Transcript Schematic model of the eye

Theme 2: The theoretical eye
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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
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Cornea
Pupil
Lens (crystalline)
Retina
• Fovea
• Optical nerve
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
• The radii of the surfaces’ curvature:
• cornea (r1c , r2c)
• crystalline (r1L , r2L, ....)
• Thicknesses:
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Cornea (ec)
Anterior chamber
Posterior chamber
Crystalline (eh)
Vitreous body
• Refractive indices:
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Cornea (nC)
Aqueous humor (nha)
Crystalline (nL)
Vitreous humor (nhv)
Geometric optics applied to the eye
Vergences
Vergence: refractive index divided by the distance
n
X 
x
n'
X'
x'
x’>0 X’>0 convergence
x<0 X<0 divergence
Unit
Diopters
Geometric optics applied to the eye
Vergences
Power of an optical system: Vergence of the image
focal distance
n´
n
P 
f'
f
Power of a spherical dioptric:
n´n
P
r
Geometric optics applied to the eye
Vergences
Relationships of conjugation
(origin of principal planes. Gauss equation)
X' X  P
X
y' 
y
X'
Geometric optics applied to the eye
n´n
P
r
Power of
a dioptric
P  P1  P2  P1  P2
H '1 H 2 H '1 H 2
e



n'1
n2
n2
n1
n1’=n2
n2’
The joining of two
optical systems
Geometric optics applied to the eye
Cardinal elements
Principal planes and points
n1’=n2
n1
n2’
H1=H1’ H2=H2’
F’2
F’1
F1
f1
f’
1
f2
f’
2
F2
P2
H1H  n1 
P
P1
'
H ' 2 H '  n2 
P
Geometric optics applied to the eye
Cardinal elements
Focal planes and points
n1’=n2
n1
n2’
H H
F’
F
f
f’
n
HF  
P
n´
H' F' 
P
Schematic model of the eye
Schematic model of the eye:
“Representation of the eye as an optical system working in the
paraxial zone within the frame of geometric optics.”
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.
Schematic model of the eye
The cornea:
Le Grand
model
Geometric representation
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
The cornea:
Geometric representation
Power
Power of the first surface
P1c 
nc  na 1.3771  1

 48.35D
3
r1c
7.8  10
Power of the second suface
P2c 
nha  nc 1.3374  1.3771

 6.11D
3
r2 c
6.5  10
Schematic model of the eye
The cornea:
Geometric representation
Power
Joining distance
H '1c H 2c ec 0.55  103



 3.99  104 m
nc
nc
1.3371
Total power of the cornea
Pc  P1c  P2c    P1c  P2c 
48.35  ( 6.11)  (3.99  104 )( 48.35)( 6.11)  42.36D
Schematic model of the eye
The cornea:
Geometric representation
Cardinal elements
Principal planes and points
P2c
 4  6.11
H1c H c  na
 3.99  10
 5.76  105 m
Pc
42.36
H ' 2c H 'c  n' ha 
P1c
48.35
 1.3374  3.99  10 4
 6.10  10 4 m
Pc
42.36
SHc  H1c H c  5.76  105 m
SH'c  SH' 2c  H ' 2c H 'c  0.55  103  6  10 4 m   6  105 m
Schematic model of the eye
The cornea:
Geometric representation
Cardinal elements
Focal distances
H c Fc  
na
1

 23.61mm
Pc
42.36
H c ' Fc ' 
nha 1.3374

 31.55mm
Pc
42.36
SFc  23.67mm
SF 'c  31.51mm
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
nha  na 1.3374  1
rc 

 8mm
Pc
42.36
Schematic model of the eye
The crystalline:
Le Grand
model
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
The crystalline:
Geometric representation
Power
Power of the first surface
nL  nha 1.42  1.3374
P1L 

 8.10D
3
r1L
10.2  10
Power of the second surface
P2L 
nhv  nL 1.336  1.42

 14D
3
r2L
 6  10
Schematic model of the eye
The crystalline:
Geometric representation
Power
Joining distance
H '1L H 2L eL 4  103



 2.82  104 m
nL
nL
1.42
Total power of the crystalline
PL  P1L  P2L    P1L  P2L 
8.10  14  ( 2.82  103 )(8.10)(14)  21.78D
Schematic model of the eye
The crystalline:
Geometric representation
Cardinal elements
Principal points and planes
H1L HL  nha 
P2L
14
 1.3374  2.82  103
 2.42  103 m
PL
21.78
P1L
3 8.10
H ' 2L H 'L  n'hv 
 1.336  2.82  10
 1.40  103 m
PL
21.78
SHL  SH1L  H1L HL  3.6  103  2.42  103  6.02  103 m
SH'L  SH' 2L  H ' 2L HL  7.6  103  1.40  103  6.2  103 m
Schematic model of the eye
The crystalline:
Geometric representation
Cardinal elements
Focal distances
H L FL  
nha
1.3374

 61.41mm
PL
21.78
H 'L Fc ' 
nhv 1.336

 61.34mm
PL
21.78
SFL  55.39mm
SF 'L  67.54mm
Schematic model of the eye
The complete eye:
Geometric representation
Power
Joining distance
H 'c HL H 'c S  SHL 6  105  6.02  103



 4.55  103 m
nha
nha
1.3374
Total power of the eye
Po  Pc  PL    Pc  PL 
42.36  21.78  ( 4.55  103 )( 42.36)( 21.78)  59.94D  60D
Schematic model of the eye
The complete eye:
Geometric representation
Cardinal elements
Principal points and planes
H c H o  na 
PL
21.78
 4.55  103
 1.65  103 m
Po
60
H 'L H 'o  n'hv 
Pc
42.36
 1.336  4.55  103
 4.29  103 m
Po
60
SHO  SHc  H c H o  1.59  103 m
SH'O  SH'L  H 'L H o  1.91  103 m
Schematic model of the eye
The complete eye:
Geometric representation
Cardinal elements
Focal distances
H o Fo  
na
1

 16.66mm
Pc
60
H 'o Fo ' 
nhv 1.336

 22.29mm
Po
60
SFo  15.09mm
SF 'o  24.2mm
Schematic model of the eye
The complete eye:
Geometric representation
Reduced schematic model (Listing)
Eye: 1 dioptric
SHo=1.59 mm1.75mm
SH’o=1.91 mm1.75mm
n'hv na
r
1.336  1
r
 5.6mm
60
SH'o  SHo  1.75mm
Po  60D 
SFo  14.92mm
SF 'o  24.02mm
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.
The pupils 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.
The pupils of the eye
Entrance pupil
Position
X 'IRIS  X PE  Pc
nha
1.3374
X 'IRIS 

 365.41D
H 'c Iris 3.66  103
X PE  X 'IRIS PC  323.05D
1
 3.10mm
323.05
SPE  3.04mm
xPE  Hc PE 
Size
X
Iris
323.05
 PE 
 0.88
PE
X IRIS 365.41
PE  1.13Iris
The pupils of the eye
Exit pupil
Exit pupil: image of the iris through the crystalline
Optical system to keep in mind: Crystalline
Position
Size
X 'PS  X IRIS  PL
PS
X
 552.64
 IRIS 
 1.04
Iris
X PS
 530.86
nha
1.3374

 552.65D
3
H LIris  2.42  10
 X IRIS  PL  530.86D
X IRIS 
X 'PS
xPS  H 'L PS 
SPS  3.68mm
1.336
 2.52mm
 530.86
PS  1.04Iris
PE  1.09PS
The pupils of the eye
Exit pupil
Entrance pupil: 0.56 mm in front of the iris, 13% greater
Exit pupil: 0.08 mm behind the iris, 4% greater