Theme 5: Accommodation and
Presbyopia
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Concept of Accommodation
Extent of Accommodation
Eye modifications during Accommodation
The retinal image and the accommodated eye
Variations of the amplitude of accommodation
with age: Presbyopia
Neutralizing Presbyopia
Concept of Accommodation
Acommodation: Eye property for focusing on
near objects
The eye focuses by varying its power (P), while in most
optical instruments focus is produced by varying the
longitude (X’)
X’ = X + P
Concept of Accommodation
Quantifying accommodation
- Far Point (fp): Conjugate point with the retina when
accommodation is zero
- Refraction (R): vergence of the far point
1
R
r
Concept of Accommodation
Quantifying accommodation
R: Refraction
A=R-X
1
R
r
1
X
x
X: Vergence of the
object
Concept of Accommodation
Quantifying Accommodation
A=R-X
If the eye has refraction zero (R=0, ojo emmetropic eye):
R = 0  A = -X
Amplitude of Accommodation
Remote Point (fp): Conjugate point with the retina where
accommodation is zero.
Near Point (np): Conjugate point with the retina when
accommodation is maximum.
Amplitude of accommodation
Amplitude of Accommodation: Maximum
Accommodation
1 1
Am  R  P  
r p
Si R  0
1
Am  P  
p
Amplitude of accommodation
Range of Accommodation: Distance that
separates the far point from the near point
Amplitude of accommodation
Range of Accommodation: Distance that
separates the far point from the near point
Example:
R0
Am  2 D
1
r  
R
P  R  Am   Am  2 D
1
1
p 
 50 10 2 m
P 2
Range of Accommodation :
r 
p  50cm
Amplitude of accommodation
Range of Accommodation: Distance that
seperates the far point from the near point
Example
R  1 Am  2 D
1
1
r 
 1m
R 1
P  R  Am  1  2  3D
1
1
p 
 3310 2 m
P 3
Range of Accommodation:
r  1m
p  33cm
Amplitude of accommodation
Clear vision zone (CVZ) and blurry (BVZ)
Amplitude of accommodation
Clear vision zone (CVZ) and blurry (BVZ)
R=0
Amplitude of Accommodation
Amplitude of accommodation for comfortable vision:
Maximum value of accommodation that can be used in
continuous work.
Am CV
2
 Am
3
•Normally 2/3 is considered the amplitude of
accommodation, but this value can be different
depending on the author consulted (1/2, 3/4)
Modifications to the eye during
accommodation
Principal modifications of the eye during
accomodation:
• Geometric changes in the Iris
• Geometric changes in the Crystalline
• Changes in the refraction index
Modifications to the eye during
accommodation
 Geometric changes to the Iris
• Decrease of pupil diameter 
Decrease circle of defocus
  PE
X

P
if PE    
Eye modifications during
accommodation
 Geometric changes in the Iris
• The iris moves forward (A=7D 0.4 mm)
Eye modifications during
accommodation
 Geometric changes in the crystalline
A=0D
A=7D
eL
4 mm
4.5 mm
r1L
10.2 mm
6 mm
r2L
-6 mm
-5.5 mm
Eye modifications during
accommodation
 Changes in the refractive index
nL
A = 0D
A = 7D
1.42
1.427
Intracapsular mechanism of
accommodation (Gullstrand)
Eye modifications during
accommodation
The theoretical
eye accommodated
Le Grand model (A=7D)
A=0D
A=7D
Cornea
1.3771
1.3771
Aqueous Humor
1.3374
1.3774
Crystalline
1.42
1.427
Vitreous Humor
1.336
1.336
Sup. posterior cornea
0.55
0.55
Sup. anterior lens
3.6
3.2
Sup. Posterior lens
7.6
7.7
Sup. anterior cornea
7.8
7.8
Sup. posterior cornea
6.5
6.5
Sup. anterior lens
10.2
6
Sup. posterior lens
-6
-5.5
Refractive Index
abscissas (respect to
the vertex of the
cornea)
Radius of curvature
Eye modifications during
accomodation
The theoretical eye
accommodated
Model Le Grand (A=7D)
A=0D
A=7D
Power
42.36
42.36
principal object plane
-0.06
-0.06
principal image plane
-0.06
-0.06
Power
21.78
30.70
principal object plane
6.02
5.47
principal image plane
6.20
5.65
Power
59.94
67.68
principal object plane
1.59
1.82
principal image plane
1.91
2.19
Cornea
Crystalline
Complete Eye
The retinal image of the
accommodated eye
 Retinal image without
accommodation
n u
y' 
P
 Retinal image of the
accommodated eye
n u
y' 
P
*
The size of the retinal image in the accommodated
eye is EQUAL to that in the unaccommodated eye
(as long as u is equal and the movement of the
principal planes is not considered)
Variations of the range of accommodation
with age: Presbyopia
With age the capacity of accommodation
decreases
Am = R- P
if emmetropic
Am = - P = -1/p
If the range of accommodation decreases
the near point (p) moves farther from
the eye.
Variations of the range of accommodation
with age: Presbyopia
Presbyopia appears when the near point
is farther than the working distance and
as a result the eyes are unable to focus
on the near objects
Variations of the range of accommodation
with age: Presbyopia
Am = R- P
if emmetropic
Am = - P = -1/p
Elevated range of accommodation
(no presbyopia)
Variations of the range of accommodation
with age: Presbyopia
Am = R- P
if emmetropic
Am = - P = -1/p
Decrease of the range of accommodation
with age (presbyopia)
Variations of the range of accommodation
with age: Presbyopia
Decrease of the range of accommodation with
age
DONDERS
Am = 12.5 – 0.2 Age
Linear variation
between 35 and 50
years
Variations of the range of accommodation
with age: Presbyopia
Decrease of the range of accommodation with age
DUANE
Am = 17.1 – 0.3 Year
Linear variation
between 40 and 55
years
Variations of the range of accommodation
with age: Presbyopia
Age at which presbyopia appears
dw= - 33 cm
pcv  d w
Amcv= 2/3Am
 pcv  33cm For emmetropic eyes R = 0:
Amcv  R  Pcv
1
1
Amcv   Pcv  

 3D
2
pcv
 3310
Variations of the range of accommodation
with age: Presbyopia
Age at which presbyopia appears
dw= - 33 cm
2
Am cv  Am
3
Amcv= 2/3Am
3
3
Am  Am cv  3  4.5 D
2
2
Variations of the range of accommodation
with age: Presbyopia
Age at which presbyopia appears
dw = - 33 cm
Amcv= 2/3Am
DONDERS
Am = 12.5 – 0.2 Age
4.5=12.5-0.2 Age
Age=(4.5-12-5)/-0.2=40 years
Variations of the range of accommodation
with age: Presbyopia
Age at which presbyopia appears
dw= - 33 cm
Amcv= 2/3Am
DUANE
Am = 17.1 – 0.3 Age
4.5=17.1-0.3 Age
Age=(4.5-17.5)/-0.3=42 years
Optical neutralization of presbyopia
Principle of neutralization: Place a lens in front of the
eye (which we call addition) that forms the image of an
object at the working distance in the near point of the
eye (near point and working distance are together)
Optical neutralization of presbyopia
Near point and working distance are conjoined through
addition
X’ = X + P
1
P
 Ad
dT
Ad  
1
 Amvc
dT
1
Ad 
 Amvc
dT
Optical neutralization of presbyopia
For a working distance of 33 cm
1
1
Ad 
 Amcv 
 Amcv  3  Amcv
2
dT
3310
For a working distance of 25 cm
1
1
Ad 
 Amcv 
 Amcv  4  Amcv
2
dw
2510
Optical neutralization of presbyopia
Vision zones of a presbyope.
far and near Clear vision zone (CVZ)
far Clear vision zone (CVZ)
r 
1
p 
Amcv
Optical neutralization of presbyopia
Near Clear Vision Zone
• pn is conjoined with np through the addition
• rn is conjoined with fp through the addition
R  RC  Ad
P  PC  Ad
For an emetrope R=0, P=-Amvc
1
rn  
Ad
1
pn  
 dw
Amcv  Ad
Optical neutralization of presbyopia
Validity of neutralization of presbyopia with an addition
rn  p
Rn   Ad
Rn  P P   Amcv
Ad  Amcv
for dw=-33cm Ad=3-Amcv
Amcv  1.5D
for
3  Amcv 1.5 D
Neutralization is
possible with Ad
Optical neutralization of presbyopia
With the passage of time Am ↓
A BLURRY VISION ZONE APPEARS
SOLUTION: An intermediate addition is added so that
an intermediate CVZ covers the BVZ generated
between fp and fpn
Optical neutralization of presbyopia
intermediate Clear Vision Zone
• pI is the conjugate of p through the intermediate addition
• rI is the conjugate of r through the intermediate addition
R  RI  AdI
P  PI  AdI
For an emmetrope R=0, P=-Amvc:
1
rI  
AdI
1
pI  
Amcv  AdI
Optical neutralization of presbyopia
intermediate Clear Vision Zone
- There are diverse values of AdI that can cover the
blurry vision zone that is generated
- For a given Ad , the AdI does not have one unique
value.
Optical neutralization of presbyopia
intermediate Clear Vision Zone
In order for the intermediate zone of clear vision to
cover the zone of blurry vision it should meet the
following condition
rI p
p I  rN
Optical neutralization of presbyopia
intermediate Clear Vision Zone
rI p
p I  rn
RI P
PI Rn
 Ad I   Am cv
 Ad I  Am cv   Ad
Ad I  Am cv
Ad I  Ad  Am cv
Optical neutralization of presbyopia
intermediate Clear Vision Zone
Keeping in mind the relation:
1
Ad  
 Amcv
dw
For a working distance of 33 cm:
Ad I  3  Ad
Ad I  2 Ad  3
Optical neutralization of presbyopia
intermediate Near Vision Zone
Ad I  3  Ad
Ad I  2 Ad  3
GRAPHIC SOLUTION
For a given Ad, there are
diverse values AdI which
allow the zone of blurry
vision to be covered
Optical neutralization of presbyopia
intermediate Clear vision zone
Ad I  3  Ad
Ad I  2 Ad  3
CONVENTION
Ad
I
Ad

2
Optical neutralization of presbyopia
Validity of the neutralization of presbyopia with an addition
Vision zones of a presbyope:
As can be seen in the
graph for Ad  2D, which is
to say for Amvc  1D, the
neutralization of prebyopia
is possible with Ad and AdI
Optical neutralization of presbyopia
Validity of the neutralization of presbyopia with an addition
Vision zones of a presbyope:
pr = ∞
pp
pri
prc
dT
ppi
SOLUTION:
PROGRESSIVE
LENS
Optical neutralization of presbyopia
Summary
If dT  p presbyopia appears:
1
1
Amvc  

dT
dT
For dT=-33 cm:
Amvc  3D
For dT=-33 cm:
Ad  3  Amvc
Neutralization:
1
Ad 
 Amvc
dT
BIFOCAL LENS
Optical neutralization of presbyopia
Summary
Para dT=-33 cm:
Intermediate
Addition:
Amvc  1.5D
Ad
AdI 
2
TRIFOCAL LENS
Optical neutralization of presbyopia
Summary
For dT=-33 cm:
Amvc  1.0D
It is not possible to neutralize presbyopia with an
addition and an intermediate addition
PROGRESSIVE LENS
Optical neutralization of presbyopia
Summary. Vision Zones of the presbyope
prL = ∞
prc
ppL
pri
r
rc  
1
Ad
1
rI
Ad I
dT
ppi
p 
pc  
1
Amvc
1
 dT
Amvc  Ad
1
pI  
Amvc  Ad I
Optical neutralization of presbyopia
Example
Amcv=1D
r 
1
1
p 
   1m
Amcv 1
Ad  3  Amcv  3 1  2D
rn  
1
1
   0.5m  50cm
Ad
2
pn  
1
 d w  33cm
Amcv  Ad
Optical neutralization of presbyopia
Example
Amcv=1D
Ad 2
AdI 
  1D
2
2
1
1
rI
   1m
Ad I
1
1
1
pI  

 0.5m  50cm
Amcv  Ad I
11