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Most important for the present topic is the energy of light, measured in electron volts (eV). One eV is an extremely tiny unit of energy, but the key point is that each wavelength or frequency of light also has a characteristic, fixed energy that is between 1.7 to 3.2 eV. So the electromagnetic spectrum can be described using three interchangeable units, as shown below.
wavelength, frequency and energy across the visible spectrum
The importance of light energy is that it can affect the behavior of electrons, which are the lightest particles of matter, in a large number of ways. That is, the electrons that normally form a cloud around the nucleus of every atom can interect with particles of light (photons) through an exchange of energy, which changes the electron's behavior.
Normally the energy exchange amounts to this: the electron absorbs a photon, which raises the electron's energy, or the electron emits a photon, lowering its energy. The emitted photon carries with it the lost energy, and the exact amount (quantum) of energy determines the wavelength of the light.
The important qualification is that electrons within atoms are constrained to a range of fixed energy states, called electron shells, and there is a limit to the number of electrons that each shell can contain, sometimes forcing individual electrons to stick where they are, or jump to a vacant position in a higher or lower energy electron shell. The dance between electrons and light is shaped by this fixed energy ladder of shells and shell vacancies within each atom.
quantum lines in gas emission spectra
emission spectra for hydrogen (H, top), helium (He, middle) and neon (Ne, bottom)
The table summarizes the major physical mechanisms of color. The point is not to explore the details of physics, but to show the astonishingly large number of ways in which color arises in the world.
The complexity of color producing mechanisms depend on a variety of atomic structures and the integral role played by the electron in chemical and crystal bonds. These are described in more detail on this page. It will be useful to explain these further.
The electron can inhabit a variety of energy levels, which are determined by the specific atomic structure of atoms and molecular bonds of the material.
The energy levels may be separated by relatively large or small intervals, and may represent relatively low or high levels of energy. Usually, only untraviolet or x ray radiation can affect electrons at high energy levels or cause them to jump across large differences in energy.
Typically the energy thrown off by the electron is less than the energy absorbed, which shifts wavelengths longer (from higher to lower energy): from ultraviolet to visble blue, from blue to red, and from red to infrared.
Light Refraction. The most common optical origins of color concern the effects of matter on light. These must be explained in terms of the wave structure rather than the particle energy of light: pigment colors and prismatic colors stand for the contrasting origins of light in its particle and wave form.
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Blah.
More familiar is sunlight refraction in raindrops, which produces rainbows. Light that strikes the raindrop anywhere near its center meets the surface of the water at close to a perpendicular angle, so it passes through the raindrop just as it would through a lens and is scattered out the opposite side. As the point where sunlight strikes the raindrop shifts toward the side, some light is reflected off the back inner surface of the raindrop and exits on the opposite side as a spectral refraction (C). This produces a primary rainbow. If the incident angle is slightly less acute, the light makes two reflections off the inner surface of the drop before emerging as a spectral refraction. This produces a secondary rainbow outside the first.
Because the inner reflection and exit angle depend on the incident angle of light, and the surface of the drop is round, parallel beams of the same wavelength do not exit the raindrop at the same angle. This causes the rays to diverge, producing a smearing in the rainbow color (D). This smearing increases as drops get smaller, and in a fog or fine mist the smearing blends the spectral colors back to white, producing a white fogbow.
Light Interference. Interference is produced by two parallel reflective layers, in oil (right).
interference produced by phase changes in light
The light comes and goes, and sometimes it cancels and sometimes it doesn't.
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 the wavefront explanation
of light refraction refraction in a prism
and in water dropsA: spectral colors from a prism;
B: parallel rays of identical color
remain parallel; C: spectral colors
from a raindrop; D: parallel rays of
identical color diverge
 iridescence in an oil film
on wet pavement |
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This section draws in large part on the insightful descriptions of photon and electron physics by Kurt Nassau, including "The Physics and Chemistry of Color: The 15 Mechanisms" in The Science of Color (2nd ed.) edited by Steven Shevell (Optical Society of America, 2003), and "The Fifteen Causes of Color" in Color for Science, Art and Technology edited by Kurt Nassau (North Holland, 1998).
 the constants of light |
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The physical distinction between a self luminous (light emitting) and illuminated (light reflecting) object does not address the perceptual issues. The moon, planets and satellites all appear as lights in the evening sky, even though they are reflecting bodies. A flat panel television or computer monitor appears as a surface, much like a slide projected on a reflecting screen, even though it is made up of thousands or millions of tiny lights.
Constants of Spectral Mixture. The additive color mixing.
an additive color mixing triangle
More about the additive color mixing.
Constants of Surface Reflectance. In most situations, human vision can distinguish a potentially very large range of luminance contrasts between dark surfaces and/or lights and reflections. For example, it is easy to see in daylight or at night the brightness difference between a 60 watt incandescent light bulb and a "white" area on a computer monitor masked to have an equal visual area; yet these differ in luminance by about 1200:1. A much larger luminance contrast, on the order of 1,000,000:1, occurs when reflections of sunlight and clouds are visible side by side in dark water. Visual experience comprises a very large range of brightness perceptions.
At the same time, human vision is always limited, in the perception of surfaces, to lightness contrasts in which the luminance ratio between the lightest and darkest values is never greater (and in natural surfaces is typically much less) than 100:1. These lightness contrasts define a closed scale anchored on perceptions of white (pale) and black (dark) produced by the local luminance contrast between to surface colors. This lightness range is a completely reliable physical constraint on surface luminance, because it depends only on the level of illuminance as redistributed by the diffuse surface reflectance of physical materials. Across both scotopic and normal (daylight) levels of illumination, it produces a constant relative perception of light or dark values.
Ralph Evans found that a luminance contrast of about 2:1 or greater between a small color area and its surroundings was sufficient to produce the perception of self luminance, independent of the color chromaticity. However, the color chromaticity has a large effect on blackness contrast, the appearance of black or dull color caused by lightness contrasts. With these clues, the overall luminance problem appears as shown in the diagram.
contrast and luminance relations between
light and object colors
A much more common light effect is the result of changes in luminosity on a surface. We can move a surface from shadow to bright sunlight and back again. What is the effect on color?
The thing of surface diffusion.
light in diffuse reflection or specular reflection
The difference between actual and effective light energy becomes important when we change our distance and/or viewing angle in relation to the light source or reflecting surface. Both of these change visible light in contrasting ways.
Light from a perfect light diffuser, also known as a Lambert surface.
light diffusion by a lambertian and semigloss surface
For measures of effective power (light as received), illuminance and retinal luminance (lux and trolands) decrease with increasing distance, because the standardized surface area used to measure the light becomes a smaller and smaller part of the many directions the light radiates.
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The rate of this decrease is governed by the inverse square law: light intensity decreases by the square of the proportional increase in distance from the light source (double the distance, and you cut the intensity by 1/4; triple the distance, and you cut the intensity by 1/9, etc.). (Thus, when you compare light sources rated in lux rather than lumens, it's important to make sure that the distances used to make the measurements are the same.)
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 diffusion exactly compensated by foreshortening
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Similarly, illuminance and retinal luminance decrease with an oblique angle of incidence. That is, if a light shines perpendicularly onto an evenly diffusing (dull or matte) surface, the amount of light reflected from the surface is strongest in the perpendicular direction, and in oblique directions it decreases — in proportion to the cosine of the angle from the perpendicular. Thus, if someone standing several feet away from you at night shines a flashlight directly down onto the pavement, it appears bright to you because the beam is concentrated on a small circular area. But if he shines flashlight onto the pavement far to one side, the illumination will appear much weaker to you because the beam has been spread over a much larger surface area.
Constants of Illuminance/Luminance. For measures of actual power (light as radiated), luminous intensity and luminance (lumens and nits) do not change with viewing distance, even though lights or objects get fainter as they move farther away. For objects that have a visible size, such as a searchlight or light bulb, the finesse is that the visual size of the object also gets smaller and in the same proportion as the distance (the inverse square law again), which means the amount of light arriving to the eye remains constant for the visual area of the source. For all evenly diffusing (dull or matte) surfaces, luminance does not change with viewing angle either.
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The reason is that viewing the surface from one side foreshortens it, reducing its apparent size, which exactly compensates for the reduction in light diffused to that side. Thus, as long as someone else holds the flashlight beam steady, it does not seem to change actual brightness as you view it from different angles or different distances. And if you are holding the flashlight, the apparent brightness of the beam does not appreciably change as you shine it on surfaces at different angles of view, because your direction of view is the same as the line of illumination created by the light. The beam seems noticeably fainter only when you shine it on surfaces far away, because this reduces its illuminance.
luminance of white to luminance of light
This diagram extends the relationship between relative luminace from a surface and its apparent lightness (shown here) to the luminance necessary to match a diffuse light source of equal size.
The table below provides some context for luminance measures as the appearance of a sheet of white paper under different lighting conditions.
luminance of white paper
in different illumination contexts |
| illuminance context | luminance level
(candelas/square meter) |
| cloudy night no moon | 0.0001 |
| clear night no moon | 0.001 |
| clear night full moon | 0.01 |
| clear sky 1/2 hour after sunset | 0.1 |
| clear sky 1/4 hour after sunset | 1.0 |
| cloudy sky at sunset | 10 |
| subdued indoor lighting | 30 |
| gray sky at noon | 100 |
| average office | 120 |
| bright indoor office | 240 |
| precision indoor tasks | 480 |
| typical outdoor shade | 960 |
| cloudy sky at noon | 1000 |
| clear sky at noon | 10000 |
| noon sunlight | 39,300 |
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Because luminous intensity and luminance do not change across changes in viewing angle and viewing distance, the eye can rely on these as invariants in comparing the relative brightness of surfaces and lights in the world, at any distance or angle of view, provided we know how far away they are and from what angle we view them. In general, for a dull or matte 100% reflecting (pure white) surface, 1 lux of illuminance creates 1/π nits of luminance. That is, a white surface illuminated from overhead at 100 lux will have a luminance of 31.8 nits in any direction. (Luminance can also be used to describe extended light sources, such as light bulbs or fluorescent light banks, provided the surface area of the light source is standardized at one square meter.)
location of highlight and angle of reflection
The location of the highlight on a spherical object, as a proportion of the distance from the center of the form to its visual edge, is equal to the sine of the angle of incidence for angles from 0° to 45°, and the cosine of the angle of incidence for angles from 45° to 90°. The figure shows some representative values.
|  the proportional luminance of surfaces and lights |
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The simple procedure for estimating complementary color contrasts is important to learn for a second reason: it mimics the effects of a colored illuminant (colored light) on the apparent color of a reflective surface.
| surface & shadow color |
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A much more common light effect is the result of changes in luminosity on a surface. We can move a surface from shadow to bright sunlight and back again. What is the effect on color?
The reflectance curves we have used to discuss paint mixing are designed so that the illuminant is not taken into account. But to describe accurately the appearance of a surface, we have to know both the surface color and the illuminant color. The color we actually see is the subtractive mixture of the two.
the subtractive mixture of light and surface color
the product of a single illuminant on two complementary colored surfaces; adapted from Jeff Beall, Adam Doppelt & John Hughes © 1995 Brown University
The figure above illustrates the basic relationship: a red biased illuminant (right) acts to discount or proportionately reduce the reflectance from the "red" end of the spectrum. If the surface color is actually an ultramarine blue (center), its apparent reflectance (right) will contain much less blue in comparison to red than it has under "white" light. The resulting surface color will appear to be a dull red violet.
This is what we would expect if we mixed ultramarine blue with a red paint. So the mixture of surface colors with illuminants is subtractive. In the comparison of color mixing demonstrations, I mentioned that subtractive color mixing can be demonstrated by passing a single beam of light through two colored filters. The colored illuminant is "filtered" to begin with (its color is not white), and the colored surface subtracts from or filters this light before the light reaches the eye.
Metameric Colors. This subtractive mixing of surface and light source produces a fundamental color ambiguity: it is possible (and commonly happens) that (1) two different reflectance curves will produce the same apparent color under the same kind of illumination, including pure white light, and (2) colors that are apparently identical under one kind of illumination will appear different under another kind of illumination, even if both light sources appear to provide "white" illumination. These situations of metamerism involve metameric colors.
restricted light emission and metamerism
the product of a single illuminant on two complementary colored surfaces; adapted from Jeff Beall, Adam Doppelt & John Hughes © 1995 Brown University
The example above shows a simple but commonplace example. The orange and blue paints shown in the previous illustration appear to be very similar shades of green when illuminated by a predominantly green light source. (A related problem arises in the color of foliage greens under changes in daylight illumination.)
If you have already made some paint wheels, these are very convenient to test colors under different illuminations. A set of paint swatches of familiar paints or the complete paint selection from a specific brand is also useful.
Visual metamers are the subtractive mixture of the surface reflectance with the illuminant, two surface colors that appear identical under one illuminant can appear different under another illuminant. (This is the bane of automotive manufacturers, who have a difficult time getting all the plastics and fabrics in a car interior to match under all kinds of illumination.)
Object Shadows. The point with shadows is: how much do they darken, how do they darken across a form, and what effects do they have on apparent color or luminosity?
Shadows on a figure.
changes in chroma and hue in the shadows across a figure
The end.
Complementary Shadow Contrasts. Consistent with the general effect of chromatic adaptation is the specific phenomenon of complementary shadow contrasts. If a yellow colored illuminant shifts the implicit white point toward yellow, then an actual white or gray would appear to shift into the visual complement, deep blue. Shadows are perceived to be color neutral, and therefore they display this color shift — often quite dramatically.
As Martin Kemp points out, the methods for producing the effect, usually attributed to J.W von Goethe, were described several times in the 18th century. The French naturalist Comte de Buffon reported on complementary colored shadows and complementary afterimages to the French Academy of Sciences in 1742. Similar descriptions were published in England by the chemist Joseph Priestly and the entomologist Moses Harris in around 1780. These shadows signal a shift toward the "internal" or psychological consequences of color.
Buffon correctly
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I haven't experimented with a full range of lights, but the effect is quite easy to produce with two lamps and several colored light bulbs, such as large (exterior) Christmas tree lights or 50W colored floodlamps. (If possible, use colored lights that are higher wattage than the white, to correct for the fact that the colored glass blocks about half the radiated light, making the lights dimmer.)
The usual description is that the shadow cast by the colored light is the complementary hue of the colored light. In fact the effect is more complex, and depends on the relationship of the hue contrast to the CIELAB a*b* plane.
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 the appearance of a red/white shadow contrast experiment
 predicting the shadow colors of contrasting colored lights shadow colors are a mixture of
shadow shine and light source
complementary color |
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A red light produces a beautiful pale turquoise green (right), and a green light produces a rich middle violet, as we would expect from the complementary color contrasts defined by the visual color wheel. These hues have a significant contribution from the CIELAB a* dimension, and therefore appear clearly.
However, an amber light produces a relatively pale blue violet, and a blue violet light (I used a 60W blacklite bulb) does not produce any visible yellow, but rather a cold gray. This is because the hue yellow requires both high chroma and high lightness to be recognizable as such, but shadows by definition have low lightness. When darkened, the yellow appears more like a gray raw umber. Thus, the CIELAB b* dimension creates qualitatively different color contrasts — chromatically weaker at both ends, and more affected by a shadow's low luminosity on the b+ (yellow) side of the color space.
The data are summarized in tabular form on this page.
A tangential question: why do watercolor artists a blue violet or purple as a foundation for shadow colors? The answer is found in the mixture of skylight and the complementary shadow hue that combine as the tint of all shadow colors (diagram, right).
Under midday sunlight, the visual complement of solar "green" (at about 550 nm) is a purple (c550 nm), which our eye imputes to any absence of solar light (shadow). This subjective color mixes visually with the shadow shine emanating directly from the blue sky, which at midday has a dominant wavelength of about 470 nm. The result is a mixed hue that appears to have a blue violet tint intermediate between the two.
However, this mixed hue can change significantly across daylight phases. In the hours just after sunrise or just before sunset, the direct sunlight has a much lower color temperature, giving it a deep yellow tint (around 590 nm), which produces a visual complement equivalent to about 475 nm. At the same time the sky appears to have a cerulean hue, matching monochromatic hues above 480 nm. The resulting visual mixture is therefore closer to a middle blue or greenish blue than the shadow color at noon.
For these reasons watercolor painters often use a blue violet or even purple mixture (such as a dulled indanthrone blue or dioxazine violet, or a neutral tint) to tint shadows created by bright or outdoor illumination, but a greenish blue (dulled iron blue or phthalo blue, or an indigo convenience mixture) as the shadow tint for indoor or late day illumination.
And concluding remarks.
The interactive tutorial on color perception hosted by the Brown University Computer Science Department includes a java applet "Reflection" that explains the combined effect of surface reflectance and illuminant color on apparent color.
| special material colors |
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Several unusual color effects occur with special types of materials, our final topic. Many of these were lovingly described by J.W. von Goethe in his Color Learning, but without an adequate explanation.
Translucent Colors. Many materials can appear translucent under certain circumstances, passing heavily filtered light. This occurs in thin sheets of opaque materials (such as minerals or hides), and very thick blocks of transparent materials (such as glass or ice).
Metallic Colors. We conclude with the phenomena of reflections and the specific visual effects that make them compelling.
Reflectivity. A related attribute is the reflective or "glossy" appearance of any surface, from window glass to lacquered boxes. Vision researchers have established that the illusion of reflectivity is enhanced by the following elements:
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 daylight shifts
in shadow colorshown on the CIELAB a*b* plane |
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• intensity of specular reflectance
• distinctness of image (when the eyes are focused on the image behind the surface)
• increased contrast between light and dark areas of the image
• absence of haze or fogging.
And so on.
| physical color changes |
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Materials can easily change color depending on how they are viewed or how the materials themselves undergo physical change. As these materials can include paints, the artist needs to understand how these changes occur.
Color and Thickness. For partially transmitting substances, color changes with changes in the material thickness.
The basic process is that the spectral transmission curve can be established for any arbitrary (usually relatively small) thickness of the material. This is the light transmitted from a "white" light baseline. If the material is thickened, the effect is the same as passing the light through a second or third layer, except that now the light is not white but is already filtered by the first layer. Essentially the transmission profile is multiplied by itself, so any area of the spectrum that is not transmitted at 100% is reduced each time. This darkens the color and causes a characteristic hue shift.
the shift in color caused by increased thickness of materials
In general "warm" colored (warm red, yellow or orange) substances become redder. "Cool" red, violet and purple substances remain approximately the same hue, only darker. Blues shift toward purple and cyans toward blue. Greens shift toward a middle green — yellow greens become cooler and blue greens warmer.
|  reflectance curves for characteristic surfaces |
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Color and Illuminance. In this case the intensity of light is increased and passes through what was an opaque appearing substance.
Color and Whitening. This shift occurs either because a paint has been diluted with water or lightened by mixture with a white paint, which in watercolors is limited to chinese white (PW4) or titanium white (PW6). In both cases, the light reflected by the paint is mixed with a significant amount of white light, but the either light reflected from the paper or the white paint. The hue shifts caused by white paint are governed by additive color mixing, because the light from the paper and the paint arrives separately to the eye, where it is "mixed" by the averaging across millions of cone responses.
Why does merely lightening a paint cause these shifts occur? Two separate processes are at work.
The fundamental explanation is simply that hue is derived from the proportional stimulation of the L, M and S cones, and these proportions change as white light or white paint is added to a color. The figure below shows how.
 
 
change in hue caused by adding white light
The reflectance curve at the top shows an idealized spectral curve for a highly saturated orange paint, with a hue similar to perinone orange (PO43). The cone response profile shows that the curve strongly stimulates the R cones and less so the G cones, with no response from the B cones.
Remember what the relative height of a reflectance curve means: when the profile is at its maximum of 100%, all of the light from those wavelengths is reflected by the paint. When the curve is at its minimum of 0%, then none of the light at those wavelengths is reflected by the paint.
By adding reflectance from the paper, we do not raise the maximum reflectance: if all the "red" light is reflected by both red paint and white paper, we don't increase the amount of reflected "red" light by mixing the two. Instead, we raise the minimum reflectance, because light absorbed by the paint is supplied by the paper (or white paint). This changes the cone response profile exactly as if we had started by shining a red orange colored light on a sheet of white paper, and then lit the area with a second, complementary (blue green) light.
direction and size of hue shifts caused
by adding white light
The diagram shows the net effect of these various changes for hues all around the color circle. The basic rules are simple to remember: scarlet to yellow warmer, red, magenta, blue and green cooler, scarlet, lemon and violet unchanged.
These are the shifts that occur while the eye is still daylight adapted. An additional shift toward blue green occurs when the illumination is at the point where both the rods and cones are active. The cones respond most to "blue green" wavelengths, and therefore contribute a distinct blue green bias to apparent colors. This Purkinje shift causes greens to appear relatively more luminous, and oranges and reds to appear dull and even dark gray or black.
N E X T : tonal value
Last revised 01.12.2004 • © 2004 Bruce MacEvoy
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