theme 2: the theoretical eye form and dimensions of the eye optical constants of the eye optical...

Theme 2: The theoretical eye

• Form and dimensions of the eye• Optical constants of the eye• Optical Geometry applied to the eye• Schematic model of the eye• Pupils of the eye

Form and dimensions of the eye

• Sphere of 12 mm

radius.• Transparent

anterior cap,

fragment of a sphere

of 8 mm radius.• Distance between

the centers 5mm.


• Cornea• Pupil• Lens (crystalline)• Retina• Fovea• Optical nerve


• Anterior chamber.

Between the cornea and

the iris. Contains the

aqueous humor.• Posterior chamber.

Between the iris, the

ciliary body, and the

crystalline lens. Contains

the aqueous humor. • Vitreous body. Between

the crystalline lens and

the retina. Contains the

vitreous humor.

Optical constants of the eye

• • cornea (r1c , r2c)

• crystalline (r1L , r2L, ....)

• Thicknesses:• Cornea (ec) • Anterior chamber • Posterior chamber • Crystalline (eh) • Vitreous body

• Refractive indices:• Cornea (nC)

• Aqueous humor (nha)

• Crystalline (nL)

• Vitreous humor (nhv)

• The radii of the surfaces’ curvature:

Vergences

Vergence: refractive index divided by the distance

''

'xn

X

xn

X

x’>0 X’>0

convergence

x<0 X<0 divergence

Unit

Diopters

Geometric optics applied to the eye

Power of an optical system: Vergence of the

image focal distance

fn

fn

P '´

Power of a spherical dioptric:

rnn

P ´

Vergences


yXX

y

PXX

''

'

Relationships of conjugation

(origin of principal planes. Gauss equation)

Vergences



22

21

1

21

2121

ne

nHH

nHH

PPPPP

'''

rnn

P ´ Power of

a dioptric

The joining of two optical systems

n1 n1’=n2 n2’


PP

nHH

PP

nHH

122

211

'''

Cardinal elements

n1 n1’=n2 n2’

H1=H1’ H2=H2’F1 F’1F’2 F2

f1f’1

f2 f’2

Principal planes and

points


Cardinal elements

n1 n1’=n2 n2’

HF F’

f f’

H

Focal planes and points

Pn

FH

Pn

HF

´''

Schematic model of the eye

Procedure in order to obtain a schematic model

• Geometric representation of the cornea.• Geometric representation of the crystalline.• Geometric representation of the complete eye.

(Association cornea and crystalline). • Obtaining the pupils.

“Representation of the eye as an optical system working in the

paraxial zone within the frame of geometric optics.”

Schematic model of the eye:

Cornea Parameters Value

Thickness 0.55 mm

Radius of the first surface

7.8 mm

Radius of the second surface

6.5 mm

Air index 1

Cornea index 1.3771

Aqueous humor index

1.3374


Le Grand model

The cornea: Geometric representation

Power

Dr

nnP

c

acc 3548

1087

1377113

11 .

.

.

Dr

nnP

c

chac 116

1056

37711337413

22 .

.

..

Power of the first surface

Power of the second suface



Power

mn

e

n

HH

c

c

c

cc 43

21 1099333711

10550

...'

D

PPPPP ccccc

36421163548109931163548 4

2121

.).)(.)(.().(.

Joining distance

Total power of the cornea



Cardinal elements

Principal planes and points

mmHHSHSH

mHHSH

mPP

nHH

mPP

nHH

cccc

ccc

c

chacc

c

cacc

54322

51

4412

5421

10610610550

10765

1010636423548

1099333741

107653642116

10993

.''''

.

...

..'''

...

.



Cardinal elements

Focal distances

mmSF

mmSF

mmPn

FH

mmPn

FH

c

c

c

hacc

c

acc

5131

6723

55313642

33741

612336421

.'

.

..

.''

..



Simplified cornea

The principal planes are

very close. Thus, the

cornea can approximate

to just one surface

mmPnn

rc

ahac 8

3642133741

..



The crystalline: Geometric representation

Crystalline parameters

Values

Thickness 4 mm

Radius of the first surface

10.2 mm

Radius of the second surface

-6 mm

Aqueous humor index 1.3374

Crystalline index 1.42

Vitreous humor index 1.336


Le Grand model


Power

Drnn

PL

haLL 108

10210

337414213

11 .

.

..

Drnn

PL

LhvL 14

106

42133613

22

..

Power of the first surface

Power of the second surface



Power

mne

nHH

L

L

L

LL 43

21 10822421104

..

'

D

PPPPP LLLLL

7821141081082214108 3

2121

.))(.)(.(.

Joining distance

Total power of the crystalline


Cardinal elements

Principal points and

planes

mHHSHSH

mHHSHSH

mPP

nHH

mPP

nHH

LLLL

LLLL

L

LhvLL

L

LhaLL

33322

33311

3312

3321

1026104011067

10026104221063

104017821108

108223361

10422782114

1082233741

...'''

...

...

..'''

..

..


The crystalline:Geometric representation

Cardinal elements

Focal distances

mmSF

mmSF

mmPn

FH

mmPn

FH

L

L

L

hvcL

L

haLL

5467

3955

346178213361

41617821

33741

.'

.

...

''

..

.



The complete eye: Geometric representation

mnSHSH

nHH

ha

Lc

ha

Lc 335

1055433741

10026106

...''

Joining distance


DD

PPPPP LcLco

609459782136421055478213642 3

.).)(.)(.(..

Total power of the eye

Power

Cardinal elements

Principal points and planes

mHHSHSH

mHHSHSH

mPP

nHH

mPP

nHH

oLLO

occO

o

chvoL

o

Laoc

3

3

33

33

10911

10591

10294603642

105543361

10651607821

10554

.'''

.

..

..'''

..

.



Cardinal elements

Focal distances

mmSF

mmSF

mmPn

FH

mmP

nFH

o

o

o

hvoo

c

aoo

224

0915

292260

3361

661660

1

.'

.

..

''

.




Reduced schematic model (Listing)Eye: 1 dioptricSHo=1.59 mm1.75mmSH’o=1.91 mm1.75mm

mmSF

mmSF

mmSHSH

mmr

rnn

DP

o

o

oo

ahvo

0224

9214

751

6560

13361

60

.'

.

.'

..

'


The pupils of the eye

The aperture of the diaphragm (DA) of an optical system is the orifice that limits the extention of the beam of light that penetrates it coming from an object point. The DA limits the passage of light through the system.

The iris is the diaphragm of the eye.

Entrance pupil

Entrance pupil: Image of the iris through the cornea

Optical system to keep in mind: Cornea


The method of

calculation that we will

use consists in

obtaining the anti-

image of the iris

through the cornea.

Position

Entrance pupil

mmSP

mmPHx

DPXX

DIrisH

nX

PXX

E

EcPE

CIRISPE

c

haIRIS

cPEIRIS

043

103053231

05323

4136510663

337413

.

..

.'

..

.'

'

'


IrisP

XX

PIris

E

IRIS

PE

E

131

8804136505323

.

...

Size


Position

Exit pupil

mmSP

mmPHx

DPXX

DIrisHn

X

PXX

S

SLPS

LIRISPS

L

haIRIS

LIRISPS

683

52286530

3361

86530

6555210422

337413

.

..

.'

.'

..

.

'

Exit pupil: image of the iris through the crystallineOptical system to keep in mind: Crystalline

SE

S

PS

IRISS

PP

IrisP

X

X

Iris

P

091

041

04186530

64552

.

.

...

Size


Exit pupil

Entrance pupil: 0.56 mm in front of the iris, 13%

greater

Exit pupil: 0.08 mm behind the iris, 4% greater

theme 2: the theoretical eye form and dimensions of the eye optical constants of the eye optical...

Documents

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crystalline index1

association cornea

eye cornea r1c

corneaschematic model

pointsschematic model

eyeschematic model

sufaceschematic model