confusion lines show that half of the normal figure and half of the normal back- ground become the alternative ~figure,. and the other half of the figure and background'become the ~background. for the dichromat. The fourth type of plate design is the hidden-digit plate. Hidden- digit plates are designed so that dichromats, but not normal observers, can see the intended figure. In the previous three types of plates, colors for figure and background are separated by large color differ- ences. This is not so in the hidden-digit plate, in which the use of three different colors and small variations in saturation prevent normal observers from seeing a figure but allow observers with -

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- y Greer,/ Normal/ \< rigure .4 . .3 \ Normal Or) _>kground ~' ~ \ .~ / ~~` Background //~~~ Prowar figure FIGURE A-S Analysis of Transformation type. of plate from Ishihara, 5th edition (plate 5 ~ . Based on data from Lakowski (1969~. red-green color defects to do so. The latter perceive two color groupings that are distinct enough from each other to follow two separate i~ochromatic lines: the more saturated orange, khaki, and yellow-green dots form the background, and the less saturated pinks, grays, and greens form the figure. Figure A-6 shows the loci for colors used in plates ,0 and 11 of the Ishihara plates (Sth edition). The ability to read the hidden-digit plates (itself an error} depends on the degree of red-green defect; those whose defects are more severe read these plates more frequently. The ability of normal observers to read them seems to be a function of age. About half of the normal subjects between 20 and 30 years of age read hidden-digit plater easily, but these plates are hardly ever read by subjects over SO or by young children. f t

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es ~ A y 3 Yellow Green \ / Khaki r art ' \ / \ /~ In figure \ FIGURE A-6 Colorimetric data for ~hidden-digit. plates from Ishihara, 5th edition (plates 10-11~. Based on data from Lakowski (1969~. Arrangement Tests Most modern arrangement tests use Munsell colors, the chromaticities of which can be displayed in the CIE chromaticity diagram. From this display we can predict the expected behavior of observer's with congenital color defects. The chromaticities of the Farnsworth Panel D-15 are shown in Figure A-7 together with confusion lines of the deuteranope and protanope. Since the confusion lines connect pairs of cape that are identical or closely similar for a given dichromat, the expectation in that the protanope or deuteranope will make a characteristic arrangement of caps, connecting caps that oppose each other in the color circle but that lie on the appropriate confusion line. For protanopes a possible arrangement is: P 15, 1, 14, 2, 13, 3, 12, 4, 11, 5, 10, 6, 9, 7, 8.

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106 0.8 0.6 0.4 0.2 o me 0.6 0~4 0 a I 1 1 ~ --1 ' -1 lo_ ' . \ _ \ 4 - 4 _ \ 1...~ _ \ P 15 ~ . ~ 1 1. 1. "1 0 0.2 0.4 - - - 1. 1 1 1 0.6 0.8 -\ ~ _ 1 1 . 1 ~ 1 1 1 ~ 1 0 0.2 0.4 0.6 0.8 X FIGURE A-7 Chromaticity coordinates of caps in the Farnsworth Panel r)-15 Test. Confusion lines are indicated by dashed lines for protanopes {upper panel) and deuteranopes (lower panel). An expected cap arrangement is indicated by solid 1inese Figure prepared by Pokorny and Smith for this report.

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107 For deuteranopes a possible arrangement is: P. 1, 15, 2, 14, 3, 13, 4, 5, 13, 11, 6, 10, 7, 9, 8. These major axes are indicated on the score sheet together with the axis for a tritanope. A fourth axis, that for the achromat, has also been defined (Sloan, 1954). A typical arrangement for an achromat is: P' 1, 2, 3, 4, 5, 15, 16, 14J 13' 7, 12' 11' 8, 10, 9. A similar analysis may be applied to the two arrangement tests designed by Lanthony. Figure A-8 shows the position of the FM 100-hue test caps in the CIE diagram, together with confusion lines of protanopes and deuteranopes in the FM 100-hue test. For administration of the test, the boxes are presented one at a time, so that color confusions across the color circle are not allowed. The errors occur for locations where a confusion line is tangent to the color circle of the FM 100-hue test. The bipolar error axis that occurs on the FM 100-hue test is therefore orthogonal to the confusion axis. For example, the major confusion axis for the deuteranope is green and red-purple. On the FM 100-hue test, the errors occur at the orthogonal axis, namely, for yellow, yellow-red, blue, and purple-blue caps. Similarly, for the protanope, the major confusion axis is red and blue-green. Errors on the FM 100-hue test occur for yellow, green-yellow, purple-blue, and purple caps. This rotation of the error axis is clearly noted when Panel D-15 confusions and FM 100-hue test errors are plotted on the same diagram (Pinckers, 1971~. Anomaloscope The experiment that became known as the Rayleigh equation was first described by Rayleigh (1881} and consisted of mixing monochromatic yellow-red with yellow-green to match a monochromatic yellow. He described three methods to obtain this equation--two involving spectral colors and one involving colored discs combined by a rotating prism. Nagel was the first one to use a direct vision spectroscope with spectral colors. An apparatus such as Rayleigh's or Nagel' ~ (or indeed any other kind of device with similar functions) is usually called an anomaloscope, that is, an instrument for specifying anomalous color vision. Today the anomaloscope is used as an instrument capable of measur ing var iations in color vision for normal, anomalous, and dichromatic observers, not only in the classic Rayleigh equation but also in other combinations of two lights to match a third. To fulfill such objectives the anomaloscope has to be validly designed, reliably administered, and the data obtained from it must be correctly quantified. The design of an anomaloscope depends on the choice of primaries used for the color mixtures, the areas that such a mixture will subtend at the retina, the level of luminance of mixture obtained,

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108 _ I I I I I 1 1~ 0.8 0.6 0.4 0.2 o /` 'A ' \ I ... - in, \ ., . _,_ ______ I I ,: \ At, _ _ `` . I I I I I I I I l 0 0.2 0.4 0.6 0.8 X FIGURE A-8 Chromaticitie~; for the 85 caps of the FM 100-hue test. Dashed lines indicate axes of confusion lines for color-defective observers. Based on data from Lakowski (1969 ~ . and the ability to vary with ease the purity and luminance of the test field to which the mixture is being compared. The choice of primaries for the Rayleigh equation has been well established, the main principle being that they ought to be chosen with the greatest separation in dominant wavelength between them. Thus in the Nagel Model II, the mixture field originally consisted of a red stimulus wavelength 671 nm [lithium line), and a green stimulus of t

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109 wavelength 536 nm {thallium line). However, for the Model I, a longer wavelength was chosen (546 no, the mercury line). Chromaticities of primaries and the test color on the Nagel Model I are shown in Figure A-9. The primaries lie on the linear portion of the spectrum locus, and, thus, on the confusion lines of red-green dichromats. The choice of primaries for the Engelking-Trendelenburg equation is not so well established. In the Nagel Model lI anomaloscope, they are at 517 nm (for green) and at 470 nm (for indigo) , while in the Pickford-Nicolson anomaloscope they are at 552 . 5 nm and 473 . 3 nm, respectively. Because neither of these pairs lies on isochromatic lines of tritanopes, desaturation of the blue-green test color is necessary in testing people with tritan defect. Normal observers also require differing amounts of desaturation. Because desaturation was not available on the Nagel Model II, the Engelking-Trendelenburg equation is rarely used. The luminance of mixtures of primaries, especially at the most frequently chosen ratio, must be well above the threshold level for cone vision but preferably at the top of the mesopic range of vision, although the critical luminance will depend primarily on the size of the viewing aperture. The larger the subtense over 1.5 the higher will be the luminance necessary. In the Nagel and Pickford-Nicolson anomaloscopes, it is about 5 cd/m2. The choice of test wavelength varies among instruments but should correspond as nearly as possible to a region in which color discrimination is good. Thus for the Rayleigh equation the wavelength should be near 590 nm, while for the Engelking-Trendelenburg equation it should be near 490 nm. With the Nagel and the Pickford-Nicolson anomaloscopes, the dominant wavelengths for the yellow tests are at 589.3 nm (originally at the sodium line) and 584.3 nm, respectively; for blue-green tests they are at 490 nm and 493.5 nm, respectively. Furthermore the luminance of the test yellow must be variable. For the Rayleigh equation, luminance variation is necessary to distinguish between protanopes and deuteranopes. The red primary appears dim to the protanope, and hence only a small amount of the yellow luminance is required for a match; a deuteranope, however, for whom the red field is as bright as it is for observers with normal vision, will require a correspondingly higher luminance in the standard yellow to match this pr imary. For the Engelking-Trendelenburg equation, it is important to vary the luminance of the standard blue-green to accommodate age changes in sensitivity and normal variation in ocular media. The size of the stimulus field and its consequent subtense at the retina is also important. Anomalo~copes vary in the field size that is used, and the visual angle may vary considerably. In the Nagel Model T. the visual angle is f ixed near 2; in the Nagel Model II it can be varied between about 1.5 and 3. Additionally, the manufacturer has supplied some Model I instruments that allow variation of field size. In the Pickford-Nicolson anomaloscope, at a viewing distance of one meter, the field varies from 0.5 to 3, but a 1.5 field is most frequently used. Red-green dichromats do not accept the classic dichromatic matches when the field size extends to 8 (Smith and Pokorny, 1977; Nagy and Boyn ton, 1979~. Thus the classification e

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0.8 0 7 0 6 0.4 03 02 01 o O 1 -02 110 = , , , 520 ~530 510 ~ \~550 500 ~ 70 N - 490~ 470\ _ _ -0.3 -0.4 ~~o~ 1 . , ~ I I I I I ~ ~ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 13 14 X FIGURE A-9 Chromaticities for primaries and test colors on the Nagel Model I and the Pickford-Nicolson anomaloscopes. Pokorny et al. (1979), by permission. Of people with red-green defects may differ from instrument to instrument when the size of target varies appreciably.