1. White is Green

It sounds philosophical, and probably is, but that phrase refers to Hal Glicksman's RWB color theory in which white replaces green as a primary color. More than that, white is defined as a very bright green. Sounds deuteranopic to me.

Reviewing the color theories of Johann Goethe and Ed Land it all makes more sense. Color as percieved by the human eye (or as translated by our brains) is a complex system not perfectly mapped to wavelength.

(In an epithany I realized this is the same phenomenom that makes some red wine appear purple, which 2 year old Olivia confirmed this evening.)

Goethe's work resulted in a color wheel only slightly different than our modern color picker, and introduced the notion of complementary colors. The wheel contined six colors, as opposed to Newtons seven (ROYGBIV) and connected the red and violet ends of the spectrum through the nonspectral color, magenta.

                     Magenta Red       
                 Violet         Yellow
                      Blue Green    

2. Color ...

Photons of light activate color receptor cells - the cones of your eyes. There are three types of cone, S, M and L. S cones are activated by photons with wavelengths between 400 and 500 nm, M cones respond to photons between 450 and 600 nm and L cones are sensitive between 500 and 700 nm (the graph above shows the relative spectral response of each receptor type.)

The three signals from S, M and L cones are combined in your occipital lobes producing the colors you see. (The pictured lobe belongs to and was imaged with funtional MRI by Alex Wade of Stanford.)

The choice of red, green and blue as primary colors appears to be driven by the physiology of light detection, that is, red light will mostly activate L cells, green light activates both M and L cells, and blue light activates mostly S cells. Colors are blended when activation of two or more types of color receptor is activated.

By selectiing wavelengths targeted to switch on only one of the cone types, colors can be mixed the largest posible gamut, or range within the colorspace of your eye. Previously the colors emitted by an lcd display were presented. Here is the spectrum of a CRT with phosphors well matched to normal human color vision:

Are three primaries really necessary for a full range of color?

Since 1810, it has been accepted that colors must be represented in a connected line, rather than by the linear spectrum alone. The spectral colors are connected through a mixed color, magenta. This forces the 'color line' into a closed loop.

The color wheel shown above, is the CIE chromaticity diagram, a way of organizing the range of possible colors acording to calculated parameters. The gamut, or 2 dimensional range, of colors possible for any set of primary colors are inside a triangle inscribed within the CIE diagram. The chosen primary colors are the verticies of the triangle. Here is a page from the fantastic York University website that explains the CIE diagram in more detail.

In fact, it is possible to convert between any two chosen sets of primary colors using just a bit of matrix arithmetic. For example,

|G| = |17.5-1.07-3.7| X |CMY|

Will convert cyan, magenta and yellow triplets to RGB values on my Powerbook's screen. Expanding this, any number of primaries can be converted to any other number of other primaries, by choosing the appropriate conversion matrix. The entire spectrum of a color can be encoded into three or more primary colors. More primary colors will result in a larger range of color, but two additive primaries are not enough to define more than a tiny portion of colors along a straight line.

Next: mutants with superpowers and colorblindness and I experiment on myself.

3: Brightness matching experiment:

Using Photoshop I made six rectangles of 450 by 220 pixels. One half of each rectangele was filled with one of six colors, and the other half of the rectangle was filled with gray. A plastic tube was placed over each rectangle so the brightness of the color and gray the gray section was adjusted with Photoshop's 'Lightness' control in the 'Hue and Saturation' dialog, until the brightness of the gray matched the brightness of the color. The brightness of the gray was then read with Photoshop's 'Info' tool.

In the Hue-Saturation-Luminance colorspace, the luminance parameter approximates the visual brightness of the color. The Luminance values (as calculated by Photoshop) are compared to the brightness that I estimated with my own vision:

Color RGB   est.
 lumin. Δ
Red FF0000  53%  57%4
Yellow F6FF00  80%  95%15
Green 00FF00  62%  79%17
Cyan 0087F9  56%  62%6
Blue 0000FF  46%  51%5
Magenta FF0081  48%  52%4

These data are illustrated by the following graph:

In the top portion, my estimated brightness is plotted with blue circles and the calculated luminance values are plotted with red triangles. In the bottom portion, the delta value - the difference between the luminance of the color and my estimated matching gray brightness - is plotted with black Xs. The Y axis is percent.

Notice the close agreement between brightness and luminance for red, cyan, blue and magenta. On the other hand, my estimates for yellow and green are dimmer than their luminance would predict. This is consistant with deuteranopic colorblindness, which I have been aware of since second grade.

Here are some links:

Ishihara color vision test
Vischeck colorblindness simulation software

Visually harmonius color mixing software
Additive and subtractive color mixing

Color space geometry explained
Jentronics color space conversion software

And, as promised, tetrachromatic mutant women.

Next: Opponents, rods and Goethe's hypothesis.

Although it is contrary to the predictions of tricolor theory, a wide range of colors can indeed be mixed from only two primaries.

In the following experiment, you will see for yourself how closely a dichromatic image matches a three color version.
Where do all the colors come from when there are only two primary colors? ... Stay tuned ...

4. Color Mixing

no filter
The picture at right is un-retouched, taken with sunlight, from a window, a 100 watt light bulb and the camera's flash. To recreate this photo using tricolor theory, three separate photos were taken from a stationary camera: one through a red filter, another through a green filter and the third through a blue filter. This filtration was done with (very expensive) pieces of colored glass, not by separating the channels in Photoshop.

red filter
green filter
blue filter

R + B + G filters
Now these separate images were combined using Photoshop's channels into a single image, seen at right. (An error caused by not matching the transmittance of the filter to the luminosity of the color lead to darker blue hues.) The (synthetic) colors in this image are within the colorspace defined by colors of the three filters.

As 'discovered' by the brightness matching experiment, my own eyes have attenuated response in the middle of the spectrum, in an area corresponding to the M-cone's sensitivity, giving me only two color receptors. What color space will result in an image by mixing only two filters? According to tricolor theory, two colors can only mix to make a small subset of colors - those that lie 'between' the two primaries. But experiments of Edward Land and Johann Goethe showed that dichromatic color (that is, color derived from two primary colors instead of three) could result in a large color space.

Mixing red and green light makes (orange) yellow light, so mixing the images made using the red and green filters in equal proportions (with Photoshop) result in a yellowish image, shown below on the left:

R + G filters

yellow filter

On the right is an image taken with a yellow filter. The color of these two images are very similar. The tricolor image above is made by mixing red, green and blue in nearly equal portions. Can a yellow filtered image replace the mixture of the red and green filters?

yellow filter

blue filter

Y + B filters
Here (at right) is a mixture of the images made with the yellow and the blue filters. (The yellow and blue images are shown at left so you don't have to scroll up.)

Although there are obvious color shifts (remember, blue is dimmed by a filter factor error), this image includes a wide range of colors including reds and greens not included in either of the parent images!

Here are the three 'full color' images:

no filter

R + B + G filters

Y + B filters

Although the three images are not identical, it appears that a larger range of color can be produced by mixing only two primary colors than tricolor mixing theory would predict.

Here are the transmission spectra of the four filters used in this experiment:

From top to bottom, they are
    Red - B+W #090 (Wratten #25)
    Yellow - B+W #023 (Wratten #15)
    Green - Tiffen #61 (Wratten #61)
    Blue - Tiffen #47 (Wratten #47)

5. Remember the colorblind test, those circular images made up of a bunch of tiny circles that formed a number in a distinctive color? Or, uh, maybe you see a nice random pattern? The Ishihara test [1] uses colors that can be confused, such as unsaturated greens, pinks, and beige's to identify color vision anomalies.

Go try this Ishihara Quickie Test to see how it works.

Plate 21 presents an interesting phenomenon. Deuteranopes can see a figure, while "normal" eyes cannot. The distinctive color we see in that image is synthesized from dichromatic data coming from two (instead of three) types of cones. You can see more synthesized colors with the after image effect, color fringing and my filtration experiment.

In order to explain this, the opponent color space has been devised, with three axes: red/green, blue/yellow and black/white (which is also called luminance.) Opponent color explains synthesized colors: yellow comes about by removing blue and green results from reducing red's contribution to the overall brightness. In this way, colorblind people can see a whole range of colors that tricolor theory would suggest cannot be seen by someone without M (green sensitive) cones. [2]

Opponent colors can be translated to tricolor coordinates:

[r,g,b] = C X [r/g, b/y, w/b]

where C is an appropriate 3X3 matrix. [3]

adapted from a diagram at York U.

The new color space arises from the interconnections between neurons within each eye. The diagram at right is a schematic of those connections. You can think of the output channels as the red channel, the blue channel and the white channel. Although deuteranopes lack M cones, thus cannot code green directly, it is synthesized by being not blue, yet not red. The green we see, however is not qualitatively the same as yours.

The red, blue, white colorspace reminds me of the starting point for this exploration. Did Goethe really see this colorscheme through his prism? Stay tuned, I'll try to recreate his observations in the conclusion. References:

1. How the Ishihara test is made.

2. A. Orazem and H. Scheibner A, Der Ophthalmologe volume 94, number 3, March 25, 1997 - a perceptual mapping of the deuteranopic colorspace as a subset of the CIE chromaticity diagram.

3. RGB to opponent channel conversion matrices (B. A. Wandell, Foundations of Vision, 1995)

Hurvich and Jameson, recreated the spectrum by mixing opponent colors in 1955 and Ewald Hering translated the color wheel into the four opponent colors in 1920

There is an alternative process that may also explain color synthesis, rod cone interactions:

Brenton and Cowen ( J Opt Soc Am. 1981 Oct;11(10):1220-3) Rod-cone interactions account for wide field trichromacy

Kilavik and Kremer (Retinal Physiology preprint 1999) Rod and L-cone Interactions in a Deuteranopic Observer

Kremers and Scholl (Vis Neurosci. 2001 May-Jun;18(3):339-51) more rod cone interactions

6. Eine wenig Geschichte:

I'm reading Goethe's Theory of Colors that I got from the college library. The book has an introduction by Deane Judd, an expert on the psychological impact of color, who wrote:

Some of the explanations are correct, but most of them spring from Goethe's own version of Aristotle's view of color, largely repudiated and so far unproductive.
Here's Goethe's work in a historical timeline:

1859  Robert Bunsen and Gustav Kirchoff invented the spectroscope
1840  Charles Lock Eastlake translated Theory of Colors
1810  Johann Goethe wrote Theory of Colors
1807  Thomas Young published the wave theory of light
1671  Robert Boyle developed a color theory
1665  Newton's experiments and theory of light
c340 BC  Theophrastus, a student of Aristotle, mused on color

I want to finish the book at the beach next week.

7. Recall that I'm reading Goethe:

From these three, light shade and colour, we construct the visible world, and thus, at the same time, make painting possible, an art which has the power of producing on a flat surface a much more perfect visible world than the actual one can be.
[Johann Goethe, Theory of Colour 1810
One of the essences of Goethe's theory is that colors result from an effect of the eye. When light is separated from darkness, yellow and blue result. In his famous experiments, Goethe looked at light and dark surfaces through a prism. Here is a look at my studio through a liquid filled prism, as Goethe is likely to have used:

There is a blue fringe atop bright areas, and a yellow edge to the top of dark areas. Moving closer to the bright lines of sun light revealed more colors, still mixing to white in the center:

When a modern flint glass prism (nD = 1.65) is substituted for the water prism (nD = 1.33), the dispersion is greater and the full spectrum is obtained.

The same area imaged through the Amici compound prism (nD (eff) = 4.95) that I use for stellar spectra:

It appears that Goethe's prism experiment may have been constrained by the equipment he had available. Green, it seems is green.

The painting at the top of this article shows the view through a prism of light - color's effect on the emotional state. Although there is no green paint, an examination of the full size painting [900K] reveals greens in abundance. The opponent nature of color - it remains a mental construct, as yet undiscovered (yet!) by science - is reflected in a painting of one's own psyche, 'more perfect than the actual one is.'

8. The Exam