Image formation and anomalies of refraction

Image formation and
Anomalies of refraction
Gauri S. Shrestha, M.Optom,
Fellow of International Association of Contact lens educators (Australia)

Lecturer and Optometrist at Institute of Medicine, Maharajgunj, KTM

Gauri S Shrestha, M.Optom, FIACLE

Image formation
 Image forms in retina in inverted position.
 The rays of light scattered in all direction from a
point source that pass through the lens to converge
in macula where the image forms.
 Since the cornea has an fixed curvature the curved
image forms in the curved retina so that the final
perception is straight and the image is erected due to
mental perception.
 In lens opacities at periphery of lens, sharp image
forms but brightness can be reduced.
 In opacities on the center, the vision may decrease.


Image formation
 In myopia image forms in front of retina
that is corrected by placing the negative
lenses.
 For hypermetropia, positive lens is placed
in the eyes to make the image fall on the
retina.
 For astigmatism, plano-cylinder or
sphero-cylinder lenses are placed to
coincide the image on retina

Main classification of ametropia
 Emmetropia
 A parallel pencils of rays from distance are sharply focused
on the retina when accommodation is at rest
 Deviation from this definition is called as ametropia
and is optical
 Category of ametropia
 Spherical
 Astigmatism
 AKA: Anomalies of refraction


Anomalies of refraction:
 The variations from perfect coincidence
of the principal focus of the eye with the
retina.


Myopia
 If sharp image is formed in front of retina the
resulting error of refraction is called myopia.
 Having an optical system too powerful for its axial
length
 Light must reach to retina in the state of divergence
 Object must be at some finite distance from the eye

 The point conjugate with the fovea of the un-
accommodated eye is called the FAR POINT
(MR)
MR
l (-ve) l’

Myopia
 Myope can focus objects with in the far point
only
 The situation becomes worsen by
accommodation
 Myope can focus object at shorter distance
than usual (craftmanship)


Hypermetropia
 If the pencils within the eye are intercepted by the
retina before reaching their focus
 Too weak to suit its axial length
 Light must reach to the retina in the state of convergence
 Far point is behind the eye
 Object can be focused into the retina by virtue of
accommodation provided sufficient eye’s dioptric
power l’

l (+ve)

Ocular refraction
 If a myopes far point= 200mm
 l= -200mm then L= -5.00D
 l’= image distance (axial length of reduced eye)
 L’= image vergence= n’/l’
 For the reduced eye
 L’=L+Fe
 L=L’-Fe
 Ocular refraction = eye’s dioptric length - its power
 Refractive error= K’-Fe
 Eye’s dioptric length= index by true axial length

Example
 A reduced eye has an axial length of 21mm
and a power of +62.00D. What is the ocular
refraction and where is the far point?

K’= n’/l’ = 4/3x1/21x1000 = +63.49D

Fe = +62.0D

L= K’-Fe = +1.49D

l= 1/L = +671mm


Axial and refractive ametropia
 In axial ametropia
 Eye assumes a standard power of +60.0D
 Defect is attributed to error in axial length

 In refractive ametropia
 Axial length of reduced eye = 22.22
 Defect is attributed to the error in the power

 Low grade of ametropia, no firm relationship
establishes b/w axial length and ametropia


 Change in ∆l’ in the value of L’ would
produce an identical change ∆l in refractive
error if Fe is constant
dL’ dn’l’-1 -n’L’2 -L’2
= = -n’l’-2 = =
dl’ dl’ n’
n’2
-L’2
∆L’ = ∆l’
n’


 If +60D is taken as a mean value for L’, this
expression becomes
∆L’ = -3600/n’ X ∆l’
= -3.6/n’ X ∆l’ (l’ in mm)
= -2.7 X ∆l’
 An increase of 1mm in the axial length would
produce a change in ametropia of -2.7D


Correcting lens
 The un-accommodated eye is in focus for
objects in the far point
 A lens second focus for distant object is
equivalent to eye’s far point

MR
l (-ve) l’
l’

l (+ve)

Spectacle refraction
 Back vertex power: the distance in meters
from the back vertex of the lens to its second
principal focus
d
F’
MR
f’sp l’
l (-ve)
l= fsp- d
1 1 Fsp
L= l = =
fsp- d 1-dFsp

Spectacle refraction

l’

MR

F’
d l (+ve)
f’sp
f’sp= d+l
1 L
Fsp= d+l =
1+dL


Example
 An eye with an ocular refraction of +5.00D is to be
corrected by a spectacle lens placed at a vertex
distance of 13mm. What should be its power?
 An eye is corrected for distance vision by a lens of
power -15.00D placed 14mm from its pricipal point.
What is the ocular refraction?
 A prescription reads -8.00at 16. What lens power
would be needed if the vertex distance were reduced
to 13mm?


Hypermetropia and accommodation
 emmetrope: accoomodate
eye for only viewing near Total hypermetropia
object
Latent Manifest
 Myopes accommodate
eye only for object Facultative Absolute
viewing nearer the far
point A person has +3.0D on
 Hypermetrope: exert retinoscopy, accept up to +2.0D
accommodation to view without blurring of vision. On
object at any distance cycloplegic refraction it is
with great effort +5.0D. Describe the
components of hypermetropia?

Retinal image in corrected ametropia
 Two stages
 Lens forms a real or virtual image
 Image is real if formed in front of eye
 Virtual if formed behind the eye

 Image becomes a object for the eye


f’sp
Q l

d l’
u
u0 u’
Q’2 h’2
h1’= h2

Q’1

Hypermetropia

Q
Myopia
Q’1
l’
h1’= h2 d
u0 u u’
h’2
Q’2
f’sp

l


Retinal image in corrected ametropia
h1’= h2 =-u0 f’sp (Radian)

h1’= h2 =-u0 f’sp/100 (prism diopter)

h’2= h2 L2/L’2 f’sp= d+l
l’= axial length of eye
h2 = h’1= image formed by
spectacle lens= -u0 f’sp


An eye of axial length 24.80mm is corrected for distance by a
-5.00D lens placed 12mm from its principal point. Find the
size of the retinal image of a distant object subtended an angle
of 15pd (n’=4/3)
 f’sp= -200mm
 h’1= h2= -u0 f’sp= -15 X -200mm/100= +30mm
 l= fsp-d= -200-12= -212mm
 L= -4.72D
 L’= n’/l’= +53.76D
 h’2= h2 L/L’= 30 X -4.72/53.76 = -2.63mm


Blurred retinal image

l k’

l’

j= l’-k’ j=g (K’-L’/K’)= g (K-L/K’)
g l’


An unaccommodated eye which has a power of +62.00D, an
ocular refraction of -6.00D, and a pupil diameter of 4mm views
a point object at a distance of 250mm. Find the diamter of the
retinal blur circle.

 L= 1000/-250= -4.00D
 L’= L+Fe= -4.0D+62.0D= +58.00D
 K’= K+Fe= -6.0D+62.00D= 56.00D

 J= g(K’-L’/K’)= 4 (56-58)= -0.14mm
56.00

L= vergence coming to eye
K= ocular refraction = refractive error

Vision in spherical ametropia
 Based on the finding of simulated myopia
study

 Log D (in feet) = 1.360 log S + 1.817

 Hirsch (1945)- up to -14.0DS
 Crawford et al (1945)

 Rubin et al (1951)


Astigmatism
 Astigmatism is defined as a
refractive condition in
which a variation of power
exists in the different
meridians of the eye.
 BB-base curve
B
 CC cross curve
 Plano/+2.00DC C C
B
 +1.50DS/+2.00DC

Ocular astigmatism
 Corneal astigmatism
 With the rule
 Against the rule

 10% of front surface astigmatism is neutralized by
back surface corneal astigmatism
 Crystalline lens (lenticular astigmatism)
 Astigmatisc surface
 decentration


Axis notation
 Standard axis notation (Tabo, Axint)
 As adopted in 1950 by the International Federation
of Ophthalmological Societies

90 180
0

135 45 135
45

180 0 90


Sturm's Conoid
CIRCLE OF LEAST CONFUSION

F1
lens

INTERVAL OF STURM

Rays of light entering cannot
F2 converge to a point focus but forms a
focal lines

Image formation in the astigmatic eye

B’β
α
B’α
F1 B’z
lens Second focal line

β First focal line

F2


Given an object at dioptric distace L, the respective image
vergence after refraction by the eye are

L’α= L+F α
L’β= L+F β


B’z
H B’β
B’α α

g
b β
a z
β

J l’α α
l’z
l’β

Length of first focal line
l’β - l’α L’α –L’β
a= g g =
=
l’β L’ α


Length of Second focal line

l’β - l’α L’α –L’β
b= g =g
=
l’ α L’ β L’z=?

Diameter of circle of least confusion

l’β - l’z L’z –L’α L’α –L’β
z= g =g
= =g
=
l’ β L’ α L’α +L’β


An astigmatic reduced eye (n’=4/3) with a pupil diameter of 5mm
has a power of +62.0D in the 30 meridian and +64.00D in the 120
meridian. Determine the main feature of the image of an axial
object point at a distance of one meter from the eye’s principal
point.

120 30
L -1.00D -1.00D
Fe +64.00D +62.00D
L’ +63.00D +61.00D
l’ (n’/L’) +21.16mm +21.86mm


Length of focal lines

L’α –L’β 63 –61
a== g
= =5
= = 0.159mm
L’ α 63

L’α –L’β 63 - 61
b== g
= =5 =0.164mm
L’ β 61

L’z= 1/2 L’α +L’β =+62.00D

l’z= n’/L’z= +21.50mm

L’α –L’β 63 –61
z =g =5 =0.081mm
= 63 +61
L’α +L’β


Clinical classification: Astigmatism
A. Compound myopic
astigmatism
B. Simple myopic
astigmatism
C. Mixed astigmatism
D. Simple hyperopic
astigmatism
E. Compound
hyperopic
astigmatism

Aphakia:
 It means the absence of crystalline lens from the eye.
 It produce high degree of hyperopia.
 Parallel rays of light are brought a the focus 31mm behind the
cornea

 Cause:
a) congenital absence of the lens.
b) surgical aphakia.
c) aphakia due to absorption of the lens matter after trauma in
children.
d) traumatic extrusion.
e) Posterior dislocation of the lens in the vitreous.


Aphakia
 Optics of the aphakic eye.
• eye becomes highly hyperopic.
• Power of the eye reduces to 44D.
• There occurs total loss of accommodation.
• The posterior focal point is about 7mm behind
the eye ball or anterior principle focus
-17.05mm in front of the cornea
• The nodal point of the eye moved forward.


To study aphakia, let’s consider G-E
schematic eye
 r= 7.8mm, n= 4/3, l’ = 23.89mm
 L’= n’/l’= 55.81D
 Fe= n’-n/r= +42.73D n’= 4/3

 L= L’-Fe= 55.81-42.73=
+13.08D
 l= 76.45mm l’= 23.89mm

 f’sp= l+d= 76.45+12=
+88.45mm
 F’sp= 1/88.45= +11.31D

Presbyopia
 The condition with physiological diminution of
amplitude of accommodation with increasing age to the
point where clear or comfortable vision at the near is
not acceptable.
 When accommodation is minimum or absent called
absolute presbyopia.
 Corrected hyperopes develop presbyopia earlier than
myopes or emmetropes
 Symptoms:
 Blurred near vision, symptom of uncorrected hyperopia, asthenopia or
headache, pupil greatly constrict, drowsy or falling sleepy while reading .
 Correction : Bifocal or (PALs) Multifocal contact lenses in
gas permeable or soft lens materials Monovision Surgery

Image formation and anomalies of refraction

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