The eye: performance and compromises.

Aperture, aberration, integration or exposure time, shutter speed, angular resolution, angular view, sensitivity... One way of presenting the physics of the eye is describe its performance, compare these to theoretical limits and to discuss the compromises between different aspects of optical performance. This page supports the multimedia tutorial The eye and colour vision.

Photon capture efficiency

    Seen from in front, the pupil of the eye looks very black – because only about 4% of incident light is reflected back. Of the light entering the pupil, about half is scattered or absorbed in the humours or the lens, so that only about half reaches the retina. Of that fraction, about 20% is absorbed by a photoreceptor, giving the eye an overall capture efficiency of 10%. This is considerably lower than that of nocturnal mammals, and much less than that of the huntsman spider. In a dark-adapted eye, about 7 photons absorbed in a few tens of ms in one photoreceptive field are required to be aware of a flash, so one could say that we need an absolute minimum of 70 photons to see. If a microwatt of light enters the eye, then the number of photons per second is 1μW/(energy per photon) = 1μWλ/hc = 2 X 1012 photons/s.

    Aperture and aberration

    These photos, from Geometrical Optics, show how reducing the aperture of a lens reduces the extent of aberration. Aberration refers to how a lens of imperfect shape fails to focus all parellel rays onto a single point. In practice, this reduces the sharpness of the image.

    At left, a large and very imperfect lens focuses an image of a light bulb on a screen. At right, the aperture of the lens is reduced by an anulus of black card.

    The image formed by the lens with reduced aperture is sharper. However, there is a compromise: the reduced aperture admits less light, so the image is less bright.

    Reducing pupil size in response to bright light

    Reducing aperture in response to bright light

    In a camera, the aperture is controlled using the f-stop ratio, i.e. the ratio of focal length f to aperture diameter d. A larger f-stop ratio gives a greater depth of focus, but it requires a longer exposure time to admit the same amount of light. Someone who requires spectacles to read in low light may be able to read without spectacles in bright light, because the small pupil produces a sharper image.

    Integration/ exposure time/ frames per second

    Increasing the number of frames per second.
      As well as increasing the aperture, another way of capturing more photons is to capture light over a longer time – increasing the exposure in a still camera, or decreasing the number of frames per second in a movie camera. At the normal Physclips rate of 12 frames per second, motion is perceptually jerky, which tells us that the the integration time of our visual system is shorter than 80 ms. Cinema runs at 24 frames per second and television at 25 or 30 frames per second, which is almost enough. So our integration time is roughly 20-30 ms under good light. High speed cameras can do much better than this, but do require very high light intensity.

      The focal length

        If we were to double the focal length and the image on the retina would be four times bigger. So the intensity of light falling on the retina is inversely proportional to the square of the focal length. The disadvantage to a small focal length is that the small image, spread over photoreceptive fields of a given size, would limit the angular resolution. (To continue the analogy with a camera: a long focal length camera can show very fine detail for a film with equal grain size, or an equal pixel density on the detector. However, it requires longer exposure times.) The wedge-tailed eagle has a focal length approximately the same as a human, which means that its eyes occupy a substantial fraction of its head.

        Stereoscopic vision

          At short distances, much of our depth perception comes from stereoscopic vision: the visual fields of our two eyes overlap and, in the overlap range, the relative position of objects (left to right) depends on their distance from us. In the example above, my right eye sees the lens obscuring more of the slinky than does the left eye. This tells me tha the lens is closer (and gives some clues about how much closer). However, in this case the fact that the lens obscures the slinky at all also tells me that it is closer, and logic of this sort is very important in our long range depth perception. The large difference tells me that the angle subtended by my eyes at the object is relatively large and, given that I know that the objects are small, I deduce that they are close.

          Angle of view

          The overlap needed for stereoscopic vision is facilitated by the large angular range of the human eye. To achieve comparable angular range with a camera would require a 'fish-eye' lens.

          This page supports the multimedia tutorial The eye and colour vision.

          Creative Commons License This work is licensed under a Creative Commons License.