Theme 2: The theoretical eye Form and dimensions of the eye Optical constants of the eye Optical...
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Transcript of 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.
Form and dimensions of the eye
• 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
Geometric optics applied to the eye
yXX
y
PXX
''
'
Relationships of conjugation
(origin of principal planes. Gauss equation)
Vergences
Geometric optics applied to the eye
Geometric optics applied to the eye
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’
Geometric optics applied to the eye
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
Geometric optics applied to the eye
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
Schematic model of the eye
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
Schematic model of the eye
The cornea: Geometric representation
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
Schematic model of the eye
The cornea: Geometric representation
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
.''''
.
...
..'''
...
.
Schematic model of the eye
The cornea: Geometric representation
Cardinal elements
Focal distances
mmSF
mmSF
mmPn
FH
mmPn
FH
c
c
c
hacc
c
acc
5131
6723
55313642
33741
612336421
.'
.
..
.''
..
Schematic model of the eye
The cornea: Geometric representation
Simplified cornea
The principal planes are
very close. Thus, the
cornea can approximate
to just one surface
mmPnn
rc
ahac 8
3642133741
..
Schematic model of the eye
The cornea: Geometric representation
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
Schematic model of the eye
Le Grand model
Schematic model of the eye
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
The crystalline: Geometric representation
Schematic model of the eye
Power
mne
nHH
L
L
L
LL 43
21 10822421104
..
'
D
PPPPP LLLLL
7821141081082214108 3
2121
.))(.)(.(.
Joining distance
Total power of the crystalline
The crystalline: Geometric representation
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
...'''
...
...
..'''
..
..
Schematic model of the eye
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
.'
.
...
''
..
.
Schematic model of the eye
The crystalline: Geometric representation
The complete eye: Geometric representation
mnSHSH
nHH
ha
Lc
ha
Lc 335
1055433741
10026106
...''
Joining distance
Schematic model of the eye
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
.'''
.
..
..'''
..
.
Schematic model of the eye
The complete eye: Geometric representation
Cardinal elements
Focal distances
mmSF
mmSF
mmPn
FH
mmP
nFH
o
o
o
hvoo
c
aoo
224
0915
292260
3361
661660
1
.'
.
..
''
.
Schematic model of the eye
The complete eye: Geometric representation
Schematic model of the eye
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 complete eye: Geometric representation
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 pupils of the eye
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
.
..
.'
..
.'
'
'
The pupils of the eye
IrisP
XX
PIris
E
IRIS
PE
E
131
8804136505323
.
...
Size
The pupils of the eye
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