Color and Colorimetry – Part 3

The human visual system (HVS) sees color using a set of three overlapping filters, which are extremely broad. As a result, the HVS is completely incapable of performing any precise assessment of an observed spectrum.

What we perceive as color is based on what might be called the envelope of the true spectrum: the result of smoothing in the frequency domain. Fig.1 shows symbolically one of the filters of the HVS. The output is a magnitude, and any one of the possible stimuli shown would give the same output. In short, a large number of different irregular spectra can exist that all appear to have the same color to a given viewer. The principle is called metamerism. Spectra that appear the same to the HVS are metamers of one another. Were it not for metamerism, color imaging would not be possible in any of the forms used today. Displays based on red, green and blue primaries simply could not produce what appears to the HVS to be a wide range of colors were it not for the effect nor would a lot of modern lighting technologies be acceptable. It follows that quite a lot will have to be said about metamerism as it is central to colorimetry.

Fig.1 - One of the broad filters in the HVS shown symbolically. What emerges from the filter is an amplitude. The same response is obtained from a stimulus a) at the peak of the response as from stimuli b) and c) that are twice as big but located at wavelengths where the eye is half as sensitive. Color vision relies totally on amplitude differences between three such filters that overlap. No detailed spectral analysis is possible.

Fig.1 - One of the broad filters in the HVS shown symbolically. What emerges from the filter is an amplitude. The same response is obtained from a stimulus a) at the peak of the response as from stimuli b) and c) that are twice as big but located at wavelengths where the eye is half as sensitive. Color vision relies totally on amplitude differences between three such filters that overlap. No detailed spectral analysis is possible.

The imprecision in spectral analysis is hardly surprising as the HVS evolved before technology when the available light was from the sun. The sheer size of the sun means that the number of photons emitted is so statistically enormous that the spectrum contains literally every wavelength under the sun. One result is that that rainbows don't have gaps between the colors. Before technology, the white sunlight could only reflect from naturally occurring things, very few of which did anything other than filter the light in a broad sense. There is some debate over why the HVS evolved to see the colors it does. One argument is that it allows colored fruit to be seen against green vegetation. Another argument is that different shades of green denote leaves of varying ages that offer different amounts of nutrition. There was no real need to evolve a visual system that offered high spectral resolution, when the only narrow-band colors in nature were those from rainbows and from certain bird feathers that act like diffraction gratings.

As the spectral response of the HVS has a peak in green that falls to nothing in the infra-red and ultra-violet, what comes out of our eyes in the presence of white light is actually green, but the HVS equalizes it and we see it as white. Most of the information in vision is in the green, which is why Bayer patterns typically have two green photosites for every red and blue site to give the green signal a better signal to noise ratio. Color imaging systems all need to preserve the green signal more faithfully than red or blue.

Fig.2 - At a) the spectrum of sunlight is flat but may be tilted to the red or blue ends by atmospheric conditions.  As shown at b), the HVS can do no more than determine the existence of a peak due to a spectral color or a dip due to a non-spectral color. The location of the peak or dip determines the hue and the deviation from white determines the saturation.

Fig.2 - At a) the spectrum of sunlight is flat but may be tilted to the red or blue ends by atmospheric conditions. As shown at b), the HVS can do no more than determine the existence of a peak due to a spectral color or a dip due to a non-spectral color. The location of the peak or dip determines the hue and the deviation from white determines the saturation.

The HVS works on a very broad-brush approach to the spectrum. The spectra in Fig.2 are of the incident light entering the eye. Fig.2 shows that light having a flat spectrum is perceived as white. Atmospheric filtering could tilt the spectrum, giving the impression of cold or warm white light. Such a tilt would result from a broad peak outside the range of the HVS, such as that of a black body radiator. A narrower peak within the range of the HVS is perceived as a spectral color, one having a single wavelength where the maximum energy lies. The position of the peak determines what we call the hue, and the height or sharpness of the peak determines what we call the saturation. A spectrum containing a dip is perceived as a non-spectral color, where there is energy at wavelengths on either side of the dip. Purple is such a non-spectral color and the deeper the dip the more saturated it seems.

One way of considering saturation is that it measures the deviation from whiteness. Red is more saturated than pink, for example. One can also consider white to be the ultimate case of desaturation. White light does not, by definition, have a dominant wavelength. For that reason, white cannot be considered to be a color and nor is black, as they differ only in brightness. We can also give a simple explanation of how a TV works, which is nevertheless correct. A given pixel on the TV screen produces white light in proportion to a signal called luma. In a black and white TV, that's all there is. In a color TV, further signals then control the deviation from whiteness. They distort the spectrum of the light to determine the depth of a peak or a dip, which is the saturation, and the dominant wavelength where the peak or dip occurs, which is the hue.

Incidentally the term monochrome is a misnomer when used to describe a black and white picture. A black and white TV produces white light, which is about as far from monochromatic as could be. In a chromatically challenged world where bright orange flight recorders are called black boxes, it's a minor matter.

Incandescent lighting is very inefficient because most of what is radiated is heat and the light is almost a by-product. With different technology, it has become possible to present the eye with spectra that were not seen in nature, from light sources that are not classical black bodies and which do not have a meaningful color temperature. Such light sources include phosphors, discharge tubes, light emitting diodes and lasers. To see what is happening we have to wander off into quantum theory. In these modern times when everything is quantized so it can be sent digitally over the Internet, it's not a big deal to accept that matter and energy are fundamentally quantized, although it was harder to swallow when the ideas were first mooted.

On a macroscopic scale perpetual motion is impossible, whereas on a quantum mechanical scale not only is it possible; it is fundamentally necessary. Imagine if the electrons orbiting nuclei slowly lost energy and ran down. There could be no matter. Quantum theory says that energy can only come out of an atom in quanta, and if no quantum of energy escapes, there is no loss and the atom can exist forever. Excepting radioactive decay, energy can only be radiated from atoms as photons. A photon is emitted when an electron falls down from a higher energy level to a lower one. The frequency of the photon is a direct function of the energy difference. It follows that different atoms emit different colors when excited by heat or electricity, and that the color is determined by the atomic structure. Astronomers use the concept to figure out what distant objects are made of, because the radiated spectrum gives away what elements are up there.

Back on Earth, the consequences are that light sources that create photons from energy level jumps tend to produce monochromatic light. Try sprinkling some common salt onto a candle flame. The resulting yellow light having a wavelength of about 590 nanometres gives away the energy level changes in the sodium. Sodium yellow light was used for street lighting. The yellow light reflected from the road surface, but was mostly absorbed by things such as pedestrians, which appeared dark against the bright road. No one pretended sodium lights were useful where color rendering mattered, but they were more energy efficient than incandescent bulbs.

Fig.3 - The spectrum of a

Fig.3 - The spectrum of a "white" fluorescent lamp is highly irregular, but it appears white to the HVS because of metamerism. The elements responsible for the dominant spectral lines are shown. The light may appear white, but objects illuminated by it may not look the same as they do in natural light. The shortest wavelength due to Europium is roughly orange in color and deep red objects will not appear to be as red or as bright as they would in daylight.

The first successful non-incandescent "white" source was the fluorescent light. Fluorescence is a phenomenon whereby light of one wavelength, typically UV, excites atoms, which then radiate light of a longer visible wavelength. Dayglo paint used to provide high visibility on airplanes and emergency vehicles works on that basis. Some washing powders incorporated fluorescent material to make garments look white. That made for interesting results when discos started to use UV lights. Fluorescent lights generate ultra-violet light from an electrical discharge, and that UV light is used to excite fluorescence in a coating on the inside of the discharge tube. The phosphors in the coating are selected to fluoresce with a range of different discrete wavelengths producing light that appears to be white to the HVS. In fact, the spectrum is not white but is a metamer of white; it looks white to the HVS, but it may not give the same results as true white light.

Fig. 3 shows the spectrum of a typical "white" fluorescent light. There are a number of strong but narrow-band radiators in the spectrum. Their relative strength has been balanced to make the light look white to a human observer. If the light were to be reflected from a sheet of white paper, then it would look white. However, that is not a very stringent test. In the absence of a spectrum analyser, there is a very simple test that can be made to assess the spectrum of any light source, and that is to use a Compact Disc as a diffraction grating. Recordable CDs seem to work best as diffraction gratings and the light needs to be reflected off them in a radial direction to take advantage of the constant track spacing that does the diffraction.

Fig.4 - A fluorescent light seen in a recordable Compact Disc used as a diffraction grating. As rainbows go, it's rubbish, but it looks white to the HVS. That's metamerism at work.  Incidentally, it is an interesting exercise to see what this image looks like on different types of display. The difference between a computer screen and a flat screen TV may be quite striking. (Photograph: John Watkinson, Mamiya 645 with macro lens).

Fig.4 - A fluorescent light seen in a recordable Compact Disc used as a diffraction grating. As rainbows go, it's rubbish, but it looks white to the HVS. That's metamerism at work. Incidentally, it is an interesting exercise to see what this image looks like on different types of display. The difference between a computer screen and a flat screen TV may be quite striking. (Photograph: John Watkinson, Mamiya 645 with macro lens).

Fig.4 shows that the result with a non-black body light source is anything but a recognizable rainbow. This is a quick way of establishing whether light sources are likely to cause metamerism problems.

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