Tag Archives: chromaticity

chromaticity diagram and RGB gamut

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You may well have seen a typical diagram showing the chromaticity diagram and the gamut of an RGB monitor. The gamut is a triangle, of course, with the vertices formed by the chromaticities of the RGB primaries. See, for example, http://colourware.wordpress.com/2009/10/04/subtractive-mixing-why-not-rgb/.

However, that triangle is a little misleading. One problem is that we are only looking at the maximum chromaticities available – this does not imply that all of these chromaticities are available at every luminance level. Take the very vertices of the triangle – these occur for the RGB values [255 0 0], [0 255 0] and [0 0 255]. The luminance of the pure red [255 0 0]  might be 27 cd/m2, of the pure green [0 255 0] 56 cd/m2, and of the pure blue [0 0 255]  might be 6 cd/m2. (These are luminance values for a typical RGB monitor – your monitor will vary a little from this and depending upon your settings.) This means that the chromaticities of the points of the triangular gamut are only available at these respective luminance levels.

For the monitor just described the maximum luminance would be obtained when RGB = [255 255 255] and the luminance of this white would be 89 cd/m2. So for very high luminances the gamut is tiny since to achieve these high luminance values you need to have all three RGB guns firing and hence by definition the colour is going to be very desaturated.

For the typical monitor described above I have calculated the gamut of colours available at three luminance levels: 10 cd/m2, 40 cd/m2 and 70 cd/m2. I have plotted these below and coloured bright red the chromaticities that cannot be obtained at that luminance. So, for example, at 10 cd/m2 you can obtain most chromaticities but not the pure blue. The reason for this is the pure blue [0 0 255] would be only 6  cd/m2 – to get 10 cd/m2 you need to add a little red or green and this desaturates the blue.

At 40 cd/m2 you can obtain a much smaller gamut and at 70 cd/m2 the gamut obtainable is very limited. To get such high luminances on this typical RGB monitor you would need high R and G values and that gives you yellows and yellowish whites.

The point of all this is that gamuts are three dimensional and looking at the gamuts in a 2-D chromaticity diagram can be very misleading.

chrom10

 

 

 

 

 

chrom40

 

 

 

 

 

chrom70

subtractive mixing – why not RGB?

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In a previous post I spoke about the difference between additive and subtractive mixing and why the additive primaries are red, green and blue or RGB for short – http://colourware.wordpress.com/2009/07/13/additive-colour-mixing/

The chromaticity diagram – see http://colourware.wordpress.com/2009/09/28/colourchat-audiovisual-guide-to-the-chromaticity-diagram/ – has a very useful property. If you plot the chromaticities of two lights, then the straight line that joins the two points on the chromaticity diagram show you the additive mixtures that can be obtained by mixing together the two lights. If we take three lights, then the additive mixtures that can be obtained are defined by the triangle that is formed if the chromaticities are the vertices of the triangle. Ok – that’s a bit of a mouthful so let’s have a practical example. The triangle in the diagram below shows the gamut that can be achieved when we have three additive primaries that are positioned at the corners of the triangle.

rgb_gamut

 From this diagram it should become obvious why the additive primaries are RGB. Say, we chose, two reds and a cyan as the three additive primaries – well, the triangle would be tiny. In other words, the gamut would not be very big. The biggest triangle in the chromaticity is one whose vertices are formed by a red, a green and a blue. WhichRGB will give the biggest triangle? I don’t know – it’s been something that has been puzzling me for the last few days and I’ll come back to this in a later post. But certainly any RGB triangle is pretty large as long as the red, green and blue primaries chosen are reasonably saturated.

So what happens if we choose RGB as the subtractive primaries? Subtractive colour mixing describes how inks and paints mix together to form colours. The first thing to point out is that subtractive colour mixing is not additive and linear – you remember I said that when you mix two lights together the colour mixtures all fall on the straight line that joins the  two points in the chromaticity diagram that represent the two lights? Well, this is only true for additive colour mixing. So to work out the gamut for subtractive systems is not an easy thing to do. However, if you do select the three subtractive primaries as RGB you’ll get a gamut that looks something like this:

rgb_subgamut

Notice that the gamut is concave. Mixing red and green lights produces a nice yellow. You can test this by going into your colour-picker in software such as Photoshop or Powerpoint and setting the RGB values to be 255:255:0. You’ll get a nice yellow. But mixing red and green paints – it will give you a similar hue to yellow but you’ll get something quite desaurated; most likely you’ll get a brown. So using RGB as the subtractive primaries would not be a very good thing at all.

It turns out that additive and subtractive colour mixing are very related. The best subtractive primaries are the ones that control the amount of red, green and blue light reflected. A yellow dye applied to textiles, for example, mainly absorbs short wavelengths in the blue section of the spectrum, allowing the other wavelengths to be reflected by the textile. The “other wavelengths” that are reflected give yellow. But the important point is that the yellow dye absorbs blue. Similarly, a magenta dye absorbs green and a cyan dye absorbs red. This leads to the idea of the optimal subtractive primaries being those that are cyan, magenta and yellow or CMY. This leads to a gamut somewhat like this:

cmy_gamut

The biggest gamut for subtractive mixing is obtained by using CMY as the primaries. But weren’t you taught at school that the subtractive primaries are red, blue and yellow? Almost certainly you were – and this is because it is accepted dogma at most art colleges and in many art and design textbooks. But it is quite easy to show that the optimal primaries – those giving the largest gamut – are CMY not RBY. If you were building a colour-reproduction system using only three colours such as a printer you would come to the conclusion – as companies such as HP, Xerox, and Epson have done – that you get the largest colour range with CMY. So why has it become commonplace for artists to refer to red, yellow and blue as the primaries? Could it be a colour naming and language issue – that they really mean cyan when they say blue and it’s just a naming error. Possible, but not likely in my opinion.  I think it is more likely that most artists are not overly concerned that RYB gives a smaller gamut than CMY because they rarely restrict themselves to three primaries. An artist would typically use 6 or more primaries. For example, they might use two blues (one that is reddish and one that is greenish), two reds (one that is yellowish and one that is bluish) and two yellows (one that is greenish and one that is reddish) in order to easily be able to mix a wide range of colours. The (mis-)identification of RYB as the subtractive primaries has much to do with colour wheels. I like to keep each of these blog posts reasonably concise – if I start writing about the problems of colour wheels now I will be writing for another 2 hours. And it’s nearly midnight now so colour wheels will need to wait for another day!