Useful numbers

Units

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

Image Formation

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

Retina

  1. Retinal size: \(5~cm\times5\) cm; 0.4 mm thick
  2. One degree of visual angle \(=0.3\) mm on the retina
  3. Number of cones in each retina: \(5\times10^{6}\)
  4. Number of rods in each retina: \(10^{8}\)
  5. 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: \(1.5~\text{mm}\times2.1~mm\) (5 deg (w) x 7 deg (h)) location of the optic nerve head: 15 deg nasal
  6. Peak cone density: \(1.6\times10^{5}~cones/\text{mm}^{2};\)
  7. Foveal cone size: 1-4 \(\mu \text{m}\) \((diameter)\times50-80~\mu \text{m}\) (length); extrafoveal cone size: 4-10 \(\mu \text{m}\) (diameter) x 40 \(\mu \text{m}\) (length)
  8. Size of rods near fovea: 1 \(\mu \text{m}\) (diameter) x 60 \(\mu \text{m}\) (length)
  9. S cone spacing (foveal): 10 arc min
  10. L and M cone spacing (foveal): 0.5 arc min
  11. Number of \((L+M)\) cones / Number of \(S~cones=14\) (though the ratio may be higher in the foveola)
  12. \(1.5\times10^{6}\) 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

  1. Area of entire cortex: \(1.3\times10^{5}~\text{mm}^{2}\) 1.7 mm thick
  2. Total number of cortical neurons: \(10^{10}\); density: \(10^{5}\) neurons \(/\text{mm}^{3}\)
  3. Synapses: \(5\times10^{8}\) synapses \(/\text{mm}^{3}\) \(4\times10^{3}\) synapses/neuron;
  4. Axons: 3 kilometers \(/\text{mm}^{3}\)
  5. Number of corpus callosum fibers: \(5\times10^{8}\)
  6. Number of macaque visual areas: 30
  7. Size of each area V1: 3cm by 8 cm
  8. Half of area V1 represents the central 10 deg (2% of the visual field)
  9. Width of a human ocular dominance column 0.5-1.0 mm; width of a macaque ocular dominance column 0.3 mm

Sensitivity

  1. Minimum number of absorptions for: scotopic detection 1-5; detectable electrical excitation of a rod 1; photopic detection 10-15
  2. The number of photoisomerisations per rod (per sec?) required to saturate the retinal rod circuit: 1
  3. 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 \(\mu \text{m}\)
  4. Highest detectable spatial frequency at high ambient light levels, 50-60 cpd; low ambient light levels, 20-30 cpd
  5. The contrast threshold (Delta \(L/L)\) for a static edge at photopic luminances is 1%.
  6. Highest detectable temporal frequency: high ambient large field, 80 Hz; low ambient, large field 40 Hz.
  7. Typical localization threshold: 6 arc sec (0.5 \(\mu \text{m}\) on the retina)
  8. Minimum temporal separation needed to discriminate two small, brief light pulses from a single equal-energy pulse: 15-20 ms
  9. Stereoscopic depth discrimination: step threshold, 3 arc sec; point threshold, 30 arc sec

Color

  1. Visible spectrum: 370-730 nm
  2. Peak wavelength sensitivity: 507nm (scotopic) and 555 nm (photopic)
  3. Spectral equilibrium hues: 475 nm (blue), 500 nm (green), 575 nm (yellow), no spectral equilibrium red
  4. Number of basic English color names: 11
  5. 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, \(10^{-5}\)