To most people, color is a pretty simple thing. It’s just something we see. To us nerds, it’s often just a combination of three prime color values or an index into a palette. But color is much more complex when we look at it in a more general, physical setting. In fact, to characterize the color of all the things we see around us day to day we need immensely more representational power than the three primaries commonly used to describe color. In this text, I’ll try to recount some interesting facts about light, optics, color perception and computerized representation of color. I aim to develop a functional description of color in the wide sense of the word, and to display that current representations of color can fail rather badly in many circumstances.
Color as we know it is just a pale, perceptually filtered depiction of what is going on in a very thin slice of the whole spectrum of electromagnetic radiation. Even within the band of visible light, the composition of this radiation can vary greatly while humans are only capable of receiving a greatly diminished description of the true diversity present. The processes shaping visible light are many indeed. Arriving at a comprehensive functional description of optical processes around us requires us to first delve into the physics of light.
We know from quantum mechanics that there are two ways of seeing light: as particles (photons) and as waves (electromagnetic radiation). In the first framework, light travels as photons, massless particles, and goes in straight lines. Each photon has its own energy, which determines its quantum mechanical wavelength, and so color. This wavelength can vary continuously, so there are an infinite variety of colors of electromagnetic radiation. The wavelengths we can sense as light range from TEMP!!! to TEMP!!!. Longer wavelengths first become infrared (or heat) radiation, then as the wavelength grows still longer microwaves and ordinary radio ones. The shorter wavelengths range through ultraviolet radiation to X‐rays, nuclear gamma radiation and high energy cosmic rays.
The shorter the wavelength, the better localised the particle and the higher its energy. This means that a given power of radiation will require significantly higher numbers of long wavelength photons to achieve, and those photons will be very poorly localised. While cosmic rays are best studied as singular particles, radio yields better to statistical analysis, and the idea that we’re actually dealing with a continuous wave motion instead of a sea of individual photons. Light somewhat straddles this boundary. This means that there are a wealth of interesting optical phenomena out there.
These two ways of seeing light are complementary and essential to understanding color: at the atomic and molecular levels, quanta are often the only way to understand how light behaves. On the other hand, there are a multitude of pure wave phenomena associated with the large scale behavior of light. Between these domains, there is the weird domain of quantum optics, where both descriptions have to be used simultaneously, and the analysis resorts to pure quantum physics.
‐dense vs. continuous spectra ‐color as a spectrum
One of the funkier properties of light is that photons do not interact with other photons. We say that they obey Bosen‐Einstein statistics, whereas matter behaves by Pauli‐Dirac ones. The principal difference is, there is no exclusion rule in effect. Arbitrary numbers of photons can exist in the precise same coordinates at the same time; more generally, in the same state. To each photon the universe looks completely devoid of other photons. This means that photons of different wavelengths can be freely mixed, and that light practically always comes in such a mixture. Thus we need a way to quantify the composition of light.
A spectrum is a plot by wavelength of the relative amounts of different wavelengths in EM radiation. It is normally drawn based on amplitude, and as is usual in perceptual applications light colorimetry, the scale will be logarithmic. What we get is a function telling us how much of each wavelength there is in a given sample of light. The function is always nonzero (there’s no such thing as antilight), and the definite square integral of a spectrum drawn on a linear scale will give the total amount of power between two frequencies.
There are two basic kinds of spectra. The first is a discrete, or line, spectrum. There all the energy is concentrated on single frequencies of which there are usually only a finite number. This means that in order for there to be electromagnetic energy at all, the amplitude at these frequencies must technically be infinite. There will be spikes visible in the spectrum. (For the pedantic ones, what we call spikes are actually delta distributions, which of course aren’t functions at all.)
The second kind of spectrum is the continuous one. Any single frequency will have zero power, but any range might have a positive amount. There are no spikes, but a continuous distribution of power over continuous ranges of frequencies.
Actual spectra may contain both discrete and continuous elements. Spectra are also used to describe processes in addition to just samples of light. Instead of depicting the composition of light emitted by an object, we might ask what comes out when an object reflects light with a given spectrum, or when light passes through the object. We can see that spectra are highly useful as a complete summary of what’s going on in a homogeneous sample of light, and can also be used to summarize processes affecting light in transit.
‐continuous vs. discrete (esp. monochromatic) sources ‐quantized transitions in electron orbitals ‐quanta emitted by such transitions ‐absorption vs. emission spectra
‐reflections ‐diffraction (CD’s!) ‐refraction ‐dual refraction in crystals ‐polarized light ‐birefringerence ‐differences based on angle of incidence (no spectral effects⇒reflectivity coefficient applicable; spectral effects⇒spectra against angle sufficient) vs. total freedom (only spectra against two angles of incidence for each angle of incoming light for each point sufficient) ‐holograms as an example ‐example of true anisotropy: Nokia 6150 cover ‐translucency+directional dispersivity and directional color for both reflected and dispersed light make things real complex!
‐fluorescense and phosphorescense ‐solitons and dispersion in crystals
So we see that the physical processes which give rise to a sensation of color are manifold. We’ll now turn to how we perceive light which has already been shaped by the environment, and is entering our eyes. This is also where the story will suddenly begin to sound familiar. While the physics is complicated, perceptual is suddenly quite easy to describe via the extremely simple framework of tristimulus theory,
‐three primary colors: RGB ‐their pigments ‐spectral response of the pigments ‐what was the linearizing scale for the responses? ‐blue is separate!
‐weighted continuous average of an incoming spectrum by the response curves ‐emissive color only needs to control the average excitation but absorptive color needs to be exact in order to account for all possible source spectra! ‐mutual overlap of phosphors/inks plus their spectra plus their maximum intensity set the limits of a color space
‐color evolved as an afterthought! ‐perception is differential between red‐green and blue‐yellow ‐notice: yellow=red+green! i.e. blue is very different with an even lower resolution ‐evolutionary need for differentiation of equal intensity objects ‐perception tilted towards the day time spectrum of the sun (no infrared!) ‐intensity and color pathways are separate (color cannot move!) ‐intensity perception is differential too⇒constancy of color
‐some unknown receptors are present ‐subjectivity in color perception ‐color blindness quite common ‐pigment sensitivities vary? ‐separate night (rhodopsin, rod) and daylight (∗3, cone) receptors: colors not seen in the dark ‐the poor space resolution (/2) of colors wrt intensity ‐intensity saturation (blinding) and refractary effects ‐neural limitations ‐sharpening processor/lateral inhibition
‐coordinates and transformations
‐mainly linear transformations (but: La*b*)
‐perceptual uniformity
‐separation of hue
‐saturation and lightness or some such…
‐pure colors from monochromatic sources!
‐conjugate colors and their dependence on the color space chosen
‐cyclic hue maps ("color wheels") are very artificial
‐naïve, useful, used as palette color as well
‐CMYK/print color
‐natural since intensity is a separate ‐saturation kind of artificial color as specified by monochromatic signals is quite artificial as well
‐any property can be attached to a palette entry⇒great power of representation