Human Eye Color Response

When we refer to the sensitivity of people to different wavelengths of light we use a unit called lumens, and lumens are defined. So at the wavelength 555 nanometers, which is green, one watt of light creates a sensation of 683 lumens. At a wavelength of 500 nanometers—which is blue—a one watt light source would only get a sensation of 220 lumens. So it is the same amount of electronic energy, but if it is concentrated at that wavelength, it produces a smaller sensation to the human observer and if we had one watt of electronic energy at 800 nanometers it would produce zero lumens—we can’t see it, it results in no sensation at all.

So we can look at the human luminosity response and there are two of these: there is our night time response which is called the scotopic response and a day time response, the photopic response. This is our overall sensation to light at a particular wavelength, and it is clear that at night we are much more sensitive to shorter wavelengths, the bluer colours, than we are during the day time.

We talked before that humans have got three types of cone cells in the backs of our eyes, the short medium and long wavelength cones. Because we have three of them we are referred to as being trichromats, tri meaning we have three color sensors in our eyes. Humans are somewhat unusual amongst mammals in having three color receptors; most mammals only have two. And this graph shows the response of the short and long wavelength cones for a typical mammal. Many birds are tetrachromats; that means that they have four different types of cones cells and the response of the bird’s cone cells are shown here.

Now clearly there must be some evolutionary advantage for birds to have four cone cells. It gives them a better ability to discriminate colors. We can argue that perhaps for the other mammals there is no need to have three cone cells, two is enough.

Not all humans have perfect trichromatic vision. Many humans suffer from color blindness and I am one of those people. I suffer from a red, green color deficiency and what that means for me is that the sensitivity of my medium wavelength cone is shifted a bit to the right, so my medium wavelength cone response overlaps my long wavelength cone response. So the two cone responses are almost equal and that makes it very hard for me to distinguish reds from greens. Now this is a hereditary defect, this particular gene is on the tip of the X chromosome and is passed from males to males via females.

Color blindness is reasonably prevalent in the community, particularly amongst males, and the particular defect that I have is shared by six per cent of men in the population. It is quite difficult to try and explain to people what it is like to be color blind. This slide is trying to illustrate to somebody with normal color vision how the world looks with these different types of color defects, whether someone is missing their L cone, their M cone or their S cone.

So here we have the spectrum of the illuminant and in this case this is the spectrum of the noon day sun as measured on the surface of the earth, so it is not the smooth black body curve that we looked at earlier, it has got lumps and bumps in it due to absorption of parts of the spectrum by molecules in the atmosphere and here is the luminance of the light that is being reflected from the brick.

And that is obtained from the reflectance function for the red brick multiplied by the illuminance spectrum. So the light from the sun reflected from the brick has got this particular luminance spectrum.

The final step is to apply a number of filters or response functions to the incoming luminance and in our eye we apply three different response functions. So there are three different versions of M; the response function. So let’s consider firstly the blue response function; so we take the incoming luminance and we filter it with the response of the blue cone and we can see that here. Now the total response of the cone is the integral of the luminance multiplied by the response function, and that is the area underneath the curve, that is what is shown here as the solid mass of blue. So the area underneath this curve is the total amount of energy, it is the total response of the blue cone in the retina for this particular incoming luminance.

Similarly for the green cone, we apply the green cones response function, its own version of M of lambda and then we integrate the area underneath the curve, and that is what is shown here as a solid mass of green and we do exactly the same thing for the red cone. We have taken an incoming luminance spectrum, applied three filters to it, integrated the response of those filters and the results are three numbers an amount of red, green and blue.

This process sounds complicated, but it has done a very clever thing. If we consider that the spectrum of illuminance, that is, the spectrum of the light that is entering out eyes from a particular object, it says something about the material properties of that object; an apple, for instance, is red; a leaf of a plant is green. All of these different objects in the world have got a different spectrum. But to describe a spectrum we need an infinite number of numbers. It is a continuous function of wavelength. It is an infinite dimensional signal. But by applying three spectral filters to this incoming light and integrating the output of the signal after it has passed to each of these filters, we are left simply with three numbers. So we have reduced an infinite dimensional signal simply to three numbers or to three dimensions … performed a massive dimensionality reduction. A consequence of this dimensionality reduction is the possibility of ambiguity; that is, that there are an infinite number of different luminance spectrum that will give exactly the same values of R, G and B. We refer to such spectra as metamers; that is, different spectra that give you exactly the same R, G and B value.

But clearly this is not a significant problem in everyday life; it is not something that we worry or stress about, so we have evolved a good enough solution to the problem. We can recognise objects by reducing the dimensionality of the signals which indicate what they are made of into just three quantities, three numbers.