What limits can we see?

Our visual system provides us with all the information we need to make our way through the world, so it is perhaps slightly odd to think of it as having limits. However, it does have some limits and these are due to both physiology and physics.

The sensitivity of the visual system to light intensity is an important point to consider. An important experiment by Hecht, Schaler, and Pirenne in 1942, provided an important result in deducing the absolute sensitivity of the human visual system. Their experiment involved finding the threshold intensity of a flash of light that could be detected by a human subject. To do this they needed to generate suitable conditions in order to allow the visual system to be at its maximum sensitivity.

In order for this to happen, the test subjects needed to be “dark adapted”. The visual system has the ability to adjust its own sensitivity according to the surrounding light conditions. This is due to the fact that the visual system has only a limited “space” in which to code sensory information – the absolute rate of firing of neurons places a limit on the range of intensities that can be coded by frequency of firing. So to compensate for light conditions, the sensitivity of the receptors on the retina adjusts to become more sensitive in dark conditions and less sensitive in bright conditions. This has the effect of translating the range of intensities that can be coded.

So a dark-adapted test subject has retinal receptors which are at their most sensitive and therefore this state of maximum sensitivity allowed Hecht et al. to find the threshold of sensitivity to intensity. There are other considerations for them to make as well. For instance they had to decide the location of the flash of light in the subjects’ visual field. In order to do this, an understanding of the distribution of the receptor cells on the retina is required.

There are two main categories of receptor cells – rods and cones. They each serve slightly different functions. Cones are key to detecting colour, whereas rods are concerned with detecting brightness of light. In the middle of the range of light intensities that we can cope with, both the cones and rods function. However as intensity increases, the rods become less and less sensitive until they do not sense at all. The converse is the case with cones – they lose sensitivity as intensity decreases until they become pretty much insensitive. This is noticeable at night. For instance, you can see flowers, but they appear to have no colour. This in itself in a part of the limits of our visual system – in dark conditions we are unable to detect colour.

The rods and cones are not evenly distributed over the retina. This has implications regarding the limits to our vision and as such needed to be taken into account by Hecht et al. At the centre of our visual field, there is an area known as the fovea. This area consists entirely of cones and they are very densely packed together. This area provides tremendous resolution of fine detail, which is why we must look directly at something to resolve its detail. This could be argued to be another limit since we can only really detect the detail of what we are actually looking directly at.

However, the further away from the fovea, the lower the density of cones. This is why we can’t really resolve the detail of objects not at 0° (or close to that) in our visual field. The rods are distributed differently. There are none at the fovea but there is a maximum density at about 20-30° from the centre of the visual field. They then become less dense as they get further from the fovea. There is, of course, another limit when taking into account this distribution and that is due to the fact that there are no rods in the fovea. We cannot really see anything we look directly at when our eyes are dark-adapted as our cones are insensitive.

Another point which could be worth making is the effect of our “blind spot”. Where the optic nerve carrying sensory input to the brain connects with the receptors in our eye there are no receptor cells at all. This has the effect of producing an area on the retina which is totally insensitive to light and it covers about 5° of arc in our visual field. We do not, however, notice the effect of this due to having binocular vision. Having two inputs means that the blind spots of each eye never coincide so we can always have a “complete” picture. What is noteworthy is how we do not see a black spot in our visual field when only looking through one eye! Somehow the brain “fills in” the missing information and will fill in the blind spot area of vision with a continuation of the general background pattern it falls in. The blind spot is a limit of sorts to our vision, but not one that has any real consequence.

Going back to Hecht et al.’s experiment, the above facts regarding receptor cell distribution prompted the experimenters decision to direct the flash of light to the test subject from 20° to left of a fixation point (since the light falling on the retina would do so on the greatest concentration of rods). They also needed to decide upon the area that the flash would produce on the subjects’ retina. They chose an area of 10 minutes of arc (a sixth of a degree) due to Ricco’s Law. Ricco’s Law states that due to the spatial summation of quanta of light falling on a group of receptor cells, there is a critical area where the same number of quanta are required to fall on areas smaller than the critical one in order for a response to be triggered (I'm afraid that's the best I can make the explaination!). This critical area for Hecht’s experiment was 10 minutes of arc (this can vary depending on the percentage that they want the test subject to detect the flash at the threshold – in Hecht’s case, this was 60% of the time, but it is arbitrary).

Another important factor was needed and that was the duration of flash. This was decided by Bloch’s Law. There is a parallel to Ricco’s Law except Bloch’s Law is concerned with temporal summation. Temporal summation is to do with the addition of incoming quanta of light over a particular time in triggering a response. In fact, when plotted, the two laws share practically identical curves. The critical duration for Bloch’s Law, for Hecht’s experiment, is about 10 milliseconds. Hecht chose a duration of only 1 millisecond for his experiment – a value well within the critical duration.

One final factor was to decide the colour of the flash of light. Although rods are not sensitive to colour in the same way cones are, they still have a peak sensitivity for light of a certain wavelength. This happens to be about 510 nanometers, so this is the figure Hecht et al. chose. This would ordinarily be seen as a green colour, but in this experiment it would appear colourless due to only the rods being activated.

Hecht et al. carried out their experiment and plotted the flash intensity against the percentage of the flashes seen by the test subjects. This produced a sinusoidal curve where towards the highest intensities, the curve levelled off to show that they were seen nearly 100% of the time, and towards the lowest intensities, the curve began with a shallow gradient and showed that these low intensity flashes were almost never seen. To find the threshold intensity, an arbitrary value was chosen for the percentage of flashes seen - this was 60%. The results become significant after some clever deduction from Hecht et al..

Firstly, Hecht et al. realised that not all of the light from the flash would actually have reached the retina. They calculated that only 90% of the quanta emitted by the flash would reach the cornea (the clear front part of the eye through which light enters the pupil) due to the scattering of these quanta by molecules and particles in the air and so forth. They then figured that 3% of the quanta would then be reflected off of the cornea and a further 50% would be absorbed by the optic media (the fluid in the eye and the other cells that lie in front of the actual receptor cells of the retina). It was calculated that only around 43 of the original 100 or so quanta that were emitted would actually reach the retina and even then only 20% of these would be absorbed by the receptors, or in other words, less than 10 quanta. They then saw that the area over which these 10 quanta fell would consist of over 350 rod cells. This has a very significant implication, and that is that it would therefore be extremely unlikely for a rod to absorb more than one quantum of light. The conclusion is that each rod is sensitive to just one quantum of light and therefore the receptors could not be any more sensitive since light cannot arrive in energy packets of less than one quantum. A receptor requires only one pigment cell to change state by interacting with a quantum of light to activate the cell. So in reality, the individual receptors are as sensitive as they could possibly be.

This conclusion is important, but there are other thresholds apart from the lowest detectable intensity. We have limits dependent on the intensity of surrounding light sources. For instance, a bright light source will overwhelm the receptors to light arriving at our eyes from other much dimmer sources. This is seen in trying to look into a dark building on a bright day, and is the reason why we cannot see someone’s retina inside their eye, since the light reflected out of the eye is far less than the intensity of that which is shined into it.

The angle over which we can see is an obvious limit to our vision, most people can see over a total angle of something approaching 90° from the centre of their vision. However, there is such a low density of receptors at these wide angles that only movement can really be detected - practically no detail at all. This does have obvious advantages to our survival. How often do we hear someone say thay caught something moving in "the corner of their eye". Another limit is the range of wavelengths of light we can see (a range of about 400-700 nanometers). We seem to have no real limit to the distance we can see. The fact that the further away an object is, the smaller the image it forms on the retina cancels out the effects of the inverse square law of the intensity of light, at least for the purposes of everyday existence.

So there are some limits to our vision, but they are in no way inhibitory to our requirements to live our lives.