What is wave front

The Cartesian ellipsoid produces a stigmatic image of only one object pointNormal 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 aberrationsApproximately 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 trefoil4th Order Aberation = Spherical and quadrafoil5th Order Aberation = Distortions / irregular astigmatism6th 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?

• Instruments that measure refractive errors

• (super auto-refractors) Sphere, cylinder + HOAs(Higher-order aberrations) ≠ corneal topography!

COAS

Measurement of optical aberrationsWave 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

• 1970s and 80s, Strategic defense• Refraction through the atmosphere• Astronomy

• Adaptive optics (AO)• Shack-Hartman wavefront sensor

History of HO aberrometry

Reagan

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. Zernike

mode: Units in microns,±sign

Absolute Zernike coefficient = magnitude

Must specify pupil size

RMS wave front error

• Total aberrations (LOAs + HOAs)• higher-orders (HOA RMS)• just third-order aberrations, etc.• The basic data = individual Zernike coefficients

RMS Znm 2

... Znm 2

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

• Prominent individual HOAs (6.0-mm pupil)• Z3

-1 (vertical coma) = 0.14 • Z4

0 (spherical aberration) = 0.13• Z3

-3 (oblique trefoil) = 0.11

Pupil diameter Mean (µm) 2x mean

6.0 0.33 0.66

5.0 0.19 0.38

4.0 0.10 0.20

Magnitude& axis

form

0

1

2

3

4

order (n)

Z0

Z40

Z31

Z20

Z11

Z22

Z33

Z44Z42

prism

sphere astigmatism

coma trefoil

sphericalaberration

quadrafoil

piston

secondary astigmatism

1

2

3

order (n)

Z1-1 Z1

1

Z11

Z2-2 Z2

2Z20

Z22

Z3-3

Z3-1 Z3

1

Z33

Z31

Z33

Combined Zernike modes

Conventional Rx:

Mode: Z2-2 Z2

0 Z22 Z3

-3 Z3-1 Z3

1 Z33 Z4

-4 Z4-2 Z4

0 Z44Z4

2

Coefficient (µm):

.56 .27 .64 -.03 .07 -.05 .06 .03 .04 .11 0 -.08

2nd order 3rd order 4th order

Zernike coefficients

Rx: +0.19 - 0.67 x 111

Pupil diameter: 5.6 mm

Total RMS: 0.76 µm Higher-order RMS: 0.51 µm

+0.25 -0.75 x 111

Unit =µm

+ or -values

HO RMS & pupil size

0

0.2

0.4

0.6

0.8

1

2.02.53.03.54.04.55.05.5

Pupil & RMS dataOD

OS

Normal

HO R

MS

(um

)

Pupil diameter (mm)

5.0 mm3.0 mm

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 affectedwhen 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 decomposethe 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 combinationof wavefront with other technologies such astopography, biometry, Scheimpflug, and/or opticalcoherence tomography, and this is likely to refinethe modeling of the eye for ideal refractive correction.Other areas related to wavefront technology, such asenhancing the precision and reproducibility of wavefrontsimulations with the adaptive optics visualstimulator and a better delivery system of the desiredwavefront pattern to the cornea with enhanced lasertechnology, can be further developed. In this way,the initial quest for super vision with customized laservision correction might someday be delivered,with the possibility of achieving better results thanthe initial CDVA.

Clinical HO aberrometry

• Laser refractive surgery

• Large HOAs

• Clinical aberrometry

• Wavefront-guided LASIK

COAS

3. How do they work?

• 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• Aberrometers measure wavefronts

• Wavefront - distorted by aberrations

• Zernike analysis - which aberrations are present

• Zernike coefficients - how bad they are

• Data in microns, with ± signs

• RMS - magnitude of grouped aberrations

• Pupil size, pupil size, pupil size !

5. Diagnosis - what’s normal?• Aberrometry - diagnoses abnormal optics• Ideal eye = zero aberrations, but …• every eye has some aberrations.• So, are those Zernike or RMS values good or

bad?• Need reference norms

OCO Norms

• JCRS Dec 2006• 2,560 normal eyes• 9 sites• Zernike & RMS norms• Data on www• Google “Dr. Salmon”

Downloadable info• 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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