This document discusses concepts related to the optical properties of the human eye including the schematic eye model. It describes how the schematic eye was developed by Gullstrand to mathematically model the eye's optics. The document also covers topics like the reduced schematic eye model, accommodation, refractive errors like myopia and hyperopia, astigmatism, and different forms of expressing cylinder powers and axes.

1. Nawat Watanachai
Sakarin Ausayakhun
2010

2. Visual optics
 Understanding the
remarkable inner workings
of the eye’s optics
 Problems
 Complicated
 imperfection
 Schematic eye

3. Schematic Eye
 Conceptualizing the optical properties of human eye
 To determine mathematic living eye models
 Developed by Gullstrand, professor of ophthalmology
in Sweden. Nobel Prize 1911

4. Gullstrand’s schematic eye

5. Reduced schematic eye
 Schematic eye can be simplified even further
 We can treat eye as it was a single refracting
element
 Ideal spherical surface separating two media of
refractive indices 1 and 1.33
 Known as reduced schematic eye
 Nodal point =
 Cornea and lens…

6. Reduced schematic eye
P=60 D.
N=1
N=1.33

7. Reduced schematic eye
 D=n/f, D=(n2-n1)/f
 D= 60 D., n(air)=1, n(eye)=1.33
 f=n/D
 Ant.focal point = 1/60 = 17mm.
 Post.focal point = 1.33/60 = 22.6mm.
 D = (n’-n)/f,
f = (n’-n)/D =(1.33-1)/60 = 5.5 mm.
 Nodal point = 22.6-17.0 = 5.6mm.

8.  Schematic eye can calculate image size on retina
Image size = Image distance
Object size Object distance
Image size = Object size
Image distance Object distance

9. Example

m
20 cm.
retinal image?
6

10. 
20 cm.
retinal lesion?
Image size = Object size
Image distance Object distance
Image size = 200 mm.
17 mm.
6000 mm.
Image size = 200x17/6000 = 0.6 mm.
6m

11. Accommodation

13. Near point (NP)

correspond
accommodation
retina
NP
w/accommodation
full

14. Far point (FP)

correspond
retina
accommodation

refraction
FP
w/o accommodation

15. Emmetropia
FP
w/o accommodation
NP
w/ accommodation

16. Myopia
FP
NP
w/o accommodation
w/ accommodation

17. Hyperopia
FP
w/o accommodation
NP
w/ accommodation

18. Far Point

conjugate
accommodation
retina
Emmetropia
Myopia
FP
FP
FP
Hyperopia

19. Near point of accommodation
 NPA
Visual axis conjugate
Retina
accommodation

NPA
amplitude of
acommodation
 Presbyopia
accommodation
progressively decrease with age  ↓ NPA (
)

20. Accommodation decrease with age

21. Presbyopia
 Acc. loss
reading required
40 ac.
reserve
33 cm.
acc.
1/33/100 = +3 D

20
reserve power 10 D

45 reserve spare = 3.5-3 = 0.5  fatigue 

22. Accommodative amplitude
 <40 yr. increase 1.00 D./ each 4 yr.
 40 yr. = 6.00 D., 44 yr. = 4.5 D., 48 yr. = 3.00 D.
 >48 yr. decrease 0.50 D./ each 4 yr.
 <- 40(6.00 D.) – 44(4.50 D.) – 48(3.00 D.) ->
 Ex. 60 yr. = 1.5 D.

23. Accommodation
 Accommodative range =
 Accommodative amplitude
A= F – N
 A = accommodative amplitude
 F = vergence
 N = vergence
FP
NP
FP
NP

24. Example

clear vision
acommodative amplitude = 8.00 D.
-4.00 D.
•
clear vision = far point – near point
• Far point = 100/4 = 25 cm.
• Near point = 100/(8+4) = 8.33 cm.
•
clear vision
8.33-24 cm.

25. Myopia
F
N
w/o accommodation
w/ accommodation

26. Example clear vision

+2.00
accommodative amplitude = 4.00D.
• Uncorrect hyperope 2.00 farpoint = 100/2 =
50 cm.
•
accommodation +2.00 D.
far
point
infinity
accommodation
2.00 D.
•
near point
100/(4-2) = 50 cm.
•
clear vision
50 cm
infinity

27. Hyperopia
F
N
w/o accommodation
w/ accommodation

28. Example
 Without correction, far point is located at
front of the eye and near point at
eye.
cm in
cm in front of the
 What is refractive error of this eye?
 What is amplitude of accommodation of this eye?

29. • FP
cm
100/100 = -1 D
rays)
F
distant correction =
divergent
N
w/o accommodation
w/ accommodation

30. 
FP
 vergence

accom.
cm
FP
- D
NP
cm
 vergence


NP
- D
A = F - N = (-1)-(-3) = 2 D
amplitude of accommodation
D

31. Reading add prescription

add
accommodative amplitude
 example
54

D
-2.
30 cm
D,
accom. Amplitude
add

32. •
•
•
cm (
accommodation 50%
add
2.50 D
F
D)
D
N
w/o accommodation
w/ accommodation

33. Example

54
accom. Amplitude
-2.00 D.
D
•
-2.00 (FP
50 cm)
• AA=1 D (NP
33 cm)
•
accommodation
30 cm,

34. Correcting myopia
P
f’
F

35. Correcting myopia
P1
F1, f1
VD1

36. Correcting myopia
f1
P
f
VD
----> f2’ > f1’
correcting lens
- D
(P2<P1)
- D

37. Correcting hyperopia
f
F

38. Correcting hyperopia
F,f

39. Correcting lens and hyperopia
f1
P
F,f
VD
----> f2 < f1
correcting lens
D
(P > P1
D

40. Vertex distance

refractive error
power

refractive error
lens power
VD
significant change
lens
D
VD
contact

41. CL power

42. 
Aphakic lens +12 D (
VD
15 mm)
prescribe

VD
Dioptric error
10 mm.

43.  +12 D, F’ = 100/12 = 8.3 cm.



R
VD 15 mm.
8.3 – 1.5 cm = 6.8 cm. = FP
VD 10 mm.
= 6.8 + 1.00 = 7.8 cm

44.  P = 100/7.8 = +12.80 D

= 12.8-12.0 = 0.8 D***
 *** VD error
+4 D

45. Example

+
D
mm
mm
power

46. : f2=110 mm = 11 cm
+ . D
power
20 mm =
/
=

47. Cylinder and Astigmatism
 Astigmatic Expression


Spherocylinder form
Combined cylinder form

48. Astigmatism
- Corneal astigmatism
- Lenticular astigmatism
Toric surface

49. Spherocylinder and its imagery
Cornea
O

50. Total astigmatism
Total astigmatism = Corneal astigmatism + Lenticular astigmatism
O
Against-the-rule astigmatism

51. Total astigmatism
Total astigmatism = Corneal astigmatism +lenticular astigmatism
42
40
O
With-the-rule astigmatism

52. Conoid of Sturm
 Anterior focal line
 Posterior focal line
 Interval of Sturm
O
 Circle of least confusion
 Spherical equivalent = sphere + (cylinder/
I

53. Spherocylinder and its imagery

55. Astigmatic dial technique

focal line
retina

56. Astigmatic dial technique

focal line
retina

57. Astigmatic dial technique

sphere
retina)
+Sph
VA
(CLC

59. Astigmatism
 Compound hyperopic
astigmatism
 Compound myopic
astigmatism
 Mixed astigmatism
 Simple hyperopic astigmatism
 Simple myopic astigmatism

60. Cylinder
 Plus cylinder
 Minus cylinder
 Power
cylinder
axis

61. Plus Cylinder
I
Axis
Power
O
O
I

62. Minus Cylinder
O
I
Axis
Power
I

64. Against-the-rule astigmatism
- .
x
retina

65. Against-the-rule astigmatism
focal line
focal lines
- .
x
retina

66. With-the-rule astigmatism
42
40
- .
x 180
retina

67. With-the-rule astigmatism
42
focal line
focal lines
40
- .
x 180
retina

68. Cylinder

cylinder
 Power
 Axis
 Power
cylinder
RE
axis
LE

69. Example
 + . D cylinder
axis 180’

power
+5.00 D
90’

@90

x 180’
+5.00@90’/plano@180’
optical cross

70. Plus cylinder form
+ .
sph + .
x

71. Minus cylinder form
-
+ .
sph - .
x 18

72. spherocylinder: 3
0
+ . x
&+ .
x
Combined cylinder
form
+3.0
0
sph 1. x
Plus cylinder form
3 sph -1. x 18
Minus cylinder form
+2.
0
-1
0
+1.
0
+3.0
0 +3.
0

73. Transposition

minus

sphere
sphere
cylinder
cylinder


plus cylinder
axis
new

74. Example

form

shp + . x
combined cylinder form
spherical equivalent
minus cylinder

75. .
+ .
x
• (+2.00+1.00) -1.00 x 180’
•
- .
x
•
• Sph. Equivalent = + .
+ (+ .
/ )=+ .
D

76. Combined cylinder form
+ .
+ . x
combined cylinder form
0’ = +3.00@180’
x 180’ = +3.00 x 90’

77. Example
 -4.00 -0.5 x 90’
 -4.50 +0.5 x 180’
 -4.50 x 90’ : -4.00 x 180’
• +2.00 -1.00 x 20’
• +1.00 +1.00 x 110’
• +1.00 x 20 : +2.00 x 110’

78. The end
 Confusing???