We started with a spectral power distribution of a light source – or reflected light from an object, e.g. bacon, lettuce, tomato – we intertwined it with the human visual response for each of the eye’s three receptors – called color matching functions – and we got three numbers: X, Y and Z.

Now, let’s look at how these numbers relate to what we humans readily perceive: brightness and color.

The lumen farm: all energies are equal - but some energies are more equal than others 

As it turns out, the middle number Y is very important: the green curve in the middle of Figure 5 in the previous chapter (included below again) – also called V(?), is conveniently chosen so that it measures our brightness sensitivity to each wavelength. So the tristimulus value Y is linked to the visual perception of ‘brightness’ of the object or image.

Figure 1 – The three color matching functions (CMFs) according to CIE 1931

Depending on the type of ‘power’ we consider from a light source – directional or ‘total’, across all angles and directions – using the process laid out above, we can derive either a quantity called ‘luminance’, measured in cd/m², nits or foot-Lamberts (directional), or a quantity called ‘luminous flux’, measured in lumens – a very important projector metric!

Now note the position and shape of this green curve. We humans are most sensitive to light at 555nm: meaning that 1W of light power would produce maximum lumens at this wavelength (683 lumens to be exact). But go down – or up in wavelength, and the ‘lumen production’ decreases. 1W of blue or red light can produce only about 100 lm or less, depending on the wavelength, and you won’t be able to see 1W of IR or UV light at all, that is… zero lumens.

Why do we care when talking about projectors? Because power is power, whether you can see it or not. 

So, in pumping watts of energy through the projector optics, lots of it will be absorbed or scattered and will heat up the optics but not all the watts that are projected produce a lot of lumens. In other words, we don’t only need projector lumens, but we need ‘smart’ (efficient) lumens – produced from the least amount of watts possible! 

Keep it cool!

The dark side of the moon

Having a way to get from a myriad of colors to only three numbers is great.

The next step is to make this even simpler.

And what is simpler than 3 numbers? 2 numbers.

Remember that we used one of the three numbers to represent luminance (the ‘Y’). What about the other two? Math comes in handy here: starting from the tristimulus values X, Y and Z, we can derive two numbers called x and y (dubbed color chromaticities), in this way: x=X/(X+Y+Z) and y=Y/(X+Y+Z).

Conveniently, this transformation kind of warps the pure wavelength spectrum (Figure 2) onto a sort of ‘horseshoe’ – the black outline around the colored chart, called the ‘spectral locus’. But instead of one colored line, we now have a line enclosing a whole 2D surface. The spectral locus colors have maximum saturation, just like the wavelengths in Figure 2. 

Inside this horseshoe you can find the mixed colors like yellow, orange, cyan, magenta (purple), or white, which have less saturation – the further a color is from the locus and closer to white, the less saturation. Outside the horseshoe is the forbidden realm. There is no color in this universe that can go out of this enclosure – those (x, y) values just do not represent any humanly ‘visible’ color. The whole (x, y) chart is called the ‘chromaticity chart’.

Figure 2 – An illustration of an x, y chromaticity chart. Note that you only see the colors that your display or paper allows you to see: in reality the colors towards the edges of this chart are much more saturated and pure. The wavelengths of the pure colors (in nm) are shown along the horseshoe line.  

This graph is the most widely used ‘color chart’ in common industry literature. However it’s the most troublesome one as well. The problem arises when we try to express color differences (distance from one (x₁, y₁) color value to another (x₂, y₂) color value. It turns out that the CIE 1931 chart is completely non-uniform – the same numerical (?x, ??y) difference can be either hugely noticeable or not seen at all, depending on the color region. So in 1976, color scientists proposed a new chart, called the u’v’ chromaticity chart. It’s also based on the CIE 1931 XYZ tristimulus values, however the ‘warping’ to the chromaticity values u’v’ happens. Figure 3 shows the details of this color space.