optical engineering...optical data of the eye property relaxed accomodated refractive power 58.63...
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Optical Engineering
Part 17: Human eye
Herbert Gross
Summer term 2020
Introduction
data
Optical properties
Eye models
Resolution and quality
Diseases
2
Contents
The Human Eye
Ref: Wikipedia
The Human Eye
cornea
pupil
iris
tear liquid
front chamber
conjunctiva
conjunctiva
lens vitreous
body
macula
(yellow)
retina
blind spot
rear chamber
muscle
muscle
nerve
fibres
fibres
outer skin
choroid
membrane
The Human Field of View
Ref: Wikipedia
Ranges:
< 10° central
< 30° near peripheral
< 60° mid peripheral
Black circle: blind spot
Optical Data of the Eye
Property relaxed accomodated
Refractive power 58.63 dptr 70.57 dptr
Focal length in air 17.1 mm 14.2 mm
Power of the crystalline lens 19 dptr 33 dptr
Pupil diameter, smallest value for high brightness 1.5 mm
Pupil diameter, largest value for night vision 8.0 mm
Abbe number (approx.) 50.23
Petzval radius -17.58 mm
Location of entrance pupil -3.047 mm
Field of view maximum 108°
Field of foveated seeing 5°
Diameter eye ball 24 mm
Distance rotation point from cornea vertex 13.5 mm
Nodal point location 7.33 mm
Principal plane location 1.6 mm
Eye Data - Overview
Terms
Sizes and lengths
retina
fovea
cornea
iris
optical disc
blind spotcrystalline lens
lens capsule
anterior
chamber
posterior
chamber
vitreous
humor
temporal
nasal
0.5 mm
3.6 mm
3.6 mm
F'
F
24.4 mm
15.7 mm
NN'PP'
1.6 mm
7.33 mm
C
13.5 mm
1.8 mm
4 mm
1.8 mm
2.5 mm
Refractive Index
Distribution of the index
along z
Smooth index variation
of crystalline lens
z
[mm]
n
0 5 10 15 20 251
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
cornea crystalline
lens
lens
capsule retina
vitreous humor
anterior
chamber
n
z
[mm]0 0.5 1 1.5 2 2.5 3 3.5 4 4.51.3
1.32
1.34
1.36
1.38
1.4
1.42
Spectral Transmission of the Eye
Absorption of the eye media prevents retina damage
Special truncation of UV and IR contributions
3000
20
40
60
80
100
500400 800600 1000 1400 2000
[nm]
T [%]
visible
after cornea
before lens
after lens
at retina
Receptors, rods and cones
Cones : Fovea, bright light, colour
Rods : Peripheral, dim light, no colour
Blind spot :
no receptors
Fovea : 2° field
eccentric
Property cones rods
Location in the fovea outside the fovea
Field of view small, 5° large, 108°
Resolution and visual acuity large small
Brightness sensitivity small, for daylight vision large, vision at night
Colour sensitivity yes no
Total number of elements 5 million 120 million
Limiting brightness 683 lm / W 1699 lm / W
Spectral maximum 555 nm 507 nm
Range Diameter
[mm] Cones Rods
Foveola 0.35
number :3500
density 190000/mm2
pitch 2.3 m
no rods
Fovea 1.85 density : 100000/mm
2
pitch : 3.2 m a few rods
Prafovea 2.85
Macula lutea
Perifovea 5.85 density : 160000/mm
2
pitch : 2.5 m
Periphery density : 5000/mm
2
pitch : 14.0 m
density : 50000/mm2
pitch : 4.5 m
Papille, blind spot 4 mm off axis
nasal 1.8 no cones no rods
Spectral Sensitivity of the Eye
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
V()
night
scotopic
rods
day
photopic
cones
cyan green
Log V()
10-1
400 450 500 550 600 650 700 750400 450 500 550 600 650 700 750
10 0
10-2
10-3
10-4
10-5
Spectral sensitivity of the eye:
- Depends on brightness
Daylight / high brightness:
cones, peak sensitivity at 550 nm
At night/ low Brightness:
rods, peak sensitivity at 507 nm, shifted towards blue
No color distinction
Accomodation
Change of accomodation range
due to aging
age in
years
D [dpt]
16
12
8
4
00 20 40 60
maximum
minimum
mean
dpt
0 20 40 8060
age
[years]
relaxed
eye
strongest
accomodation
immobile
point
4
0
-4
-8
-12
Adaptation
Aging effect on adaptation
Aging effect on adaptation speed
8
6
4
2
00 20 40 60 age in
years
pupil diameter
[mm]
cones
rods
Log Ithresh
[a.u.]
2
3
10 20 30 40
4
5
6
7
8
time
[min]
80 years
50 years
30 years
17 years
7
kink of
Helmholtz
rod mono-
chromate
night
blindness
Gullstrand Model Eye
Six media
Crystalline lens with shell
Data for relaxed and accomodated eye
Simple version : single crystalline lens
Relaxed Accomodated
Parameter Notation Value Value
Focal length object sided f [mm] 17.055 14.169
Focal length image sided f' [mm] 22.785 18.930
Refractive power F [dpt] 58.636 70.57
Location entrance pupil p [mm] 3.045 2.667
Location exit pupil p' [mm] 3.664 3.211
Principal point object sided P [mm] 1.348 1.772
Principal point image sided P' [mm] 1.602 2.086
Nodal point object sided N [mm] 7.078 6.533
Nodal point image sided N' [mm] 7.332 6.847
Length L [mm] 24.387
30°
10°
0°
0°
486 nm 587 nm 656 nm
10°
20°
Resolution of the Eye
Resolution of the eye
depends on the shape
The quantitative measure
is given as angle
Rough measure : 1'
x'c = 75 m
so = 250 mm
L = 22 mm
c
x
distance
cones
a) letter
5'
b) grating
2'c) two points
1'
d) nonius
10''e) binocular 5''
Visual Acuity
Recognition of simple geometrical
shapes :
1. Landolt ring with gap
2. Letter 'E'
Blur of image on retina with distance
a)
5a
a
a
3a
3a
a
3a
b)
distance 6.096 m
block
letter
E 8.9
mm
image
height
25 meye
original blur : a/2 blur : a blur : 2a blur : 3a blur : 4a
3a
Spectacles
Correction of refraction error by spectacle lenses
1. Myopia : negative lens
2. Hyperopia : positive lens
eye binocular
eye binocular
Eye Diseases
Four major defects
a) refraction error b) glaucom
c) retina defects d) cataract
original