Effect of Veiling Reflections on Vision of Colored Objects
James A. Worthey

Introduction
Familiar light sources vary by a factor of about 10⁶ in the bright solid angle they present. Table 1 ranks a number of sources according to the solid angle subtended by their bright areas, based on simple measurements and calculations. For instance, the filament area for the unfrosted 60 W bulb is calculated from the observation that the coiled coil appears to be 1 mm diameter by 20 mm long. For the ordinary frosted lamp, naked-eye observation shows the bright spot to be a circle of about 20 mm diameter. For the Soft White lamp, the bright spot is taken to be a circle of the bulb diameter. Obviously, the choice of 2 m distance for the individual electric lights is arbitrary and affects their comparison with the sun and the luminous ceiling. Nonetheless, the range of variation is great. (In Table 1, I forgo power-of-ten notation for solid angles in order to dramatize the range of magnitudes.)

Light source area has such an effect on highlight size and the abruptness of shadow edges that the three incandescent types are sold side-by-side in US supermarkets. A recent paper¹ looked at two effects of light source size: how larger sources make it more difficult to avoid veiling reflections, and how source size affects the luminance of veiling reflections. An important conclusion was that veiling reflections are never negligible if they veil blacks and dark colors.

The three 4-percent rules
An important set of conclusions in the earlier paper concerned the amplitude of surface reflections. If a dielectric material is assumed to have index of refraction n = 1.5, and light enters the material approximately normal to the surface, then 4 percent of the incident light will be reflected at the surface. For unpolarized incident light, the reflected fraction remains approximately 4 percent up to about a 40 degree incident angle, then rises to 100 percent at grazing incidence. For polarized light, other angles of incidence, and other refractive indices, the reflected fraction is given by formulas found in Reference 1 or in elementary optics books. Putting aside those complexities for the sake of a simplified discussion gives us three "4-percent rules." To understand these rules, picture a piece of black glass, which reflects only specularly, next to a diffusely reflecting white surface. [Click for a drawing.]
 1) If light is incident more or less normal to an air-dielectric interface, such as the black glass, about 4 percent will be reflected at the surface.
 2) If a source is imaged in a shiny dielectric surface, the luminance of the veiling reflection (or highlight) is about 4 percent of the source luminance.
 3) Under spherical lighting (or a luminous ceiling extending to infinity), the veiling reflection in the black glass is about 4 percent of the luminance of the white surface next to it. (Since the white surface has the same luminance as the spherical source.)

Veiling reflections example
By extracting facts from that earlier paper, let us work an illustrative example. Suppose that the visual task is a shiny book whose half-width in its narrow dimension is 10.8 cm (4.25 inches). Suppose that the light source is circular and oriented toward the book, and that its angular semi-subtense (its angular "radius") is 27 degrees. Then if the source is 30 degrees off the line of sight (over the shoulder), the book must be tipped about 7.5 degrees off the line of sight and away from the light in order to avoid veiling reflections, or a total of 37.5 degrees away from the light. This turning from the light dims the book by (1 − cos37.5° ), or about 21 percent, without dimming the surround. Further calculations, taking account of the non-linearity of human lightness perception, show that if the reader does not tip the book and does not avoid the veiling reflection, but allows it to wash out the blacks on the page, it discards about half the dynamic range of black-white perception. The calculations underlying this example are far from trivial, but were handled by reading numbers off the graphs in the earlier paper.¹

The present paper extends the demonstration that veiling reflections are seldom negligible. We shall examine the extent to which veiling reflections reduce the saturation and diversity of colors seen in colored objects. To do this, we must introduce some quantitative methods that are used in talking about object colors.

The concept of a "color solid"
If a patch of light is created in a physics laboratory by a mixture of red, green, and blue lights, then this light may be described by a set of three numbers that may vary independently from 0 up to the limit of radiant power available. If the three numbers are taken to comprise a vector in cartesian space, then this vector can vary within a rectangular parallelipiped bounded by the power limits—a simple and perhaps not very interesting fact.

Now consider the range of ordinary non-self-luminous objects, which are seen only by reflected light. If the illuminant spectral power distribution (SPD) is specified, then three numbers (called tristimulus values) can be calculated, or measured, which describe the object as a stimulus to color vision. This would be done by the ordinary methods of colorimetry, and might lead to a luminance and chromaticity (L, x, y), for instance. If the illuminant is held fixed, the variation of the triplet (L, x, y) is now limited by the condition that the spectral reflectance function of the object varies only between 0 and 1. This limits (L, x, y) to a curved solid, the shape of which expresses information concerning the light source, human vision, and the constraint on spectral reflectance. This color solid expresses the trade-offs involved in attempting to make pure colors with pigments; a pigment can isolate one wavelength band only by absorbing other wavelengths. It will have an irregular pyramid shape, indicating that a saturated ("strong") pigment color will in general be a dark one; only yellow pigments can be both light and saturated.

The most used color solids incorporate additional facts, and are not pyramidal, but more of an irregular football shape (North American football), small at the top (the white end) and at the bottom (the black end). Because of lightness constancy² and color constancy,³ colors are located in the solid based on their surface reflectance, rather than their absolute radiance. A color's position in the color solid can be calculated from its spectral reflectance. Position and distance within the solid correspond approximately to human perception of colored objects. From bottom to top through the solid is the axis of achromatic colors: blacks, grays, and whites. On the surface are the most saturated colors. The solid tapers toward black at the bottom to represent the fact that dark colors appear less-than-fully saturated, even if they reflect in just a narrow wavelength band. The solid's shape shows that yellows can be saturated and high in lightness, while the most saturated reds and blues are dark. The calculation relating a surface color to a point within the solid is nonlinear, corresponding to the nonlinear way that color differences are perceived. The exact range of possible colors depends on the spectral power distribution of the light that is assumed to illuminate them. [To see one color solid from all sides, go to Bruce Lindbloom's web site, http://www.brucelindbloom.com/ , then click "Info" and "Lab Gamut Display."]

If a standard light source, such as Illuminant C, is considered to light the objects, then the source SPD can be considered as background information and a color solid can be taken to represent the boundaries of object color perception by humans. Any realistic object spectral reflectance function will map to a point within or on the surface of this solid, and that point can be related to a color name, such as "dark red,"¹ "pale blue," or to some appropriate set of three numbers that will predict the object's color appearance. Descriptions of two such color solids, apparently written by Dorothy Nickerson, appear in the American Heritage Dictionary at the entry word color.4 The exception that proves the rule with respect to color solids is fluorescent pigments. These violate the restriction that light radiated cannot exceed light incident at each wavelength; and indeed the eye can recognize this, that a fluorescent pigment displays a combination of lightness and saturation which is outside the limits of normal pigments.

Figure 1—Reduction in the range of lightness and saturation of surface colors due to veiling reflections. Data are plotted in the cylindrical-polar version of the CIELAB uniform color space, at four selected hue angles (h*). Radial coordinate c* represents saturation, while axial coordinate L* is a measure of lightness. The solid lines represent the limits attainable with real pigments, according to Pointer.10 Chains of arrows show successive shifts as veiling reflection is increased to 4, 8, 12, and 16 percent of white. At these selected hue angles, the shifts stay in the constant-hue plane, but at other h* values, they don't. At all hue angles, including those not shown, a similar systematic loss of saturation and of lightness occurs.

Figure 2—Comparison of the range of Munsell colors available in the glossy and matte sets. Two constant-hue planes (10Y and 2.5R) are shown, similar to Figure 1. Rectangles with numbers stand for glossy chips that are available. The heavy line indicates the range of matte chips available. For instance matte chips are available, but not glossy ones for notations 10Y9/8 and 10Y9/10. Glossy papers, but not matte, are available for 10Y4/4 and 10Y4/y.

For instance, the rightmost rectangle in the top row under "10Y" indicates that there is (Figure 2) a glossy paper for notation 10Y 9/6. (10Y indicates hue, a yellow; 9/ tells the Munsell value; and 6 indicates chroma or saturation.) The heavy line encloses those rectangles for which a matte paper is available. At hue 10Y, we see that eight hues are lost, but two are gained in going from glossy to matte. At hue 2.5R (a red), nine hues are lost and none are gained. The solid line bisects the rectangle for 2.5R 2/2 to indicated that a chip is sold at 2.5R 2.5/2. Where possible, matte chips are made with the value 2.5, since none can be made with value 2. In the neutral series, the pure whites, grays and blacks, the glossy series goes down to value 0.5/, while the matte series stops at 1.75/ on the black end.

Poor man's anti-reflection coating
We may conclude that a shiny surface is a poor man's anti-reflection coating. To use this anti-reflection coating, the poor man must have a dark surface near his light source that he can put at the specular angle.

Discussion
The loss of saturated colors due to veiling reflections compounds any loss that is due to color rendering deficiencies of the light.¹⁴ For instance, Xu⁸ found that a Warm White fluorescent lamp reduces the volume of accessible colors by 25 percent from its value under Standard Illuminant A. Xu's concept of a color solid volume is similar to that in the present paper, although his calculation differs in important details.

Summary and conclusions
Light sources vary in the solid angle they subtend by a factor of almost 10⁶. A previous paper¹ showed that veiling reflections are easy to avoid if the source is small and has a dark area next to it, but harder to avoid when the source is large. Because of the nonlinear way that the eye perceives whites, grays, and blacks, the bottom few percent of the reflectance scale is especially important, and it was suggested in the earlier paper that veiling reflections are not negligible, even under spherical lighting conditions.

This paper has gone further in showing why veiling reflections are not negligible. Dark and saturated colors are particularly prone to being washed out by the surface reflection of a light source. Spherical lighting, for instance, reduces the range of possible colors by 37 percent, compared to lighting with a compact source whose image can be moved off the page. This is the net loss, with dark and strongly saturated colors being lost, but a few lighter colors are gained.

Choosing a matte finish rather than a shiny one is roughly equivalent to lighting the shiny surface by spherical lighting. Shiny surfaces are used for colored pictures and paints in order not to lose the "deep" colors. This was emphasized by Figure 2, which shows how the deep colors are lost from a set of paint chips, in going from glossy to matte finish.

The conclusions extend to lighting of three-dimensional objects. If a shiny colored object is lighted by a compac source near a dark area, the source image will be a bright white highlight, and the image of the dark area will define a region in which the object's pigmentation can be clearly seen.

Acknowledgement
The author wishes to thank Dr. Michael H. Brill for writing the subroutine used to calculate the volume of color solids. This work was supported by the National Institute of Standards and Technology.