Aberrations

Lens Aberrations and
ophthalmic lens design
Gauri S. Shrestha, M.Optom, FIACLE
Lecturer
B.P. Koirala Lions Centre for Ophthalmic
Studies

Introduction
An optical defect where rays from a point object do
not form a perfect point after passing through optical
system

Degrades the optical performance of a lens or prism

Imperfection of image formation due to several
mechanisms

Aberroscope-instrument for observing aberration,
designed by Tscherning

Gauri S Shrestha, M.Optom, FIACLE 2

Introduction
Chromatic aberration is caused by the
material from which the lens is made and is
caused by the material having different
refractive indices for light of different
wavelength

Monochromatic aberrations occur when
incident light is not confined to paraxial rays


Chromatic Aberration
Dispersion (dispersive power)
 longitudinal (axial) chromatic aberration of
an optical material: the secondary focal
length of the lens is different for each of the
monochromatic constituent of light


Longitudinal (axial)
 Bichrome Test (Red/Green Balance)

Lens Retina

Definitions
Dispersion is represented with the
symbol ω and called “omega”

nF - nC
ω=
nD - 1


Dispersion

C = 656 nm

d = 587 nm

F = 486 nm

mean dispersion = nF - nC
ω=
mean refractivity = nd - 1

Reciprocal of dispersion is the Abbé
number
1
V=
ω

 Low dispersion = high Abbé number
 Glass lenses with V > 50 crown glass
 Glass lenses with V < 50 flint glass


Longitudinal (axial)

F
LCA = ωFd =
V

Transverse (lateral) - lens

y

TCAlens = y’C - y’F

yF
TCAlens = TCA = ω ε 0
V

Transverse (lateral) - prism

ε
TCAprism =
V


Example 1: What is the chromatic aberration of a
+6.00D crown glass lens with an Abbe number of 65?
FD
Longitudinal Chromatic Aberration =
V

6
= = +0.092 D
65


Example 2: A +5.00D lens has indices of 1.52, 1.53 and
1.54, for the C, D and F Fraunhofer lines respectively.
What is the amount of chromatic aberration?
FD
Longitudinal Chromatic Aberration =
V

Know
nF - nC 1.54 – 1.52
F = +5.00
ω= = = 0.0377
1.53 – 1.00
Find V nD - 1


Example #2 continued:

ω = 0.0377 V = 26.5

FD = +0.19 D
V


Reduction of Chromatic
Aberration
Chromatic aberration cannot be
eliminated in an optical element
made of a single material

Achromatic system--two elements
(doublet) of different materials that
produce equal but opposite
dispersions

Aberration
Achromatic lenses
r1 r1 ’
FTOTAL = F1 + F2
crown

flint
F1 F2
r1’ = -r1 --- +--- = 0
V1 V2
r2 r 2’

Example
What is the power of each element of a -2 D
achromatic doublet composed of glass
materials with Abbé numbers of 60 and 40,
respectively?
V1
F1 = F TOTAL
V1 - V 2

60 (-2) = -6 D
F1 =
60 – 40
V2 40
F2 = F TOTAL = (-2) = +4 D
V1 – V 2 60 - 40

Aberration
Achromatic prisms
ε1 ε2
=
crown
V1 V2

flint

ε = ε 1- ε 2

Example
What is the power of each element of a 2∆
achromatic doublet prism composed of
glass materials with Abbé numbers of 60
and 40, respectively?
V1
ε1 = εTOTAL
V1 - V 2

ε1 = 60 (2) = 6 p.d.
60 - 40

V2 40
ε2 = εTOTAL = (2) = 4 p.d.
V1 - V 2 60 - 40

Introduction
Geometrical optics assumptions
 Monochromatic light
 Rays of light involved in image formation
are confined to a small cylindrical region
immediately surrounding the optical axis
(paraxial region)


Introduction

In 1850’s Ludwig von Seidel described 5
monochromatic aberrations which affect the
image when the object is far enough off axis
or the area of the lens used is far enough
from the axis


Introduction
Seidel aberrations
 third-order (non-paraxial) aberrations
 series expansion of sine function, where angle
α is in radians:

α3 α5 α7
1st order: sin α = α - + - + …
± 10 deg 3! 5! 7!
3rd order:
± 23 deg

Introduction
Seidel aberrations
Depends on lens diameter, object size,
and/or lens position
Independent of wavelength
Full correction of one aberration requires
correction of all previous aberrations


Introduction
Monochromatic aberrations, a.k.a.
Seidel aberrations
 spherical aberration
 coma

 oblique astigmatism

 curvature of image

 distortion


Spherical Aberration
Occurs when a pencil of light is refracted
by a large-aperture optical system,
which occurs because different zones
of the aperture have different focal
lengths.


Longitudinal spherical aberration
Caustic Surface
aperture

LSA
LSA increases with the square of aperture


Transverse spherical aberration
Confusion Disc

aperture
TSA

TSA increases with the cube of the aperture


Only important for lenses of high power
(+10.00D or more)
Controlled by using aspheric surfaces
or
using a crossed lens
Crossed lens -- front surface power is
greater than the back surface power by
a factor of 6

Spherical aberration
Larger the pupil size, greater the difference in
focusing between two rays
Distance in diopters=longitudinal spherical
aberration
+ve sph aberration= when peripheral rays are
refracted more than paraxial
-ve =when peripheral rays are refracted less
than paraxial.
Relaxed human eye-small amount of +ve sph
aberration(upto 1D for pupil of 8mm diameter)

Correction of spherical
aberration
Occluding the periphery of lens by use of
stops
Use of Plano convex lens
Use of aplanatic surfaces( peripheral
curvature less than central curvature)
Use of doublet principal lens and a weaker
lens of different refractive index cemented
together
Use of aspheric lenses

Correction of SA
 aspheric surfaces - also reduce oblique
astigmatism and distortion


Correction of ocular
spherical aberration
Anterior corneal surface is flatter peripherally than
centre (aplanatic surface)
Nucleus of the lens has higher refractive index
than the lens cortex
Iris acts as stop to reduce spherical aberration
Pupil eliminates the marginal rays
Retinal cones are much more sensitive to paraxial
rays than oblique/peripheral rays


Coma

Occurs when oblique rays are refracted by a large-
aperture optical system. Affects the sharpness of
image points.
Spherical aberration occurs for beams of light
parallel to the optic axis; coma occurs for oblique
beams

Rarely a problem with spectacle lenses the limiting effect of
the pupil


Coma
Factors that control coma
 aperture size
 lens form

 angle of obliquity

Composite image is not circular, but
elongated like coma or comet


Treatment of Coma..
By eliminating the peripheral rays

Limiting rays to the axial area of lens

By using the principal axis of lens rather
than subsidiary axis


Oblique Astigmatism

Occurs when oblique rays are refracted by a small-
aperture system and affects both sharpness of image
points and image position.
A.K.A. radial astigmatism; marginal astigmatism
Astigmatic form for off axis object points

Affects both sharpness of image points and image position
Inability of lens to form a point image of an oblique point
object (toric effect)

Oblique Astigmatism
Definition
 Inability of a lens to form a point image of
an oblique point object
 Interval of Sturm, 2 line foci and the circle

of least confusion


Oblique Astigmatism
Tangential & Sagittal foci and Petzval surface
S P
T PT = 3 PS

ST
PS =
2
When lens forms an image of a plane object, the
image lies along a curved surface=Petzval surface

Oblique Astigmatism
Tangential and Sagittal foci
 Teacup & Saucer


Oblique astigmatism
Formation of interval of strum of line foci and
circle of least confusion
Management of Oblique astigmatism-
 Restricting the aperture of lenses
 Use of meniscus lenses than biconvex/biconcave
 Orientation of lens such that incident light is parallel to
the principal axis


Oblique Astigmatism
Tscherning ellipse
 relationship between surface power (front
or back) and back vertex power of a thin
lens for which oblique astigmatism is
eliminated
F +
F2 = -13.85 -- √ 30 – 2.87F – 0.182F2
2
Above equation determines the back surface
power, F2, for a given lens power F for which
there is no oblique astigmatism
Limit= +7.25 to -23.00D


Curvature of Image

Manifests itself as a curved image surface for a
flat object surface and primarily affects image
position
Affects image position

Treatment-the curvature of retina compensates for curvature
of field


Curvature of Image
Definition
 inability of a lens to form a plane image of
a plane object
 Image surface is known as Petzval’s
surface

n = index of refraction of lens
rPETZVAL = -nf´
f´ = 2° focal length of the lens


Curvature of Image
Definition
 far-point sphere is the locus of points
conjugate to the fovea as the eye rotates,
where rFPS = s - f’

plus lens minus lens

Curvature of image
Aberration of curvature of image is absent
 Image surface (Petzval’s surface)= far point
surface
 rFPS = s - f’= 0.027-f’
 -nf’ = 0.027-f’ or f’ = 0.027/(1-n)
For any lens whose power is other than -19.37D
for COR= 27mm, little can be done to cause the
Petzval surface of the lens to correspond to the far
point sphere of the eye in the absence of oblique
astigmatism


Distortion
Occurs when the magnification of an
extended object varies with its
distance from the optical axis.
Distortion affects image shape and
lateral position, but not image clarity


Distortion
 inability of a lens to form an image of the
same shape as the object
 when the ratio of the image size to the
object size has a constant value for all
object sizes, no distortion exits and the
condition of orthoscopy exits


Distortion
Pupil of the eye acts as a stop behind a
spectacle lens

pincushion (plus) M.Optom,barrel (minus) 48
Gauri S Shrestha, FIACLE

Distortion
Magnification differences may not be
evident with certain objects

plus minus


Distortion
Mainly a problem for lenses of high
power
Aphakes
Can be reduced with aspheric lenses


Aberrations

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Aberrations