Imagine that we have three projection lamps at the back of a hall – one has a red filter and so produces a beam of red light, and the other two use filters to produce green and blue beams. We project these onto a white screen and get three circles of light (one, red, one green and one blue). We then move the angles of the projectors so that the circles of light overlap. We get something that looks rather like this:
Where the red and green light overlap we get yellow. We get magenta and cyan for the other two binary mixtures. So,
red + green = yellow
red + blue = magenta
green + blue = cyan
This is called additive colour mixing as I am sure you know. And if we mix all three primaries we can achieve white (or other neutral colours). The primaries could be single wavelengths of light – so we could use a primary at, say, 700 nm (for the red) and one at 450 nm (blue) and one at 530 nm (green). So green light (530 nm) and red light (700 nm) additively mix together and generate yellow. When this happens what is being mixed and where does this mixing take place? Take a few moments to consider this before reading on.
Notice I said that they additively mix to generate yellow – I specifically avoided saying that they mix to generate yellow light. When I sat down with a couple of students last week and asked then what they though they said that the red and green light mixed together to create yellow light and when I pressed them, they went further to say that the yellow light was at about 575 nm.
If we measure the part of the screen that is yellow we would see that we have some light at 700 nm and some at 530 nm. The wavelengths are not mixed; they don’t mix together to generate some third wavelength of light such as 575 nm. So no physical mixing takes place other than – I suppose one could argue – that the red and green lights are mixed in the sense that they are spatially coincident. But that’s not really mixing, for me, and certainly doesn’t even begin to explain why we have the sensation of yellow when we look at these wavelengths together. It also makes me think that additive colour mixing, if it can be said to occur anywhere in particular, occurs in the eye. And I do mean eye, not brain.
There are two phrases I keep seeing written down all over the internet that cause my blood pressure to increase.
The first is that the colour primaries are red, yellow and blue (RYB). And the second is that the primaries are colours that cannot be made by mixing other colours. Neither of these statements are true, of course.
The first statement makes no distinction between additive colour mixing (of lights) and subtractive colour mixing (of paints and inks) but subtractive colour mixing is normally implied. However, RYB is a relatively poor choice for three colour primaries. The range of colours that can be produced is actually quite small. For most painters and artists it doesn’t matter because very few work in just three primaries – if they did so they would probably be frustrated by the small gamut of colours achievable. Many artists (painters) will use 10 or more basic colours to mix their palette. However, there is a group of people who care passionately about the gamut of colours that can be obtained by mixing three colour primaries – that is the people who work for companies such as HP and Canon. These companies make CMYK printers for the consumer market and their jobs depend upon consumers liking their printers. They understand that the largest gamut (in subtractive mixing) can be obtained if the primaries are cyan, magenta and yellow (CMY). The teaching of RYB as the (subtractive) primaries should be stopped. It’s already gone on for far too long.
One reason I don’t like the teaching of RYB as being the subtractive primaries, in addition to the fact that it is wrong, is that it confuses people who are trying to learn colour theory. This is because red, yellow and blue seem to be quite pure colours and this encourages people to hold the second belief I don’t like which is that the primaries are pure colours that cannot be mixed from other colours. If people understood that the primaries were CMY it would be less tempting to hold this belief about the purity of the primaries. Of course, if you make a palette of colours of three primaries then it is true that no mixture of two or more colours from that palette can match any of the primaries. However, there are other colours (that are outside the gamut of the primary system) that could be mixed together to match the primaries. This false notion of purity confuses the real issue – that is, that the subtractive primaries are cyan, magenta and yellow because the additive primaries are red, green and blue. Look at this picture below:
The additive primaries are red, green and blue and the secondaries are cyan, magenta and yellow. Correspondingly, the subtractive primaries are cyan, magenta and yellow and the subtractive secondaries are red, green and blue. Simple.
I wrote about this before so for a slightly different perspective see my earlier post.
Perhaps I am so agitated about it today because I am just watching England getting trounced by Ireland at rugby when the Grand Slam was so tantalisingly close. Or maybe I will feel just the same tomorrow.
In my job I probably use the phrase “colour space” every day and have done for the last 20 years. So imagine my surprise when I was talking with a colleague recently and after a few minutes he said “Can I stop you for a second there Steve – when you say colour space, what exactly do you mean?”.
A colour space is like a map. A map of New York, for example, shows the location of various landmarks with reference to the xy coordinates (the position in horizontal x and vertical y units on the map). A colour space or colour map does the same thing with colours. Perhaps the simplest colour space is the spectrum, see below:
As we look from right to left on the spectrum the wavelengths changes from around 700nm on the far left to about 400nm on the far right. So this map shows colour with reference to wavelength. Although it is a commonly used colour space it is limited because it only really describes how hue changes with wavelength. Hue is only one of three ways in which colour can change or vary.
The most well-known really useful colour space then is the CIE chromaticity diagram – see below.
The CIE chromaticity diagram shows colours arranged on a 2-D plane. We can easily refer to any colour by how far from the left it is (the x coordinate) and how far from the bottom it is (the y coordinate). This space only shows two of the dimensions of colour; the hues are arranged in a somewhat circular way and the colourfulness increases as we move outwards from the white point (a position near to the centre of the diagram). However, we can also consider the third component of colour (brightness) if we imagine a dimension coming out of the page towards you (http://colourware.wordpress.com/2009/07/18/cie-system-of-colorimetry/). The CIE defines several different colour spaces; the CIELAB colour space, for example, is another 3-D space that defines a colour by its L*, a* and b* values.
It is useful to think of an image-display device as also having a colour space. Consider the display on which you are probably reading this blog. The display shows colour by changing the amount of the red, green and blue light emitted at each point on the screen. The diagram below is a representation of what the RGB colour space of your display device may look like.
In the RGB cube, black is in the bottom left. As the RGB values increase colours are created and white results from each of the RGB primaries at full strength. So the RGB colour space defines the relationship between RGB values and colour. However, here’s the really interesting thing: The colour space for different display devices is very different. Even if we take a single device – such as the one that you are reading this blog on – then as we change settings (the brightness, the contrast, the gamma, the colour temperature, etc.) then the colour space changes. That is, the relationship between RGB and colour changes as you change those settings. This is a huge problem. Imagine if there were many maps of New York and each showed the position of, say, the Empire State Building to be in a different position. How confusing would that be? Well, that’s the problem with colour-display technology. If we didn’t do anything about this problem then every time we looked at a colour image on a different display device the colours could change markedly. This is why we need colour management. Colour management can make compensations to the RGB values that are sent to each display device so that the colours always appear the same (well, nearly the same). To make this compensation the colour management software (which is embedded in your Windows or Apple operating system) needs to know about the colour space of each device connected to the computer. Each device needs to have a profile that describes the relationship of its own colour space with respect to some standard colour space.
How good is colour management? Well, that depends upon many factors. Most printers, cameras, scanners, and screens (LCD, CRT, etc.) come with a driver that includes a crude colour profile. This ensures that there is a basic level of colour management and for a great majority of users this is more than adequate. However, if you want better performance then you need to think about making some measurements that will allow a more accurate colour profile to be built. In a recent blog I described a new device that you can buy to enable you to do this – http://colourware.wordpress.com/2009/07/29/colormunki-colour-management/. There are many such devices on the market. I highly recommend Andrew Rodney’s book Color Management for Photographers which is both clear and accurate (though the edition I have works on Adobe’s CS2 package whereas the latest package is CS4).
However, no matter how hard you try, colour management is never likely to be perfect. This is because different devices have different colour gamuts; a printer is likely to be able to display some colours that your display physically cannot and vice versa.
For about 100 years there has been an international system for colour specification – it’s called the CIE system. The acronym comes from Commission Internationale de L’Eclairage.
This system is based on the notion of additive colour mixing – http://colourware.wordpress.com/2009/07/13/additive-colour-mixing/
Since it is possible to mix together three primary lights and make a wide gamut of colours (though not, of course, all colours) the principle is that the amounts of these primaries that an observer would use to mix togther to match a colour is a useful specification of that colour. We refer to these amounts as tristimulus values. One could imagine a visual colorimeter whereby an observer would try to match a colour that is to be specified by adjusting the intensities of three primary lights that are mixed together – once a match is obtained then the tristimulus values would define or specify the colour. All that would be necessary would be to able to decide on a set of primaries and manufacture the visual colorimeters so that they are very consistent from one device to the next. It would be a little clumsy though to have to use one of these visual colorimeters. But in principle it could work.
Fortunately the CIE does not require the use of such visual colorimeters since in 1931 the CIE measured the trismumulus values that observers made when matching various colours. These were averaged to create the so-called CIE standard observer. And here’s the really clever bit. Having defined the CIE standard observer it is possible to calculate the tristimulus values (the amounts of the three primaries that an observer would use to match a colour) without any further observations. All that is required is that we know the amount of light at each wavelength reflected by a sample or (in some cases) emitted from a device such as computer display and then – by using our knowledge of the CIE standard observer – it is possible to calculate the tristimulus values.
So what were the primaries. If you have read my previous post, What is a colour primary – http://colourware.wordpress.com/2009/07/08/what-is-a-colour-primary/ – you’ll know that the choice of colour primaries is somewhat arbitrary. Well, in fact the original determination of the standard observer what carried out in England using red, green and blue primaries. But the data obtained were later modified to refer to a different set of primaries known as X, Y and Z. It was necessary to make this adjustment because using any set of real primaries it was impossible to match any colour with mixtures of the primaries; using RGB meant many colours could be matched, but not all. So a set of so-called imaginary primaries was conceived which could – in theory – be used to match all colours. So the tristimulus values of the CIE system are known as X, Y and Z.
In fact, it didn’t really matter which set of primaries was used; the CIE system was concerned with colour matching. If two samples have the same tristimulus values then they would be a visual colour match no matter which set of primaries was used. So the choice of primaries really was not critical.
Today many instruments are commercially available – colorimeters, reflectance spectrophotometers, radiometers) – that, with the use of software, allow the CIE XYZ values to be measured; these instruments are extremely valuable in many industrial and commercial applications. The CIE system is still very much alive today, though many users often prefer to use one of the more advanced colour spaces – such as the CIELAB colour space – which was defined by the CIE in 1976 and whose values are very easily calculated from the CIE XYZ values. For further information about the CIE please visit their web site – http://www.colour.org/
I try to keep my blogs short. But this is going to be difficult!
Let’s start with what a primary is not. The primaries are often quoted as being red, yellow and blue. And on the BBC website – of all places – it says “Primary colours are three key colours – Red, Yellow and Blue. They cannot be made from any other colour”. For the BBC site visit http://www.bbc.co.uk/homes/design/colour_wheel.shtml.
The statement that primary colours cannot be made from any other colour is simply not true. Further, it gives the mistaken impression that there is something special about these primaries (red, yellow and blue) that makes them stand apart from the other colours. Another false statement that one often sees even in quite scholarly work is that any colour can be made by the mixture of three primary colours.
What is true is that if we select three appropriate colours and mix them together we can make a suprising range of colours. These colours – let’s call them primaries – can combine to make a huge range of different colours but unfortunately there are no three primaries that can be selected such that in mixture they can create any other colour. Depending upon the choice of primaries the range (or gamut) of colours that can be created in mixture is larger or smaller. What makes a good set of primaries? Well, I think it is reasonable to say that a good set of primaries is one where the gamut of colours that can be created is large; indeed, I would argue that the optimal primaries are those that create the largest possible gamut.
There are certain sets of primaries that can easily be predicted to give a small gamut. For example, if any of the primaries are dull and desaturated then the gamut will not be very big. Also, if the three primaries are similar to each other then the primaries are not likely to be a good set. And finally, if it is possible to combine two of the primaries together to make the other one then the gamut will be tiny. This is where – I believe – the misleading statement on the BBC website comes from; for a good set of primaries it is important that the primaries are independent (that two cannot be mixed to match the other one) but this is a long way from the BBC statement. Once we havs selected three suitable priamries then it’s true that they cannot then be made by any other colours that the primary system can make – but to argue that this is why they are primaries is clearly a circular argument.
There is nothing special about red, yellow and blue. In fact, they are not even the optimal primaries! To say what the optimal primaries are we need to specify the type of mixing: additive or subtractive. Additive mixing describes the behaviour of light-emissive systems such as computer displays, subtractive mixing describes how paints and inks mix. For subtractive mixing the primaries are often quoted as red, yellow and blue, as in the BBC article. However, a larger subtractive gamut is obtained if we use cyan (instead of blue) and magenta (instead of red) – see figure below.
One of my current research interests is to understand why red, blue and yellow became known as the artists’ primaries when a larger gamut is obtained if a bluish red is used (something closer to a magenta) and if a greenish blue is used (something closer to cyan). One only has to look at the primary colours used in inkjet printers for example (where the manufacturers have a vested interest in being able to create a large gamut) to realise that cyan, magenta and yellow are the optimal subtractive primaries.
For additive colour mixing the optimal primaries are red, green and blue. The additive and subtractive primaries have an interesting relationship – but that’s for another blog, another day.