From photon to signal
Rods and cones contain millions of molecules of visual pigment: an opsin protein bound to retinal (a derivative of vitamin A). A photon straightens the bent retinal molecule (from the 11-cis to the all-trans form). This sets off a cascade of proteins that closes ion channels in the membrane. Curiously, a photoreceptor is excited in the dark and constantly releases a neurotransmitter — light quiets it. Bipolar cells pass this signal on, and ganglion cells turn it into nerve impulses that travel along the optic nerve to the brain.
Different opsins absorb different wavelengths best. How much energy a single photon carries is given by Planck's formula:
h = 6.626·10⁻³⁴ J·s (Planck's constant), c ≈ 3.00·10⁸ m/s, 1 eV = 1.602·10⁻¹⁹ J.
| Pigment | Peak λ | Photon energy |
|---|
Visual acuity: one arcminute
A healthy eye resolves details seen at an angle of about 1′ (one arcminute, or 1/60 of a degree). That corresponds to 20/20 vision (“1.0” on a metric eye chart). How large is such a detail at a distance d?
From 6 m that's about 1.7 mm; from 40 cm (reading distance), about 0.12 mm. On the retina 1′ is about 5 µm, and the cones in the fovea are spaced about 2.5 µm apart — the detail has to cover roughly two cones.
Pupil and brightness
The approximate formula of Moon and Spencer describes the pupil diameter D (in mm) at an ambient luminance L (in cd/m²). The amount of light reaching the retina is proportional to luminance times pupil area; this quantity is measured in trolands (Td).
The formula gives diameters from about 1.9 to 7.9 mm. The real pupil also depends on age (it shrinks with age), the size of the bright field, emotions, and even whether we are looking at something up close.
Color is the brain's work
Three kinds of cones are only the beginning. Already in the retina the signals are subtracted from each other: “red versus green” and “blue versus yellow” (opponent processes). That's why there is no “reddish-green” color, and why the afterimage of red is greenish. Missing one kind of cone flattens this color space to two dimensions — that is dichromacy.