A Brief Organized List of vision science numbers

Contents (click to jump to a section)

• Preface
• Evolution
• Units
• Image Formation
• Retina
• Cortex
• Sensitivity
• Colour

Preface

I have not myself checked most of the facts listed here.

N.B. "X^2" means X raised to the second power i.e. X squared. And "X^-3" means X raised to the power -3 i.e. 1 divided by X cubed.
A "mu" means a micron i.e. 10^-6 of a metre (one thousandth of a millimetre).

Evolution

• There are at least 10 fundamentally different types of eye (using different principles).
• Eyes have independently evolved between 40 and 60 different times.

  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); 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: 1mm -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 area: 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))
  
• 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 = 100
  
• 1.5x10^6 optic nerve fibers/retina
• Ratio of receptors to ganglion cells: in fovea 1:3; 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
  
• 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 (cpd = cycles per degree of visual angle)
  
• 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
  

  Colour

• 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
  (White, black, red, green, yellow, blue, brown, purple, pink, orange, grey)
  
• Incidence of:
  
  • anomalous trichromacy (3 colours, but a different 3 from the rest of us), 10^-2 (male), 10^-4 (female);
    
  • protanopia and deuteranopia (long and medium wavelength cones missing), 10^-2 (male), 10^-4 (female);
    
  • tritanopia (short wavelength cones missing), 10^-4;
    
  • rod monochromacy (rods only), 10^-4;
    
  • cone monochromacy (one cone type only), 10^-5