ABERRATION

1. ABERRATION
SURAJ CHHETRI

2. CONTENTS
• INTRODUCTION
• CHROMATIC ABERRATIONS
• MONOCHROMATIC ABERRATION
SEIDELABERRATIONS
ZERNIKE POLYNOMIAL
• CLINICAL CO-RELATIONS

3. INTRODUCTION
Aberration : Defect in the image formed on the optical
system
Or defect in image forming property of the optical element.
Aberration word comes from Latin word ABERRARE,
which means “to stray”

5. CHROMATIC ABERRATIONS
• Chromatic aberration is due to the material have different
refractive indices for different wave lengths of light.
CHROMATIC ABERRATION:
1. Longitudinal (axial) chromatic aberration
2. Transverse (lateral) chromatic aberration.

6. CHROMATIC ABERRATIONS
1) Longitudinal chromatic aberration:
• Secondary focal length of a lens will be different for each of
the monochromatic constituents of white light.
• It can be expressed as the dioptric difference between two
extremes.
, , , where, ω=dispersive power ;
power of the lens &
ν=abbe value

7. Longitudinal chromatic aberration
• Secondary focal length of a lens will be different for each of
the monochromatic constituents of white light.
• It can be expressed as the dioptric difference between two
extremes.
where, ω=dispersive power ;
=power of the lens&
ν=abbe value

8. Longitudinal chromatic aberration

9. CHROMATIC ABERRATION IN HUMAN EYE
• For electromagnetic radiation ranging from 380 to 760 nm,
the human eye exhibits about 2.50 D of longitudinal
chromatic aberration, corresponding to linear distance of
0.93mm.[1]
• Research suggests that chromatic aberration may be a cue to
accommodation. For instance, the ability to accommodate
accurately is impaired under monochromatic conditions.[2]
1. Kurger et al.1993
2. Aggarwal et al 1995

10. Transverse chromatic aberrations
a. Difference in image magnification (image size)- It is the
difference in size between the images formed by two
different wavelengths.

11. b. Difference in prismatic effect
(angular dispersion)
• Prisms – Difference in prismatic
effect for light of two different
wavelengths (without changing the
vergence of light).
• Lenses – Prismatic effect will depend
on the distance from the optical
center of the lens.
lateral chromatic aberration
Transverse chromatic aberrations

12. Transverse chromatic aberrations

13. PARAXIALASSUMPTION
SinƟ = Ɵ, (Ɵ= radian)
This assumption only accurate when following condition :
1. Small angle of incidence with refractive surface,
commonly referred as paraxial rays
2. Image produce by spherical surface
This assumption become less accurate as angle of incidence
increases , so better estimation of sinƟ given by following
expansion:

14. PARAXIALASSUMPTION
• When the third order approximation {Ɵ-(Ɵ3/3!)} is used,
image formation differ from what is predicted by the paraxial
equation in five ways.
• These interrelated deviations referred as Seidel or classic
aberration

15. SEIDELABERRATIONS
• 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.
• Monochromatic aberrations, a/k/a Seidel aberrations
• spherical aberration (S1)
• Coma(S2)
• oblique astigmatism (S3)
• curvature of image(S4)
• Distortion(S5)

16. SEIDELABERRATIONS
Depends on lens diameter, object size, and/or lens
position
Independent of wavelength of monochromatic light
Theoretically to avoid aberration requires correction of
all previous aberrations

17. Spherical Aberrations
• It is on-axis aberration.
• Light rays striking the periphery of the lens (non-paraxial
rays) are focused closer or nearer to the lens than those
striking near its center (paraxial rays).
• Problem for mainly large aperture optical system.
• It affects the sharpness of image points.

18. Spherical Aberrations
Positive spherical aberration: Peripheral rays have shorter
focal length than central rays.
Negative spherical aberration: Central rays have shorter
focal length than peripheral rays.
Figure: Ray diagram of
Positive spherical
aberration

19. SHPERICALABERRATION VS SHAPE
FACTOR OF LENS
spherical aberration is minimized for lenses with approximately
planoconvex shapes that are oriented so that the front surface is
more convex.
NOTE: All the lens
have same power

20. ORIENTATION OF PLANO CONVEX LENS
The orientation of the lens is critical—turning it around so that
the front surface is flat increases spherical aberration

21. NEGATIVE SPHERICALABERRATION
• It is possible to have negative spherical aberration with spherical
lens??
• Non-spherical lenses, where the periphery of the lens is flatter than
its center, may suffer from negative spherical aberration.
• In this case, the paraxial rays are focused closer to the lens than
are the non-paraxial rays.

22. OTHER CLINICALAPPLICATION OF
SPHERICALABERRATION
• The unaccommodated eye typically (but not always)
manifests positive spherical aberration, which tends to
increase with age. [1]
• The spherical aberration would be even greater if not for the
aspheric nature of the cornea—the periphery of the cornea is
flatter than its center.
• As the eye accommodates, the amount of positive spherical
aberration decreases.[2]
• 1 Guirao et al. 2000)
• 2 Ivanoff et al. 1956)

23. NIGHT MYOPIA
Under dim lighting conditions the pupil dilates, exposing the
retina to nonparaxial light rays.
These light rays may be focused in front of the retina, making
the eye myopic. This can be one contributing factor to night
myopia
Clinically, consideration should be given to prescribing
lenses with slightly more minus power (or less plus power)
for those patients who do considerable nighttime driving.
Empty-field accommodation probably another contributing
factor for night myopia.

24. COMA
• It is off-axis aberration.
• It affects the sharpness of image points.
• Image of a point object resembles a comet or teardrop or ice
cream cone shape.
• Imagery is not symmetrical with respect to the optic axis or
chief ray.
• Problem for mainly large aperture optical system.

25. POSITIVE AND NEGATIVE COMA
• When the tip of the comet is pointed toward the optical axis,
the coma is said to be positive.
• When it is pointed away, the coma is negative.

26. ON AXIS COMA, POSSIBLE OR NOT???
• On axis coma can also occur with on-axis objects when the
optical components are non-centered and tilted with respect
to each other.
• This is the case in the eye, where coma may be a major
foveal aberration.

27. OBLIQUE ASTIGMATISM
• Also known as marginal or radial aberrations.
• It is off-axis aberration.
• When small bundle of light strikes the spherical surface of a
lens from an angle, oblique astigmatism causes the light to
focus as two line images , known as tangential and sagittal
images , instead of a single point.
• It affects the both sharpness of image points and image
position.
• Present even in the absence of spherical aberration and
coma.

28. SAGITTALAND TANGENTIAL PLANS

29. IMAGE SHELLS

30. SAGGITALAND TANGENTIAL SHELLS -
RECAP

31. CLINICAL CO-RELATION
• Even when oblique astigmatism is minimized through proper
selection of the front surface power, it can still be
problematic when .the lens is tilted with respect to the eye.
• Lets take common example, wrap-around sunglasses may be
tilted with respect to the horizontal plane of the face (i.e.
horizontal frontal plane.)
• This is referred to as face-form; it induces cylinder whose
axis is 090 degrees and sign (plus or minus) is the same as
tilted lens.

32. CLINICAL CO-RELATION
• The effective lens power induced by face form can be
calculated using the following formulae:

33. CLINICAL CO-RELATION
• Question: A patient with prescription of -6.00DS selects a
frame with a face form angle of 20 degrees. If the lens is
made of polycarbonate , what is the effective power that
patient experience??

34. CLINICAL CO-RELATION
• These calculations tell us that when a −6.00 DS
polycarbonate lens is placed in a frame with 20 degrees of
face-form, the effective lens power is −6.22 − 0.80 × 090.
• So, the dispenser or fabricator of the glasses will make
calculations and adjust the prescription to compensate for
face-form prior to making the lenses.

35. PANTOSCOPIC TILT
• QUESTION: What is the effective power of a −8.00 DS
polycarbonate lens that is mounted in a frame that has a
pantoscopic tilt of 15 degrees?

36. PANTOSCOPIC TILT
When a −8.00 DS lens is in a frame with a pantoscopic tilt
of 15 degrees, the effective power experienced by the
patient is −8.17 − 0.57 × 180.

37. PANTOSCOPIC TILT
• Pantoscopic tilt increases a minus lens’s minus power. It is
for this reason that undercorrected myopic patients
sometimes intentionally tilt their spectacles to improve
distance vision.

38. CURVATURE OF IMAGE
• Assumption of paraxial optics
• Plane object forms a plan image

39. CURVATURE OF IMAGE
• In the absence of other aberration , plan object forms the
curve image which is known as curvature of image.
• This is because all the points on the extended object are not
at the same distance from spherical converging lens

40. CURVATURE OF IMAGE
• Petzval surface is free from any astigmatism.
• Principally problem for optical instrument (especially for
camera ) because camera use plan image film for image
capturing.
• Less problem with eye because retina is curved.
TELEPHOTO LENS

41. DISTROTION
• Image produce is sharply defined
• Lies in single plan i.e. no curvature
• Magnification of extended image varies with the distance of
the cross-ponding object from optical axis
• It affects image shape and lateral position, but not image
clarity.

42. DISTORTION
Symmetrical
Pincushion
Barrel
Asymmetrical

43. DISTROTION
Symmetrical: when formed by a centered or co-axial,
optical system and has radial symmetry about the optic axis.
• Pincushion- Image size to object size ratio increases with an
increase in object size.
• Barrel – Image size to object size ratio decreases with an
increase in object size.
Asymmetrical: when formed by non-centered optical
system(prism produced asymmetrical distortion).

44. Asymmetric distortion

45. Zernike polynomials- INTRODUCTION
• In reality, the rays emerging from an actual eye are not
perfectly parallel to each other, and the resulting pattern
formed by the lenslets is not a regular grid. (Shack-Hartmann
aberrometry)
• The manner in which the pattern deviates from a regular grid
reveals the nature of the eye’s aberrations and is quantified as
Zernike polynomials (i.e., second order, third order, etc.).
• It is now common to characterize the eye’s aberrations as
Zernike polynomials rather than as Seidel aberrations

46. INTRODUCTION
The mathematical functions
were originally described by
Frits Zernike in 1934.
• They were developed to
describe the diffracted
wavefront in phase contrast
imaging.
• Zernike won the 1953 Nobel
Prize in Physics for
developing Phase Contrast
Microscopy

47. INTRODUCTION
• Conventional refraction breaks the wavefront down into only
basic terms – sphere, cylinder and cylinder axis.
• Zernike polynomials are equations which are used to fit the
wavefront data in three dimensions.
• These polynomials have unique qualities, the principal one
being that they decompose the shape of the wavefront into
terms which describe optical aberrations such as spherical
aberration, coma etc

48. INTRODUCTION
The individual modes, or terms, in the polynomial have two
variables:
ρ (rho) and Ɵ (theta)
• ρ is the normalised distance from the pupil centre.
• Ɵ is the angular subtense of the imaginary line joining the
pupil centre and the point of interest to the horizontal.

49. INTRODUCTION
• The key point here is that aberrations are dependent on pupil
size. Therefore, all aberrometry measures must be related to
the patient’s pupil diameter.
• Wavefront measures must be referenced to a pupil size.

50. NOMENCLATURE
• This nomenclature groups each term according to the radial
order (n) and angular frequency (m), thus each term is
written in the form Zm
n
• The radial order (n) groups Zernike modes in terms ρ (rho),
whereas the angular frequency (m) groups the modes in
terms of θ (theta).

51. NOMENCLATURE
• In each Zernike polynomial form Zm
n the subscript n is
the order of aberration, all the Zernike polynomials in
which n=3 are called third-order aberrations and all the
polynomials with n=4, fourth order aberrations and so on.
• The superscript m is called the angular frequency and
denotes the number of times the Wavefront pattern repeats
itself
• Let us take the example of secondary astigmatism

52. NOMENCLATURE
• Normalisation of each mode means that observation of the
coefficients immediately gives an indication of the level of
influence each type of aberration has on the total aberration.
• The radial term, in this case of the fourth order, describes the
variation of the wave-front error with distance from pupil
centre.
• The angular frequency describes the number of repeat cycles
which are made over 360 degrees.

53. ORDER OF ABERRATIONS
ORDER OF ABERRATIONS NAME OF ABERRATIONS
0 PISTON
1 TILT ALONG X AND Y AXIS
2 SPHERICAL REFRACTIVE ERROR AND
ASTIGMATISM
3 COMA AND TREFOIL
4 SPHERICAL ABERRATION, SECONDARY
ASTIGMATISM AND TETRAFOIL
5 SECONDARY COMA, SECONDARY TREFOIL
AND PENTAFOIL

54. Zeroth Order Zernike Polynomials
• This term is called Piston and is usually ignored.
• The surface is constant over the entire circle, so no error or
variance exists.

55. First Order Zernike Polynomials
• These terms represent a tilt in the wavefront.
• Wavefront equivalent to vertical and horizontal prism.
• Describes the location of the image in space, being
independent of its quality.
• Piston and tilt are not actually true optical aberrations as they
do not represent or model curvature in the wavefront.

56. Second Order Zernike Polynomials
• These wavefronts are what you would expect from Jackson
crossed cylinder J0 and J45 and a spherical lens.
• Thus, combining these terms gives any arbitrary
spherocylindrical refractive error.
• It is low order true aberration.

57. Third Order Zernike Polynomials
• The inner two terms are coma and the outer two terms are
trefoil.
• These terms represent asymmetric aberrations that cannot be
corrected with convention spectacles or contact lenses.

58. Fourth Order Zernike Polynomials
• These terms represent more complex shapes of the
wavefront.
• Spherical aberration can be corrected by aspheric lenses.

59. Three-dimensional representation of some
aberration

60. Colour-coded wavefront error map(2D)

61. ADVANTAGE OF ZERNIKE POLYNOMIAL
1.Zernike polynomials are of great interest in many fields :
Optical design
Optical metrology
Adaptive optics
Ophthalmology (corneal topography, ocular aberrometry)
Freeform optics…
• For a circular pupil, Zernike polynomials form an
orthonormal basis.
• Hence formalism is easier Set of basis shapes or topographies
of a surface “Real” surface (wavefront, Deformable mirror)
is constructed from linear combination of basis shapes or
modes

62. DISADVANTAGE OF ZERNIKE POLYNOMIAL
• There are some optical systems with noncircular pupils :
Telescopes : Hexagonal pupils
Lasers : Squared pupils
• In these cases, there exist specific orthonormal polynomials
other than the Zernike ones
• In certain cases, Zernike polynomials may provide a poor
representation of the wavefront. Some of the effects of air
turbulence in astronomy and effects of fabrication errors in
the production of optical elements may not be well
represented by even a large expansion of the Zernike
sequence

63. REFERENCES

64. THANK YOU