# Useful numbers

## 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 102 ; sunlight 105; max intensity of common CRT monitors, 102
• One Troland (Td) of retinal illumination is produced on the retina when the eye looks at a surface of 1 cd / m2 through a pupil of area 1 mm2.
• 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; index's thumbnail = 1 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 105 cones/mm2;
• 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 105 mm2; 1.7 mm thick
• Total number of cortical neurons: 1010; density: 105 neurons / mm3
• Synapses: 5 x 108 synapses / mm3 4 x 103^ synapses/neuron;
• Axons: 3 kilometers / mm^3
• Number of corpus callosum fibers: 5 x 108
• 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