Useful Numbers in Vision Science

In early 1994, I began compiling a list of numbers to describe some of the major features of the visual pathways Many of the students in my classes at Stanford found such a list of numbers useful. Also, I planned to include the numbers inside the cover of my textbook, Foundations of Vision (Sinauer Press, e-mail to orders@sinauer.com).

In early 1995, on the spur of the moment, I sent a message to CVNET asking for numbers others found useful. Many people generously shared their work with me. Using my own values and these contributed values, I created one organized list of numbers. I have also compiled the much larger list of e-mail responses I received. The e-mail responses have been edited only slightly (personal annotations were removed; also, longer addresses including fax numbers and so forth were removed). Both of these lists can be obtained by clicking below.

The numbers on this list are not precisely accurate, and some may even be wrong-headed. If you wish to make additions to the list, please feel free to send me a message and I will try to post your message or a correction to this list.

Thanks to all of who replied to my query. If you who would like to take over managing this list of numbers, please send me a message.

Brian Wandell

A Brief Organized List

Units

Radiometric units represent physical energy (e.g., radiance has units of watts sr^-1 m^-2)
Colorimetric units adjust radiometric units for visual wavelength sensitivity (e.g. luminance has units of cd m^-2); scotopic units are proportional to rod absorptions; photopic luminance units are proportional to a weighted sum of the L and M cone absorptions
Typical ambient luminance levels (in cd m^-2): starlight 10^-3; moonlight 10^-1; indoor lighting 10^2; sunlight 10^5; max intensity of common CRT monitors, 10^2
One Troland (Td) of retinal illumination is produced on the retina when the eye looks at a surface of 1 cd / m^2 through a pupil of area 1 mm^2.
Lens focal length: f (meters); lens power = 1/f (diopters)
Conversion of linear units (X) to decibels: Y = 20 log10(X); a change of 0.3 log10 units is a factor of 2, or 6 dB

Image Formation

The eyes are 6 cm apart and half-way down the head
Visual angle of the sun or moon = 0.5 deg
At arm's length: thumbnail = 1.5 deg; thumb joint= 2.0 deg; fist = 8-10 deg
Monocular visual field measured from central fixation: 160 deg (w) x 175 deg (h)
Binocular visual field measured from central fixation: 200 deg (w) x 135 deg (h)
Region of binocular overlap: 120 deg (w) x 135 deg (h)
Range of pupil diameters: 2mm -8mm.
Refractive indices: air 1.000; glass 1.520; water 1.333; cornea 1.376
Optical power (diopters): cornea, 43; lens, 20 (relaxed); whole eye, 60
Change in power due to accommodation, 8 diopters
Axial chromatic aberration over the visible spectrum: 2 diopters

Retina

Retinal size: 5 cm x 5 cm; 0.4 mm thick
One degree of visual angle = 0.3 mm on the retina
Number of cones in each retina: 5 x 10^6
Number of rods in each retina: 10^8
Diameter of the fovea: 1.5 mm (5.2 deg); rod-free fovea: 0.5 mm (1.7 deg); foveola (rod-free, capillary-free fovea): 0.3 mm (1 deg); size of the optic nerve head: 1.5 mm x 2.1 mm (5 deg (w) x 7 deg (h)) location of the optic nerve head: 15 deg nasal
Peak cone density: 1.6 x 10^5 cones/mm^2;
Foveal cone size: 1-4 mu (diameter) x 50-80 mu (length); extrafoveal cone size: 4-10 mu (diameter) x 40 mu (length) Size of rods near fovea: 1 mu (diameter) x 60 mu (length)
S cone spacing (foveal): 10 arc min
L and M cone spacing (foveal): 0.5 arc min
Number of (L + M) cones / Number of S cones = 14 (though the ratio may be higher in the foveola)
1.5 10^6 optic nerve fibers/retina; ratio of receptors to ganglion cell in fovea 1:3; ratio of receptors to ganglion cells for whole retina, 125:1

Cortex

Area of entire cortex: 1.3 x 10^5 mm^2; 1.7 mm thick
Total number of cortical neurons: 10^10; density: 10^5 neurons / mm^3
Synapses: 5 x 10^8 synapses / mm^3 4 x 10^3 synapses/neuron;
Axons: 3 kilometers / mm^3
Number of corpus callosum fibers: 5 x 10^8
Number of macaque visual areas: 30
Size of each area V1: 3cm by 8 cm
Half of area V1 represents the central 10 deg (2% of the visual field)
Width of a human ocular dominance column 0.5-1.0 mm; width of a macaque ocular dominance column 0.3 mm">.

Sensitivity

Minimum number of absorptions for: scotopic detection 1-5; detectable electrical excitation of a rod 1; photopic detection 10-15
The number of photoisomerisations per rod (per sec?) required to saturate the retinal rod circuit.
Following exposure to a sunny day, dark adaptation to a moonless night involves: 10 minutes (photopic); 40 minutes (scotopic); change in visual sensitivity 6 log10 units
Highest detectable spatial frequency at high ambient light levels, 50-60 cpd; low ambient light levels, 20-30 cpd
The contrast threshold (Delta L / L) for a static edge at photopic luminances is 1%.
Highest detectable temporal frequency: high ambient large field, 80 Hz; low ambient, large field 40 Hz.
Typical localization threshold: 6 arc sec (0.5 mu on the retina)
Minimum temporal separation needed to discriminate two small, brief light pulses from a single equal-energy pulse:15-20 ms
Stereoscopic depth discrimination: step threshold, 3 arc sec; point threshold, 30 arc sec

Color

Visible spectrum: 370-730 nm
Peak wavelength sensitivity: 507nm (scotopic) and 555 nm (photopic)
Spectral equilibrium hues: 475 nm (blue), 500 nm (green), 575 nm (yellow), no spectral equilibrium red
Number of basic English color names: 11
Incidence of: anomalous trichromacy, 10^-2 (male), 10^-4 (female); protanopia and deuteranopia, 10^-2 (male), 10^-4(female); tritanopia, 10^-4; rod monochromacy, 10^-4; cone monochromacy, 10^-5

VISTA LAB

Useful Numbers