How we see: Divorcing Biology from Physics
Many people will remember the colors of the physical spectrum from a high school (secondary school) or university physics class. In such classes, students are taught the mnemonic “ROYGBIV” for red, orange, yellow, green, blue, indigo and violet. As a result of this training, people learn that different colors occupy different ranges within the “visible spectrum”, and that each color is distinct based upon its wavelength. While this model works great for astronomers studying absorption spectra for stars, studying human stars through a telescope is generally a fast ticket to a restraining order. Instead, biology has a different idea of how to handle the visible spectrum, and it is quite a bit different than what the physicists use.
In the human eye, there are sensors called “rods” and “cones” that actually create the nerve impulses in response to light. Rods and cones can be subdivided into four different functions. Three different types of cones are responsible for what we see as red, green and blue. A fourth type of sensor, rods, provides humans with their night vision.
Where the biology really leaves the physics behind is in how these sensors respond to the visible spectrum. Instead of distinguishing between different wavelengths like one might expect from the ROYGBIV model, each type of rod responds to a range of wavelengths, much like a bandpass filter (physicists think in terms of absorption spectrum). Given this broad range of sensitivity, a given combination of wavelengths will appear as a particular color to the brain, but those combinations are not unique. In other words, a combination of wavelengths may produce an emerald green color, but they will not necessarily be the only combination of wavelengths that produce emerald green. One thing that the eye does do well, though, is to distinguish between quantities of light. We will perceive the same emerald green differently depending upon whether there is a lot of light or a little.
While the wavelengths present do control what color we see, rods are sensitive to varying degrees for each wavelength. As one might expect, there is one or more peaks where the individual rod is most sensitive, and then its sensitivity falls off rapidly for longer and shorter wavelengths. As a result, what we see as one “color” is actually an amalgamation of wavelengths. Conceptually:
- The color green peaks at around 550 nm, and dominates how humans sense illumination.
- The color blue peaks at around 440 nm. Interestingly, we are least sensitive to blue intensity, but are more sensitive to color deviations in blue than in either green or red.
- The color red is actually bi-modal (two “humps” in its sensitivity distribution) with the main peak at around 600 nm, and a smaller peak at around 440 nm.
Collectively, red, green and blue are considered the primary colors in an emissive color model. We can then derive secondary colors as combinations of the three primaries:
- Cyan is a combination of blue and green.
- Magenta is a combination of red and blue.
- Yellow is a combination of red and green.
What we perceive as white light is actually all of these primaries combined in a defined proportion of red, green and blue. Our concept of white is actually relative – the human eye adapts to its environments and perceives as white the maximum intensity to which it is currently sensitized. This is why white can be redefined by various standards-setting bodies based upon their needs. The implication of this is that what we perceive as black is actually the result of no light being produced, and the color gray actually contains the same mix of red, green and blue – just at a lower intensity level than the current reference white!
For most displays, the colors of the primaries are relatively fixed by the manufacturer (e.g., phosphor colors for CRTs, dichroic filter colors for digital displays). There can be some latitude here by making adjustments to a display’s primary color matrix, but this is a super advanced adjustment. On the other hand, the secondary colors can be adjusted by changing the mix of the constituent primary colors…but more on that later.
Measuring Color: the ABCs of XYZ
Because everybody is slightly different, and each of us probably sees colors in slightly different ways, the CIE (Commission Internationale de l’Eclairage, the international body responsible for the measurement of color) established a theoretical model called the standard observer in order to provide analytical consistency to how colors are measured. As a result, they also established three baseline measures of color that align with the three color sensors in the human eye: X, Y, and Z (the capitals matter, by the way):
- X corresponds with the intensity of light perceived (spectral power distribution or SPD) by the “red”cones,
- Y corresponds with the intensity of light (SPD) perceived by the “green” cones, and
- Z corresponds to the intensity of light (SPD) perceived by the “blue” cones.
Because the eye adapts to the amount of light that is present, the amplitudes of the spectral power distributions for X, Y and Z are relative, rather than absolute, the values for X, Y and Z are usually presented in a normalized form. Since the Y value corresponds to how the eye senses the quantity of light, X and Z are scaled against it when they are normalized. The most common methods are to scale Y in the range of 0.0 to 1.0 or 0.0 to 100.0. The XYZ Data Grid in CalMAN shows the raw XYZ values returned by the meter, but the xyY Data Grid shows Y values normalized in the range of 0.0 to 1.0.
While X, Y and Z loosely relate to red, green and blue, it is not really exact. Instead, X, Y and Z each contribute to our sensation of red, green and blue in varying proportions. The reason for this is because there is not a true definition for “red”, “green” and “blue” in nature. Instead, a color standard defines what constitutes each of these primary colors, and depending upon that definition, varying amounts of X, Y and Z are needed to produce that color. In other words, think of XYZ as the “raw” data, and “RGB” as the finished product. Since Y determines how the eye perceives the quantity of light, X and Z only really affect our sensation of the color of light the eye is receiving.
Red, green and blue add together to produce white light (Grassman’s Law). In XYZ notation, this is the same as Y.
While XYZ are the basic color measurements, the CIE also developed a Cartesian system for presenting color information independently of its intensity (the CIE Chromaticity Diagram). There is a defined algorithm for converting XYZ data into xy coordinates. However, you need to have the Y data as well to have a complete specification of color (xyY).