Terachrome Color Science

The Color Science of Terachrome

Efforts to quantify and synthesize color have occupied humans for millennia, including some of the greatest scientific minds of the 19th and 20th centuries. The field has had many successes and yet remains unmastered. A key challenge is that past approximations are not sufficient for modern technology. What worked for broad-spectrum incandescent sources has problems with solid state LEDs.

The following visualizations arose from the fundamental research leading to Terachrome’s color synthesis. We hope this provides a feel for the technology without the fairly extensive science and math required for precise description.

1 - Emitters

This shows radiant intensity vs. wavelength for three LUXEON LEDs as measured by a spectrometer, with the curves colored according to their apparent hue. These form primary colors which are sufficient, in theory, to synthesize all other colors.

2 - Color Gamut

Here is a chromaticity diagram, a representation of all human-visible hues, with a superimposed triangle showing the region of colors that can be synthesized by mixing the three primary light sources above. Because web pages cannot reproduce the entire human gamut, the displayed colors are only approximate.

3 - Luminance Gamut

A problem with color gamut [2] above is that it does not show the differing brightness over the gamut. To the left is a three-dimensional representation where the Z-axis shows the luminance of each hue in the gamut. Note that the peak luminance is not white. This is a function of the relative intensities and wavelengths of the emitters [1].

4 - Device Colorspace

This Terachrome innovation combines gamuts [2] and [3] into a simple diagram illustrating the color mixing capabilities of a set of primary colors. The triangle center is the peak luminance, the vertices correspond to emitters, and the perimeter shows maximum saturation. In this example one can see that green is weak and peak luminance is pink.

But What About Aesthetics?

Sometimes three primary colors are not enough. Luminaire color rendering relies on light energy over the entire spectrum. Gaps in the spectrum, such as the “valley” between green and red in [1] above, can cause metameric failure, where different colors appear to be the same. For displays, narrow spectral bandwidth is associated with greater observer variation where people see the same light energy as different colors. An excellent cure for this is to broaden the spectrum with more primaries, also enabling more colors by increasing the gamut. Unfortunately more primary colors create a mathematical challenge resulting in visual artifacts that severely compromise the aesthetics. Solving this problem is a key Terachrome achievement.

(In mathematical parlance, the system of equations involved is nonlinear and underdetermined, but numerical solvers are inherently noisy. Terachrome’s algorithms employ fast analytic techniques instead. Conventional wisdom says that color mixing is linear. But consider the sharp edges and curved lines of luminance gamut [3]. This is neither linear nor continuously differentiable.)

5 - Seven Emitters

This shows radiant intensity vs. wavelength for seven LUXEON LEDs as measured by a spectrometer, with the curves colored according to their apparent hue. More primary colors increase the available hues, improve color rendering, and reduce observer variation.

6 - Larger Gamut

More primary colors allow a polygonal gamut that can more closely approximate human visual capabilities. Compare this with the three-primary gamut [2] above.

7 - Device Colorspace

Like the three-color device colorspace [4] above, this shows the color mixing capabilities of the chosen set of primary colors. Green is still weak, but the secondary colors (cyan, yellow, and magenta) are far better than before.

8 - Luminance Gamut

The illustrations below show the seven color luminance gamut viewed from several directions. Please note the facets, which are inherent to human vision and the cause for many challenges in color mixing. These models required special plotting software for rendering.