Introduction to Bruneni Lecture ASCO2007

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Introduction to Bruneni Lecture ASCO-2007
Wavefront Aberrometry for Clinicians Larry N.
Thibos, PhD School of Optometry, Indiana
University, Bloomington, IN 47405 thibos_at_indiana.
edu http//research.opt.indiana.edu
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Lecture outline

• What is wavefront aberration map?
• How are aberration maps determined?
• How are aberrations classified?
• How are aberrations specified?
• How are aberrations measured?

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Image formation by a simple, symmetrical lens
GO approach apply Snell's law of refraction to
rays
Lens
Object
Power Cross
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Concept of optical path length (OPL)
Number of oscillations frequency (cyc/sec)
time(sec) freq d / v
(freq / c) d n d n / ?vacuum OPL d
n Number of oscillations ?vacuum
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Spheres are perfect wavefronts
Point sources produce spherical wavefronts.
Spherical wavefronts collapse onto point images.
Lens
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Image formation by a simple, symmetrical lens
Lens
Image Wavefront
Object Wavefront
a'
c'
b'
Object
a
b
c
n'
n Index of medium
Definition image wavefront locus of points
that are the same optical distance from object
wavefront
an bn' cn a'n b'n' c'n
Theorem If image wavefront is spherical, then
lens is perfect.
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Definition of the perfect lens
If image wavefront is spherical, then lens is
perfect.
Image Wavefront
Object Wavefront
Lens
a'
c'
r
b'
s
Object
r
s
a
b
c
n'
n Index of medium
rn sn an bn' cn a'n b'n'
c'n rn sn
OPL (central ray) OPL' (marginal ray) OPD
OPL' - OPL 0
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OPD0 for perfect retinal images
P
rays
perfect
retinal
P
image of
object point
Object point

• Key points
• All rays from P intersect at common point P on
  the retina.
• The optical distance from object P to image P is
  the same for all rays.
• Wavefront converging on retina is spherical.

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OPD 0 for distant object in perfect emmetropic
eye
Parallel rays from distant point source, P.
P
perfect

retinal

image

• Key points
• All rays from P intersect at common point P on
  the retina.
• The optical distance from object P to image P is
  the same for all rays.
• Wavefront converging on retina is spherical.

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Definition of wavefront error
Reference sphere Wavefront
For each point in pupil, WFE z-axis sag between
wavefront and reference sphere with center at
retinal image.
y
r
Sag
Line-of-sight
z
x
Pupil margin
WaveErrorwave-reference W(x,y) -OPD(x,y)
(Rect.) W(r,?) -OPD(r,?) (Polar)
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Lecture outline

• What is wavefront aberration map?
• How are aberration maps determined?
• How are aberrations classified?
• How are aberrations specified?
• How are aberrations measured?

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A spherical example
Wavefront - Reference sphere
Wavefront error
Ref.
y
y
y
x
x
x
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An astigmatic example
Wavefront - Reference sphere
Wavefront error
Ref.
y
y
y
x
x
x
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An irregular astigmatic example (coma)
Wavefront - Reference sphere
Wavefront error
Ref.
y
y
y
x
x
x
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Lecture outline

• What is wavefront aberration map?
• How are aberration maps displayed?
• How are aberrations classified?
• How are aberrations specified?
• How are aberrations measured?

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Zernike wavefront decomposition
Order 0 Piston, Z00
0
0
Order 1 Prism, Z11
1
1
Order 2 Sphere, Astigmatism Z20 , Z22
2
0
2
2
Order 3 Coma, Trefoil Z31 , Z33
3
3
3
1
Order 4 Spherical aberration, Secondary
astigmatism, Quadrafoil
4
4
4
0
4
2
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Zernike table (rectangular form)
0
Meridional frequency
Radial order
0
1
-1
1
1
0
2
-2
J0
J45
2
M
2
2
1
3
-3
-1
3
3
3
3
0
2
4
-4
-2
4
4
4
4
4
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Periodic table of Zernike functions
0
Defocus
1
Astigmatism
2
Radial order
Coma
3
SA
4
5
0
1
2
3
4
5
-1
-2
-3
-4
-5
Meridional frequency
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Anatomy of Zernike basis functions
order
frequency
Astigmatism
polynomial
harmonic
normalization constant
Coma
20
Zernike expansion weighted sum of modes
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Lecture outline

• What is wavefront aberration map?
• How are aberration maps displayed?
• How are aberrations classified?
• How are aberrations specified?
• How are aberrations measured?

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Wavefront vergence
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Wavefront vergence examples
Spherical focus
Astigmatism (axis 45)
Vmax
Vmin
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Limitations of the vergence concept
This definition of vergence makes sense only if
ray stays in the plane of the diagram. This holds
for the principal meridia of an optical system
with 2nd order aberrations. In general, rays are
skew with the z-axis so vergence must be defined
in terms of local curvature.
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Local vergence of wavefronts
For 2nd-order aberrations, principal curvatures
are the same for all points in the pupil.
For higher-order aberrations, principal
curvatures vary across the pupil.
V gt 0 V lt 0
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Dioptric measure of wavefront blur
If defocus (M) is the only aberration present,
then
If other aberrations contribute to wavefront
error, then M is the "equivalent defocus" the
amount of defocus that would produce the same RMS
wavefront error.
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Lecture outline

• What is wavefront aberration map?
• How are aberration maps displayed?
• How are aberrations classified?
• How are aberrations specified?
• How are aberrations measured?

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Commercial instruments measure in object space

• Shack-Hartmann wavefront sensor
• Alcon LADARWave
• Bauch Lomb Zywave
• Visx WaveScan
• Aesculap Meditec CRS-Master
• Wavefront Sciences COAS
• Topcon Wavefront Analyzer KR-9000PW
• Talbot wavefront sensor
• Ophthonix Zview

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Measuring ocular aberrations in object space
Optical path length from P to P? is independent
of direction of propagation of light.
P
"fundus beacon"
rays
P
reflected wavefront
Image point
OPD in object space OPD in image space
LASER
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?x
Point source (fundus beacon)
?y

• Multiple pupil locations are sampled
  simultaneously
• Ray aberrations are measured by ?x, ?y
  displacements of each image of "fundus beacon"
  from its reference location made by pinhole
  cameras.

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Shack-Hartmann Aberrometer
Spot position encodes wavefront slope
Relay lenses
(conjugate to eyes pupil)
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Diffraction Aberrometer (US Patent
2003/0231298A1) (per Laurence Warden, VP
Engineering, Ophthonix, Inc.)
Distortions in grid encode wavefront slope
Retinal point source
Near field diffraction pattern (Talbots
self-imaging effect)
Checker-board grid aperture (Can be manufactured
holographically)
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Recovering wavefront phase from slope measurements
Raw data wavefront slope
Integrate ? dxdy
Differentiate
Curvature
Wavefront phase
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Mathematical representation of wavefront error
For a distant reference point, W(x,y) Z(x,y)
y

Pupil circle
Wavefront
Z(x,y)
P
z
x
Error
Ideal reference plane-wave
W(x,y)
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Reference books for further reading
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The end.