2013-07-08 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

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