Objects and images. (a) A distant object subtends the same angle α inside and outside the eye when the ray passes through the nodal point N. The focal length (f) is the distance from the nodal point to the image. (b) The finest grating that an eye can resolve has an angular period of 2ΔΦ, where ΔΦ is the inter-receptor angle (s/f) at the nodal point, and s is the separation of the receptor centres.
O/U = α = I/f
The finest resolvable grating on the retina has a period of 2s. This can be expressed as an angle:
2s/f radians.
It is often more useful to speak of a grating’s spatial frequency (the reciprocal of the period, in cycles per radian) because the frequency increases as the resolution improves, whereas the period decreases. The spatial frequency with which the retina samples the image is the sampling frequency, designated by vs.
Thus: vs = f/(2s) = 1/(2ΔΦ)
This equation suggests that there are two ways to increase the sampling frequency, and so improve the eye’s resolution. The focal length f might be increased, or the receptor separation s decreased. It is not possible to decrease s below about 2 μm, because receptors narrower than this become leaky to light, as discussed later. Once this limit is reached, as it is in many animals, the only way to improve matters is to increase the focal length, and this necessarily means having a larger eye.
Land, Michael F.; Nilsson, Dan-Eric. Animal Eyes (Oxford Animal Biology Series) (p. 50-51). OUP Oxford. Kindle Edition.
Most the facts below are derived from the book Animal Eyes by Mike Land and Dan-Eric Nilsson. This book is absolutely superb and I cannot recommend it highly enough. The two features of an eye that set a limit to the detail that can be resolved in bright light are the fineness of the receptor mosaic and the quality of the image.
A small object of size O at a distance U from the eye makes an angle of α = O/U radians at the nodal point (a radian is the angle made by an arc of a circle one radius in length at the circle’s centre: 1 radian = 180°/π, or 57.3°), and inside the eye the image I subtends the same angle α at the nodal point. The best definition of the focal length (f), for our purposes, is the distance from the nodal point to the image of a distant point.
Land, Michael F.; Nilsson, Dan-Eric. Animal Eyes (Oxford Animal Biology Series). OUP Oxford.
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
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
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
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”>.
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: 1
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
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
Cornea - 10/0 nylon
Sclera - 8/0 Nylon
Limbus - 10/0 Nylon
Conjunctiva - 8/0 Vicryl
Skin - gut, nylon, vicryl
Endophthalmitis rates multiple injections
BJO Canadian data no gloves no masks no drapes no speculum 1/6500.
Therefore over a course of 25 injections the cumulative risk is 1/250 - 1/333.
(6499/6500)^25
Over a course of 100 injections the cumulative risk is 1/75.