Measuring, and predicting, colors
Ideally, the color of something (a colored patch on screen, or a physical object) is determined with a spectrophotometer. The amount of light at every wavelength (in practice, a group of wavelengths at 5nm, 10nm, or even 20nm spacing) is measured.
For colors on screen, the white is also measured. For physical colors, the light which is illuminating the object (the amount of illuminant light at each wavelength) must also be measured.
The spectrophotometer can then calculate the XYZ and Lab or LCH values.
Objects measure very differently under different lights. They also look different, but much less so (this is called color constancy). The process whereby our eyes change from seeing one color as white, to seeing another color as white, and finding that most objects look similar to what they did before, is called chromatic adaptation.
As long as we retain the original measured spectral data, we can calculate what the object would have looked like under any other illuminant.
Often though we don't have the spectral data; either it wasn't saved, or the color was measured by a colorimeter which just passes the light through three filters and directly reads out in XYZ.
If you have a color measured under one illuminant, the corresponding color is another color which looks the same under a second illuminant.
A chromatic adaptation transform is a way of predicting the corresponding color.
To save the trouble of measuring illuminant spectra all the time, standard illuminants exist.
For example, Illuminant A is the orangeish light produced by a tungsten electric lightbulb (specifically, one with a filament temperature of 2,856K).
Illuminant C, an early attempt to simulate natural daylight, is Illuminant A with a specific blue filter. (it is rarely used nowadays, but there is a lot of experimental data measured with it so it is useful to adapt from).
Illuminant D65 represents the light in the shade (no direct sunlight) at noon, and has a color temperature of 6500K.
Illuminant D50 is similar but represents direct sunlight at noon. Illuminant F2 is a particular type of fluorescent lamp, and so on.
However, you can measure the specific type of light in a given situation and use those measured XYZ values, if you want. To allow comparison, the XYZ values are normalized, so that the Y value (luminance) is exactly 1.
Types of Chromatic Adaptation Transform
There are different chromatic adaptation transforms (CATs), which vary in complexity and accuracy.
If the first illuminant is, say, D50 (XYZ 0.96422, 1.00000, 0.82521) and the second one is D65 (XYZ 0.95047, 1.00000, 1.08883), the XYZ scaling method says hey, to go from one white to the other, we just scale X by 0.96422/0.95047 and scale Z by 0.82521/1.08883. Simple, let's do exactly that to all the other colors.
This doesn't predict corresponding colors at all well so we don't implement it. But you can do it yourself if you want:
let W1 = Color.whites.D65; let W2 = Color.whites.D50; let Xscale = W2.x/W1.x; let Zscale = W2.z/W1.z; let color = new Color("rebeccapurple"); let color2 = color.xyz /// aah nevermind this isn't going to work
Named after an early 20th century color scientist, this method converts the first illuminant from XYZ to cone responses (the relative stimulation of the three types of cones in the human retina). Same for the second illuminant, and a cone scaling is calculated to go from one white to another. This scaling is used to change all the other colors: convert XYZ to cones, scale, convert back to XYZ.
von Kries works much better than XYZ scaling, as long as the two illuminants are fairly similar to daylight, and the colors to be adapted are not very saturated.
let W1 = Color.whites.D65; let W2 = Color.whites.D50; let color = new Color("rebeccapurple"); // okay this isn't going to work either
Invented by Lam at the University of Bradford, this method uses modified (sharpened) cone responses with less overlap between the three cone types. While this doesn't represent the actual physilogical responses, it does give better predictive accuracy. The originally published CAT also incorporated a correction for the non-linear resonse of the short wavelength ("blue") cone. Later studies found that this correction did not significantly improve accuracy, and prevented round-tripping, so it was dropped. The simplified (linear) bradford transform is what we implemented.
The International Color Consortium, when they were tightening up the specification of ICC color profiles, specified that the linear Bradford CAT must be used by all ICC software.
Linear Bradford is thus our default CAT. If you specify a color in, say sRGB or display-P3 (both of which use a D65 whitepoint), and then convert it to LCH (which uses a D50 whitepoint), the XYZ values are automatically passed through a linear Bradford CAT before being converted to Lab and then LCH. Normally, this is exactly what you want, and gives compatibility between our code and results obtained via ICC profiles.
At the close of the 20th century, the International Lighting Commission (CIE) came up with a color appearance model which used a modified form of the original, non-linear Bradford CAT. It has since been superceeded by later models which are more accurate, easier to calculate, and more numerically stable. We therefore haven't implemented CAT97s.
Based on early experience with CAT97s and the result of a lot of numerical optimization to give the best predictive accuracy on a large dataset of corresponding colors, CAT02 has entirely replaced CAT97s. Like the Bradford method, an optimized, sharpened set of cone responses is used.
CAT02 also allows for partial adaptation to the new whitepoint. When the illumination changes, Fairchild & Reniff measured that our eyes become 60% adapted in a couple of seconds and are 95% adapted after 90 seconds. Because it is difficult to measure the state of adaptation, we implemented the simplified, fully adapted CAT02 transform.
CAT02 fails to predict corresponding colors when the illuminant is very far from daylight such as vividly colored stage lighting.
TODO how is this better than CAT02.
CAT16 gives somewhat better predictions that CAT02, particularly with vivid non-white illuminants.
CAT16, as originally published, has been criticized by Smet & Ma for incorrectly scaling by a reference white luminance, which is usually but not always 1.0. Our implementation omits this scaling, which is becoming recommended practice.
CAT16 defines both a one-stage and a two-stage CAT; in the latter, colors are first adapted to an equal-energy white and then to the destination white in a second step. We have only implemented the one-stage CAT, which gived idential results for full adaptation.
By default, only linear Bradford is available and only two whitepoints are supported: D65, as used by most RGB colorspaces, and D50, as used by Lab, LCH, XYZ and also ProPhoto RGB and most CMYK colorspaces. Attempting to use another whitepoint or a different method will give an error.
let color1 = new Color("p3" 0.22 0.63 0.42); // D65 white let color2 = new Color("prophoto" 0.15 0.54 0.21); //D50 white color1.lch; // linear Bradford was used to adapt to D50 before conversion to Lab color2.lch; // no CAT was needed, whitepoints the same
The optional CATs.js module uses an extension hook to add a number of other standard illuminants, and several other CAT methods. Because these are all one-stage linear transformations, the choice of source whitepoint, destination whitepoint, and CAT method produces a single matrix transform, which our code will automatically use whenever the source and destination colorspaces have different whitepoints.