Transcript Z 3 -1

What is wave front
The Cartesian ellipsoid produces a stigmatic image of only one object point
Normal eye and most of optical systems are not free from aberration.
Reference sphere: a circular arc centered on the image point with
a radius equal to the image distance
Wave front aberration: the difference between the
reference sphere and the wave front
Optical aberrations
Approximately 80% - 90% of visual aberration error can be explained
through the low order (first and second order) aberrations :1st Order
Aberation =Tilt (prism)
2nd Order Aberation = Defocus (sphere) and cylinder
The less frequent high order aberrations represent the residual
10% to 20%: (mostly induced surgically)
3rd Order Aberation = Coma and trefoil
4th Order Aberation = Spherical and quadrafoil
5th Order Aberation = Distortions / irregular astigmatism
6th to 8th Order Aberation = Significantly increasing levels of
irregular astigmatism,
Diffraction
Chromatic aberrations
Refractive errors of the eye can be described in terms of the shape of a wavefront of light that has passed through the eye's
optics. With aberration-free optics, wavefronts exiting the eye are perfectly flat (top). Refractive errors, such as myopia, distort
the wavefront (bottom). Other refractive errors, including higher-order aberrations, cause wavefront distortions that differ in
shape from those seen in simple myopia
The difference between the wave front and the reference sphere is the
Wave front aberration
What are aberrometers?
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Instruments that measure refractive
errors
(super auto-refractors) Sphere, cylinder +
HOAs(Higher-order aberrations) ≠ corneal
topography!
COAS
Measurement of optical aberrations
Wave front analyzer systems
.Hartman-shack aberrometry (outgoing aberronetry), a low intensity laser beam is
directed onto the retina, a lens array focuses the outcoming light rays onto a photoreceptor
(CCD)
.Tscherning aberrometry (ingoing aberrometry), a collimated beam is passed through a
mask of holes and into the eye, a high magnification camera captures the image onto the retina
.Retina ray tracing technique (ingoing aberrometry), a laser beam is used to scan
across the pupil in a sequential manner, each position focus a single point on fovea
History of HO aberrometry
Reagan
1970s and 80s, Strategic defense
• Refraction through the atmosphere
• Astronomy
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• Adaptive optics (AO)
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Shack-Hartman wavefront sensor
Shack
Zernike analysis & Zernike coefficients
Breaks the wave front down into the
Standard Zernike modes or Magnitude & axis form
Each Zernike mode = one aberration
Z analysis also provides a value for each.
mode: Units in microns,±sign
Absolute Zernike coefficient = magnitude
Must specify pupil size
Zernike
RMS wave front error
RMS 
m 2
n
Total aberrations (LOAs + HOAs)
• higher-orders (HOA RMS)
• just third-order aberrations, etc.
• The basic data = individual Zernike coefficients
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
Z   ... Z 
m 2
n
J Cataract Refract Surg. 2006 Dec;32(12):2064-74.
Normal-eye Zernike coefficients and root-mean-square wavefront errors.
Salmon TO, van de Pol C.
METHODS:
Data were collected from 10 laboratories that measured higher-order aberrations (HOAs)
in normal, healthy adult eyes using Shack-Hartmann aberrometry (2560 eyes of 1433
subjects). Signed Zernike coefficients were scaled to pupil diameters of 6.0 mm, 5.0 mm,
4.0 mm, and 3.0 mm and corrected to a common wavelength of 550 nm. The mean signed
and absolute Zernike coefficients across data sets were compared. Then, the following
were computed: overall mean values for signed and absolute Zernike coefficients; polar
Zernike magnitudes and RMS values for coma-like aberrations (Z(3)(+/-1)
and Z(5)(+/-1) combined); spherical-like aberrations (Z(4)(0) and Z(6)(0)
combined); and 3rd-, 4th-, 5th-, and 6th-order, and higher-order aberrations (orders
3 to 6).
RESULTS:
The different data sets showed good agreement for Zernike coefficients values across
most higher-order modes, with greater variability for Z(4)(0) and Z(3)(-1). The most
prominent modes and their mean absolute values (6.0-mm pupil) were, respectively,
Z(3)(-1) and 0.14 microm, Z(4)(0) and 0.13 microm, and Z(3)(-3) and 0.11 microm.
The mean total higher-order RMS was 0.33 microm.
CONCLUSIONS:
There was a general consensus for the magnitude of HOAs expected in normal adult
human eyes. At least 90% of the sample had aberrations less than double the mean values
reported here. These values can serve as a set of reference norms.
HOA results
Pupil
diameter
Mean (µm)
2x mean
6.0
0.33
0.66
5.0
0.19
0.38
4.0
0.10
0.20
Prominent individual HOAs (6.0-mm pupil)
• Z3-1 (vertical coma) = 0.14
• Z40 (spherical aberration) = 0.13
• Z3-3 (oblique trefoil) = 0.11
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0
Magnitude
& axis
form
piston
Z0
1
prism
Z11
2
sphere
Z20
3
coma
trefoil
Z31
4
Z33
spherical
aberration
quadrafoil
Z40
order (n)
astigmatis
Z22 m
Z42
Z44
secondary astigmatism
Z1-1
Combined Zernike modes
Z11
1
Z11
Z2-2
Z20
Z22
2
Z22
Z3-3
Z33
Z31
3
Z31
Z3-1
order (n)
Z33
Conventional Rx:
+0.25 -0.75 x 111
Zernike coefficients
2nd order
Mode: Z2-2 Z20 Z22
Coefficient
(µm):
.56 .27 .64
Rx: +0.19 - 0.67 x 111
Pupil diameter: 5.6 mm
Total RMS: 0.76 µm
Higher-order RMS: 0.51
µm
3rd order
4th order
Z3-3 Z3-1 Z31 Z33
Z4-4 Z4-2 Z40 Z42 Z44
-.03 .07 -.05 .06
.03 .04
.11
0 -.08
Unit =
µm
+ or -
values
HO RMS & pupil size
1
OD
Pupil & RMS data
OS
0.8
HO RMS (um)
Normal
0.6
3.0 mm
5.0 mm
0.4
0.2
0
5.5
5.0
4.5
4.0
3.5
3.0
Pupil diameter (mm)
2.5
2.0
Tscherning aberroscope. Modern techniques use a projected grid of dots (left) and
images the resultant pattern distortion on the retina (right) to determine aberrations.
The MTF: measures the contrast loss with increasing spatial frequency when
transferring an object to animage through an aberrated optical system.
Spatial frequency is defined by the number of cycles
(line pairs) per distance. It is known that fine details
(high spatial frequencies) are the first to be affected
when the quality of an optical system is degraded.
As a functionof the diffraction and the importance of optical aberrationsof the system
studied, it is possible todetermine the fashion in which the optical system reducesthe
contrast between specific spatial frequenciesand to deduce the optical quality of the
image that isrendered.
One disadvantage of Zernike is that in highly aberratedeyes, such as in
keratoconus, the Zernike decompositioninvolves the creation of numerous basisf
unctions that require complex calculations to representt accurately.
The Fourier polynomial
system was later suggested as an alternative
to decompose
the wavefront map based on the claim that given a limitedset of basis functions, the
Fourier expansionwould be more efficient and more reliable in reproducingthe overall
wavefront map
Fiber Multi-Object Spectrograph (FMOS)
FMOS is a powerful wide-field spectroscopy system that enables near-infrared
spectroscopy of over 100 objects at a time. It is composed of three subsystems: 1) an
infrared unit at prime focus (PIR) that includes a wide-field corrector lens system and
fiber positioning system ("Echidna"), 2) a fiber bundle unit of 400 optical fibers, and 3)
two spectrographs. Echidna can precisely position all 400 fibers in just 15 minutes. This
high speed for repositioning allows observers to reconfigure Echidna, observe multiple
fields during a night and rapidly observe hundreds of faint targets that can be compiled
as data for statistical analysis...
An exciting new promising application is the combination
of wavefront with other technologies such as
topography, biometry, Scheimpflug, and/or optical
coherence tomography, and this is likely to refine
the modeling of the eye for ideal refractive correction.
Other areas related to wavefront technology, such as
enhancing the precision and reproducibility of wavefront
simulations with the adaptive optics visual
stimulator and a better delivery system of the desired
wavefront pattern to the cornea with enhanced laser
technology, can be further developed. In this way,
the initial quest for super vision with customized laser
vision correction might someday be delivered,
with the possibility of achieving better results than
the initial CDVA.
Clinical HO aberrometry
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Laser refractive surgery
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Large HOAs
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Clinical aberrometry
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Wavefront-guided LASIK
COAS
3. How do they work?
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Light is projected in.
Reflect off the retina
Light passes through
the eye’s optics.
Catch the light.
Analyze it.
Reconstruct the optical
wavefront’s shape
Summary 4. Interpreting the data
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Aberrometers measure wavefronts
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Wavefront - distorted by aberrations
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Zernike analysis - which aberrations are present
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Zernike coefficients - how bad they are
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Data in microns, with ± signs
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RMS - magnitude of grouped aberrations
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Pupil size, pupil size, pupil size !
5. Diagnosis - what’s normal?
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Aberrometry - diagnoses abnormal optics
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Ideal eye = zero aberrations, but …
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every eye has some aberrations.
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So, are those Zernike or RMS values good or
bad?
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Need reference norms
OCO Norms
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JCRS Dec 2006
2,560 normal eyes
9 sites
Zernike & RMS norms
Data on www
Google “Dr. Salmon”
Downloadable info
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Full article in PDF
Norms table - PDF & Excel
Signed Zernike coefficients
Absolute values
Combined (polar) Zernike modes
RMS for HOA and orders 3, 4, 5, 6
http://arapaho.nsuok.edu/~salmonto
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