New Chromaticity Diagram

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:






I OPTICS

Type: Broadband, immersed, anamorphic, afocal, 4-element with field corrector & collimator **
CharacteristicValueComment
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 amplitude points
Avg.in-band transmission >90% 425 to 1200 nm.
Iris, opening7.0+ to 2.0- mm. max. to min.
       time constant6.0 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 mspherical 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
Air1.00032
Cornea1.376
Aqueous humor1.336
lens (avg)1.386
vitreous humor1.336


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



II RETINAL MOSAIC

Retinal Topography

Zones of the Retina (following Hogan, 1971)

....Central

Foveola0.35 mm diam~175 PC's in diam. ~23,000 PC's
Foveanext zone out to 1.85 mm diam.~750 PC's in diam. ~4 x 105 PC's
Parafoveanext zone out to 2.85 mm diam. ~1,250 PC's in diam.
Perifoveanext zone out to 5.85 mm diam.~3,000 PC's in diam.

....Peripheral

Near periphery1.5 mm zone around the central retina
Mid periphery 3.0 mm zone around near periphery
Far periphery9-10 mm wide on temporal side, 16 mm wide on nasal side
Ora serrata2 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 Membranechemical isolation: vitrea from IRP
Optic fiber layeraxons of ganglion cells
Ganglion cell layer ganglion cells
Inner plexiform layerbipolar to ganglion connections/lateral cells
Inner nuclear layerbipolar/lateral cells
Outer plexiform layer dendrites of bipolar cells/lateral cells
(synapse area)pedicels and spherules of photoreceptors
Fiber layeraxons of photoreceptors
Outer nuclear layerphotoreceptor cell nuclei
Outer limiting membraneisolation; IPM from IRP
Inner segment layertranslation region
Outer segment layertransduction region
Retinal epithelium layerchromophore production & maintenance
Bruch's membranechemical isolation; retina from choroid
Choroidstructural 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.


III PHOTODETECTOR CELLS

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 stack25:1nominal
   
Disk thickness220 Angstromat the fold
160 Angstromat the center
Protein (Opsin) thickness64 Angstromsingle layer
Coating thickness15 Angstromeach side of bilayer
   
Disk formation rate1 per hour/stacknominal / warm blooded mammals
Disk transport velocity250 Angstrom/hr0.6 m /day
Disk operating life12 weeksnominal/ warm blooded mammals

Transduction functionTwo step processphoto/piezic in transducer; piezo/electric transfer to neuron
Transducer typephoto/piezic
MaterialRhodonine1 of 4 dyes emanating from the retinal epithelium and coating the disks of above spaceframe as a monomolecular liquid crystal
Excitation time< 200 femtosecondsBased on similar retinoid, Wang (1994)
De-excitation time      in-vivo15-100 millisecondsDependent on temperature, excitation level and presence of intact dendritic structure.
     in-vitro> 10 minutesIn the absence of an appropriate exciton receiver.
Spectral Peak  
     Rhodonine 90.437 m amplitude width, 0.075 m
     Rhodonine 70.532 m amplitude width, 0.065 m
     Rhodonine 50.625 m 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.



TransducerResonant chain length ll lm mhQ
rhodonine (5)50.5950.6250.65510.4
rhodonine(7)40.5000.5320.5658.2
rhodonine(9)30.4000.4370.4755.8
rhodonine(11) [UV]2 **0.3000.3420.3854.0


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 conversionunity gain 
Adaption function  
transistor amplificationtypically 3500:1 electron (current) amplification




    Synaptic function @ pedicel

Each electrotonic synapse contains multiple synaptic disks
Synaptic disk diam.0.3-0.5 micronsEach contains a hexagonal array of Activa (frequently labeled boutons)
Activa diam.50-60 Angstrom
Activa spacing90 Angstromcenter to center in array
Presynaptic lemma thick.70 Angstromemitter of Activa
Post synaptic lem. thick.70 Angstromcollector of Activa
Synaptic gap45-100 AngstromBase of Activa
Gap material hydronium in crystalline form
Activa typePNP




IV SIGNAL PATH PARAMETERS



Energy Threshold of Adaptation Amplifier



Nominal energy threshold of first Activa in photoreceptor adaptation amplifiers >2.0 Electron-voltsequiv. 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) msdominant 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



AttackXXX secdominant 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
1st3 secondselectronic
2nd (1st vascular)2 minutesvascular, est. from Spillmann
3rd (2nd vascular)10 minutesvascular    "      "      "    "

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) poleXXX Due to adaptation amplifier collector circuit
High frequency poleXXX  

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 polenone
High frequency poles at 
1/t = 2p x f = 1.9 0.3 Hzfrom 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, tR0.012 msec
Time constant of pulse fall,tF0.25 msec
Switching time, tS0.075 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 channelszerono 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 channels100 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:

NameAbsolute maximum TypeRelative 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


V Optic Nerve Parameters


(Includes vascular support to the ocular globe and retina)
optic nerve artery divides into choroid and retinal portion.

Total number of neurons106
Efferentfew dozen
Afferent 
     non-signalfew dozen
     signal to LGN106
     signal to Pretectum2 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


VI MOTOR PARAMETERS


Spatial Pointing

Field of Rotation--
Saccadic MotionLarge SaccadesSmall Saccades
Controllargely voluntaryinvoluntary
Amplitude--a few to XXX degreesa few minutes of arc
Max. Velocity   
     Horizontal700 degrees/sec. 
     Vertical400 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


VII CIRCULATION PARAMETERS



HYDRAULIC PARAMETERS



Retinal rate of flow1.6-1.7 ml. per mm. per gm. of retina (est.) Anderson et. al., 1964
Mean retinal circulation time4.7 +/- 1.1 sec. Hickman & Frayser, '65
Mean retinal transit time3-4 sec. Friedman et. al., 1964
1st vascular time constant2 min.estimated value
2nd vascular time constant10 min.estimated value, see Section IV time constants above


MOLECULAR WEIGHTS OF BINDING PROTEINS



apo-SRBP~21,000
SRBP+retinol+TTR+albumin~80,000
CRBPunknown
CRALBPunknown
IRBPunknown


VIII RESOLUTION PARAMETERS



Spatial Resolution



Pixel size in & at fovea0.31 minutes or 18.5 secondsBased on 2. 0 micron diameter Outer Segment and a f. l. of 22.2888 mm. from Le Grande (check this re: index)
Limiting Resolution45 line pairs per mm (one black & one white line) 
Peak Signal Amplitude versus spatial frequency30 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 irradianceLuminanceChrominanceAppearance
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.