www.iap.uni-jena.de

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