STANDARDIZED HUMAN EYE
Last Update 05 July
09
Rhodonine™ and Activa™: See Citation Page
Measured values for in vivo humans
EXCEPT AS NOTED. See also note 1 at the end
This HTML formatted document is an abridgement of a more complete and current document, with references, available in PDF format.
This tabulation is divided into a series of subparts:
Type: Broadband, immersed, anamorphic, afocal, 4-element with field corrector & collimator **
Characteristic | Value | Comment |
Cornea (element 1) | 43 diopters | on-axis, varies with field angle |
index of refract. | xxx | |
surface | | elliptical |
Lens (element 2) | 16-26 diopters | on-axis, varies with accommodation and field angle |
index of refract. | | variable both axially and radially, see text |
surface | | elliptical |
Retina (element 3) | field plate | variable thickness of neural layer acts as corrector element |
Collimator (element 4) | 2.0 mdiam. | array of "ellipsoids" in front of each PC |
Spectral Width | <425-->1300 nm. | Between ½ amplitude points |
Avg.in-band transmission | >90% | 425 to 1200 nm. |
Iris, opening | 7.0+ to 2.0- mm. | max. to min. |
time constant | 6.0 sec./1.2 sec. | open/close |
Focal length of main group | | |
paraxial F. L. (LeGrand) | 22.2888 mm. | (no accommodation) |
Complete focal equation | (F. L.)sin theta mm. | lens power varies to maintain focus on spherical retina |
Depth of focus (on-axis) | +/- 8.0 m | +/- 3.0 @ f/2.4; +/-17.0 @ f/8.5 |
Back focal length | | (no accom.) |
Geometric demagnification | 450:1 | Numeric is on-axis value--at 10 m. |
Snell's Law demag. | 1.33:1 | Due to immersion optics |
Total demag. | 600:1 | On-axis value, without collimator |
Field Corrector | | consisting of neural tissue and
supporting tissue in the optical path. Typical thickness 500
m thinning to 100 m
in Foveola |
macula lutea | 2.0mm/0.8mm | horiz./vert. yellowish in color |
| | |
Collimator lens | 2.0 m | spherical lens, index = 1.40 |
Focal length | | nominally fixed |
** This optical description incorporates the parameters of Gullstrand's
Schematic Eye (xxx). Upon elimination of the collimator lens, the field
corrector, the continuous gradient index of refraction for the lens, and
limiting the field angle to ~0.0; the resulting simplified paraxial (Gaussian)
optics is identical to that of Gullstrand. Gullstrand used an index of
refraction which varied by zone in his calculations. The resulting values are
also very similar to those of LeGrand's Full Theoretical Eye which used a
single index of refraction for the lens.
Tabulation of individual optical parameters
The following values are for educational purposes only. They are not adequate for optical design purposes where five decimal place accuracy is
needed. See Chapter 2 of the text or contact the author for more precise values.
Refractive indeces (at 500 nm.)
These values are a function of wavelength and temperature
Air | 1.00032 |
Cornea | 1.376 |
Aqueous humor | 1.336 |
lens (avg) | 1.386 |
vitreous humor | 1.336 |
Optical power of surfaces (at 500 nm.)
anterior surface of cornea | +49D |
posterior surface of cornea | -6D |
anterior surface of lens (nominal) | +6D |
posterior surface of lens (nominal) | +9D |
Retinal Topography
Zones of the Retina (following Hogan, 1971)
....Central
Foveola | 0.35 mm diam | ~175 PC's in diam. ~23,000 PC's |
Fovea | next zone out to 1.85 mm diam. | ~750 PC's in diam. ~4 x 105 PC's |
Parafovea | next zone out to 2.85 mm diam. | ~1,250 PC's in diam. |
Perifovea | next zone out to 5.85 mm diam. | ~3,000 PC's in diam. |
....Peripheral
Near periphery | 1.5 mm zone around the central retina |
Mid periphery | 3.0 mm zone around near periphery |
Far periphery | 9-10 mm wide on temporal side, 16 mm wide on nasal side |
Ora serrata | 2 mm wide on temporal side, 0.7-0.8 mm. wide nasally |
....Macula (a.k.a. Macula Lutea)
Overlay of retinal area 2.0 mm. wide and 0.88 mm. vertically centered on the Fovea
Generally believed to be colored due to presence of cytoplasmic inclusions of Xanthophyll
Retinal Cross-section
(following Rodieck, 1973 distal to proximal)
Inner Limiting Membrane | chemical isolation: vitrea from IRP |
Optic fiber layer | axons of ganglion cells |
Ganglion cell layer | ganglion cells |
Inner plexiform layer | bipolar to ganglion connections/lateral cells |
Inner nuclear layer | bipolar/lateral cells |
Outer plexiform layer | dendrites of bipolar cells/lateral cells |
(synapse area) | pedicels and spherules of photoreceptors |
Fiber layer | axons of photoreceptors |
Outer nuclear layer | photoreceptor cell nuclei |
Outer limiting membrane | isolation; IPM from IRP |
Inner segment layer | translation region |
Outer segment layer | transduction region |
Retinal epithelium layer | chromophore production & maintenance |
Bruch's membrane | chemical isolation; retina from choroid |
Choroid | structural support |
Total thickness between the Inner Limiting Membrane & Bruch's membrane varies from 0.11 mm. at the edge to 0.23 mm. at the Fovea.
Type: Neuro-secretory cell with attached (but external) photo/piezic transducer
Secretory function | | Secretes structural protein,
Opsin which provides a spaceframe of disks to hold transducer material. |
Spaceframe (cylindrical disk stack) | 50
m x 2.0
m diam. | 2000 disks, 250 Angstrom spacing |
Aspect ratio of stack | 25:1 | nominal |
| | |
Disk thickness | 220 Angstrom | at the fold |
| 160 Angstrom | at the center |
Protein (Opsin) thickness | 64 Angstrom | single layer |
Coating thickness | 15 Angstrom | each side of bilayer |
| | |
Disk formation rate | 1 per hour/stack | nominal / warm blooded mammals |
Disk transport velocity | 250 Angstrom/hr | 0.6
m /day |
Disk operating life | 12 weeks | nominal/ warm blooded mammals |
Transduction function | Two step process | photo/piezic in transducer; piezo/electric transfer to neuron |
Transducer type | photo/piezic |
Material | Rhodonine | 1 of 4 dyes emanating from the retinal epithelium and coating the disks of above spaceframe as a monomolecular liquid crystal |
Excitation time | < 200 femtoseconds | Based on similar retinoid, Wang (1994) |
De-excitation time in-vivo | 15-100 milliseconds | Dependent
on temperature, excitation level and presence of intact dendritic structure. |
in-vitro | > 10 minutes | In the
absence of an appropriate exciton receiver. |
Spectral Peak | | |
Rhodonine 9 | 0.437
m | ½ amplitude width, 0.075
m |
Rhodonine 7 | 0.532
m | ½ amplitude width, 0.065
m |
Rhodonine 5 | 0.625
m | ½ amplitude width, 0.060
m |
(peak values are accurate to two places; more specific values are given in next table)
Active transduction materials
The chromophores of human vision are four members of the Rhodonine family of retinoids, existing in the liquid crystalline state, and derived
from retinol (Vitamin A1) available in the bloodstream. The chromophores form a film on the surface of the protein substrate, opsin. This film
has the smectic type A structure. The unique properties of this family are directly related to the length of the resonant conjugate chain existing
between the two auxochromes of each of these molecules.
Transducer | Resonant chain length |
ll |
lm |
mh | Q |
rhodonine (5) | 5 | 0.595 | 0.625 | 0.655 | 10.4 |
rhodonine(7) | 4 | 0.500 | 0.532 | 0.565 | 8.2 |
rhodonine(9) | 3 | 0.400 | 0.437 | 0.475 | 5.8 |
rhodonine(11) [UV] | 2 ** | 0.300 | 0.342 | 0.385 | 4.0 |
where l, m and h indicate the low half amplitude point, the mid wavelength point
and the high half amplitude point. The mid wavelength point is the average of
the low and high values because the function is so broad that the center point
is ill defined. The bands are separated by 0.095 +/-0.005 microns which is a
typical spacing for these homologs.
**The UV photoreceptors of the human eye are effectively shielded by the limited
transmission of the optical system. They are significant in the performance of
the aphakic human eye.
Molecular weight of the chromophores
Rhodonine(5) | 285 |
rhodonine(7) | 299 |
rhodonine(9) | 285 |
rhodonine(11)[UV] | 299 |
The molecular weight of the substrate Opsin is irrelevant to the photodetection process.
Translation function | | |
piezo/electric conversion | unity gain | |
Adaption function | | |
transistor amplification | typically 3500:1 electron (current) amplification |
Synaptic function @ pedicel
Each electrotonic synapse contains multiple synaptic disks
Synaptic disk diam. | 0.3-0.5 microns | Each contains a hexagonal array of Activa (frequently labeled boutons) |
Activa diam. | 50-60 Angstrom |
Activa spacing | 90 Angstrom | center to center in array |
Presynaptic lemma thick. | 70 Angstrom | emitter of Activa |
Post synaptic lem. thick. | 70 Angstrom | collector of Activa |
Synaptic gap | 45-100 Angstrom | Base of Activa |
Gap material | | hydronium in crystalline form |
Activa type | PNP |
Energy Threshold of Adaptation Amplifier
Nominal energy threshold of first Activa in photoreceptor adaptation amplifiers |
>2.0 Electron-volts | equiv. to 600 nm. Not over 2.34 EV based on
Sliney data |
Time Constants
Iris-- closing 1.2 sec
opening 6.0 sec
Photoexcitation/De-excitation process
Intrinsic t |
0.5(25) ms | dominant during falling edge in P/D equation |
Dynamic,
s*F*t |
s*F*0.525 sec. |
dominant during rising edge of P/D equation.
Where F = radiant flux in photons/sec micron2;
s
= absorption
coefficient in electrons-microns2/photon; product usually much less than
t |
absorption coefficient,
s |
0.76 | (From file, Fulton_Rushton79 fg 3.ai for the scotopic region) |
Adaptation amplifier
Attack | XXX sec | dominant during increase in illumination |
The attack characteristic is due to a "charging" circuit and depends on the illumination level. |
Recovery | | dominant during decrease in illumination |
1st | 3 seconds | electronic |
2nd (1st vascular) | 2 minutes | vascular, est. from Spillmann |
3rd (2nd vascular) | 10 minutes | vascular " " " " |
The recovery time constants vary dramatically with position in the retina mosaic.
They are a function of the impedance of the cell wall, the vascular supply and
the capacitance shunting the collector of the Activa. The first time constant,
interpreted from the recording of the Class C waveform by Baylor (1984), is
electronic and has a value of three seconds.
Nominal pass band of signaling channels
Low frequency (RC type) pole | XXX | Due to adaptation amplifier collector circuit |
High frequency pole | XXX | |
Nominal transmission velocity of signaling channels
Phase velocity of signals within the electrolytic medium |
4,400 m/sec. at 37C |
Group velocity of action potential signals between regenerative nodes |
44 m/sec. at 37C |
Nominal spectrum of P/D equation (& generator potentials)
Low frequency pole | none |
High frequency poles at | |
1/t
= 2p x f = 1.9 |
0.3 Hz | from LaPlace of P/D equation |
s
x F = 2
p
x f =
| XXX | |
Nominal action potential parameters
Nominal action potential pulse shape @ 37 C
Time constant of pulse rise, tR | 0.012 msec |
Time constant of pulse fall,tF | 0.25 msec |
Switching time, tS | 0.075 msec |
[For VQ
= zero; VM
= -95 mV, VS
= -94 mV, tR
= 0.012 msec, tS
= 0.075 msec & tF
= 0.25, Temp. 37 Celsius. Parameters from Schwarz &
Eikhof]
Nominal action potential frequency
dark adapted luminance channels | zero | no pulses are generated absent illumination |
dark adapted chrominance channels | 30 Hz | 33 ms.between pulse peaks |
dark adapted polarization channels | 30 Hz | assumed, lacking data |
Maximum action potential frequency
all signal projection channels | 100 Hz | nominal value, may be exceeded |
Perceived Spectral Response Characteristics
There are four distinctly different regions of the luminosity function; the
hyperopic, photopic, mesopic and scotopic. Each exhibits different absolute
maxima and various relative maxima depending on the state of adaptation of the
three individual chromophores. Confirmation experiments must use narrow
band filters, express the state of adaptation of each chromophoric channel
individually and specify the color temperature of the source.
The nominal peaks in each are:
Name | Absolute maximum | Type | Relative maxima or inflection point |
Hyperopic | 580 nm. | Perceived | 437, 494, 523, 625 |
Photopic | 523 nm. | Chromophoric | 437, 494, 580, 625 |
Mesopic | 523 nm. | Chromophoric | details change significantly with intensity |
Scotopic | 494 nm. | Perceived | 437,494 |
Note that none of these absolute maxima are related directly to a chromophoric
peak. Additional selective adaptation must be employed to observe the other
chromophoric peaks. The above peaks are obtained with instrumentation of less
than five nanometers spectral bandwidth. The
following values were defined based on averaging, and smoothing, of
wideband filter data collected at relatively uncontrolled color temperatures.
CIE Photopic 555 nm. Smoothed
CIE Scotopic 507 nm. Smoothed
(Includes vascular support to the ocular globe and retina)
optic nerve artery divides into choroid and retinal portion.
Total number of neurons | 106 |
Efferent | few dozen |
Afferent | |
non-signal | few dozen |
signal to LGN | 106 |
signal to Pretectum | 2 x 104 |
Important features;
Transposition, and first bifurcation at the optic chiasm to support binocular vision
Second bifurcation to support both the LGN and Pretectum
Spatial Pointing
Field of Rotation-- |
Saccadic Motion | Large Saccades | Small Saccades |
Control | largely voluntary | involuntary |
Amplitude-- | a few to XXX degrees | a few minutes of arc |
Max. Velocity | | |
Horizontal | 700 degrees/sec. | |
Vertical | 400 degrees/sec | |
Tremor
Size of high frequency tremor--20-40 arc seconds in object field, 1 to 2
photoreceptors in fovea
Frequency of high frequency tremor--30-90 Hertz (reports to 150 Hertz)
Servo-loop delay for shutters, iris and lens
Total delay approx. 50 ms. (Ditchburn, pg. 162.)
Blink duration, Several tenths of a second
(Yarbus, pg. 123)
During blink, ocular makes a characteristic motion; up, medial, and back again,
that typically takes 0.1--0.2 seconds
HYDRAULIC PARAMETERS
Retinal rate of flow | 1.6-1.7 ml. per mm. per gm. of retina (est.) |
Anderson et. al., 1964 |
Mean retinal circulation time | 4.7 +/- 1.1 sec. |
Hickman & Frayser, '65 |
Mean retinal transit time | 3-4 sec. |
Friedman et. al., 1964 |
1st vascular time constant | 2 min. | estimated value |
2nd vascular time constant | 10 min. | estimated value, see Section IV time constants above |
MOLECULAR WEIGHTS OF BINDING PROTEINS
apo-SRBP | ~21,000 |
SRBP+retinol+TTR+albumin | ~80,000 |
CRBP | unknown |
CRALBP | unknown |
IRBP | unknown |
Spatial Resolution
Pixel size in & at fovea | 0.31 minutes or 18.5 seconds | Based on 2. 0 micron diameter Outer Segment and a f. l. of 22.2888 mm. from Le Grande (check this re: index) |
Limiting Resolution | 45 line pairs per mm (one black & one white line) | |
Peak Signal Amplitude versus spatial frequency | 30 line pairs per mm | |
Above values measured using a high resolution monitor
Temporal Resolution
The temporal performance of the human eye is a function of which signal path is involved and the irradiance level. The following selected values
have been gleaned from the literature.
Maximum detectable frequency at high irradiance | Luminance | Chrominance | Appearance |
Fovea | | 45 Hertz | |
Parafovea | | | |
[outer limits] | | | |
Electrical Passband
Tremor in the eye causes a sharp edge in the object field to be sampled at up to 90 Hertz. For larger repetitive patterns, the small saccadic motion
causes similar sampling of fixed images at up to XXX Hertz. These frequencies appear in the image information presented to the photoreceptors
of the eye. If the light level is sufficiently high, the P/D equation will support the transmission of information at these frequencies to the signal
circuitry of the retina.
Note 1: The values in this compendium are for the human at 37 Centigrade. Temperature plays a major role in the biology of vision. However, it does not follow the Arrhenius Rule. Biological activity essentially stops at zero Centigrade and fails due to denaturing near 50 Centigrade.
Other recent sources providing parameters related to the Human Eye are;
Foundations of Vision, (1995) | Wandell, B. | Primarily psychophysical analyses |
The first steps in Vision (1998) | Rodieck, R. | An introductory text |
The Human Eye (1999) | Oyster, C. | A general text, with a good glossary |
Many of the values in these texts were drawn from disparate sources without attempting
to correlate the values within a consistent framework. One of the authors actually
solicited individual parametric values over the INTERNET. Some of the values in these
texts are not supported here and must be interpreted in the light of the Theory of this work. Example, the terms "rods" and "cones" are morphological ones that have
no functional significance. Example, the Posterior nodal distance of
LeGrand's Theoretical Eye only applies to the on axis condition.