The colorful world of tomatoes and lasers: why is a tomato red?
読み終わるまでの時間：約5分
Light properties
The first property of light is its speed. Einstein taught us that everything is relative except the speed of light… So for the sake of saving our sanity – and also because this property has no impact on projection and displays – we chose not to delve any further into this.
Another fundamental property of light (being a wave) is its wavelength. Humans only perceive light between around 400 and 700nm. Below this range is ultra-violet (UV) light, and beyond, infra-red (IR) light.
A third property of the light is its polarization – but we won’t discuss this either.
The last property of light which we will consider is its energy, or better, power (energy per unit of time). The power of light is measured in W (watts), like electric or thermal power. Not to be confused with the wattage of the (now extinct) incandescent light bulb or LED lamp. That wattage is electric – but such a lamp will lose quite some electric watts in heat before producing light power.
Note that color and brightness are not fundamental properties of light – these are the result of the above, in interaction with how we perceive light.
This article will tell you all you need to know about it – and it’s actually quite fundamental to understanding how our projectors and displays work.
The color of wavelengths
Take a look at Figure 1 below. We can probably give a certain color name to each and every wavelength. For example, 465nm is very definitely blue, as 532nm is clearly green and e.g. 638nm is pretty bloody red. We can argue about the ones in between in terms of ‘ish-ness’, but nevertheless we can still give them a name.
Figure 1 – A representation of the visible colors vs. wavelength with some key laser wavelengths. Note that you only see the colors that your display or paper allows you to see. In reality, the colors on this chart are much more saturated and pure.
Also, a single wavelength of a certain color has the highest ‘saturation’: nowhere in the universe will you find a more ‘saturated’ or a more ‘colorful’ blue, green, yellow or red than the colors produced by a single wavelength.
A typical natural light source has a very broad mixture of wavelengths (for example the sun, a candle, or a projector lamp). In fact, such a light source has all possible wavelengths – at least in the region of visible light and just around it. Only the distribution of these wavelengths – the amount of power per wavelength – is different from one source to another. This distribution is called the ‘spectral power distribution’ (SPD or simply ‘spectrum’). Check Figure 2 for an example.
Figure 2 – A typical spectrum of a Xenon projector lamp. Note the peaks in the IR region. Bad.
When light from such a lamp or the sun falls on an object – a human face, lettuce, tomato – it’s reflected by this object. But not all light is reflected. Because of the object properties, some of the wavelengths might be absorbed. These object properties will change the wavelength distribution and the perceived color of that object – and as you can see in Figure 3 – that’s why tomatoes are red and lettuce is green. I don’t really know exactly why the tomato is red – i.e. why it only reflects the reddish part of the light. If you care to know, you can always google it.
Butter however reflects both yellow-red and the blue part of the spectrum. As a result it’s yellowish.
Figure 3 – A tomato is red, and lettuce is green, because…
So how do we know upfront what color any given wavelength bunch represents? And why are some colors brighter than others?
We realize that using wavelengths is not an efficient way to describe colors in everyday life. We’ve got to make this simpler. We need to squeeze all of these wavelengths and their distribution in just a few meaningful numbers that kind of corresponds to our way of naming colors.
From many to just three
As it turns out, humans only have three sorts of visual receptors: a short, medium, and long wavelength-range receptor. Wonderful! So in some way, we already interpret all of the wavelengths in terms of just three numbers! Not being able to hook up a sensor behind our eye nerves, we need a model that corresponds to how our receptors and brain do this.
Several models exist, the first one was presented in 1931 by the International Commission for Illumination CIE (so called CIE 1931). And people are still working on improvements…
Figure 4 – The three color matching functions (CMFs) according to CIE 1931
Such a model employs what is called a ‘color matching function’ (or CMF for short, check Figure 4). It determines how much each particular wavelength ‘weighs’ related to each of the three receptors. Multiplying the SPD with this weighing function for each wavelength and summing the result up across all wavelengths, we finally come to just three numbers called the ‘tristimulus’ values (X, Y and Z) that are kind of linked to the output of our three different ‘sensors’. In reality, it’s a bit more complicated than this, but you get the picture.
Now we’re talking! We finally have just three numbers that can represent each and every color in this universe. Done with wavelengths, SPDs and CMFs!
We’ll end this post with a very important principle: the metameric principle. According to this principle two colors will look the same to a person if they have the same tristimulus values (X, Y and Z), no matter what the spectral power distribution is behind them. These two colors are called ‘metamers’. That was the whole premise behind deriving the CMFs and the tristimulus values in the first place, and also the whole premise behind representing a real world color (many wavelengths!) by just three additive RGB display primaries.
Missed our first article on color? Read ‘The colorful world of tomatoes and lasers: why I still miss my black and white TV set’ now.