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The performance of the eyes AO system is not perfect. Although the lens aims to
maintain as sharp an image as possible on the retina there are limits as to what shape it can
take on. The main aberration the lens can reduce is that of defocus. However, in the eye
there are a host of other imaging degrading aberrations. These aberrations are often more
severe than in a man-made optical system owing to tilts and decentrations in the optical
Iris
Cornea
Optic nerve
Fovea
Ciliary body Sclera
Choroid
~ 5
~ 22 mm
Sensor
Controller
Corrector
Retina
Brain
Lens
Figure 1. Schematic of the human eye highlighting the components that are analogous to anadaptive optics system. (The colour version of this figure is included in the online version of thejournal.)
Contraction of ciliary body
Zonules
Accommodated
Relaxed
Object at 8
~ 10 cm (Young healthy eye)
Figure 2. Process of accommodation. To bring closer objects into focus on the retina, the power ofthe lens is increased by contraction of the ciliary body. (The colour version of this figure is includedin the online version of the journal.)
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where is the wavelength, f is the focal length, n is the refractive index and D is the pupil
diameter. Hence, for a fixed wavelength, the larger the pupil the smaller the width of the
PSF and the higher the resolution.
Figure 4 shows how the width of the PSF varies with pupil diameter D, taking as
550 nm, f as 22.2 mm and n as 1.33. The cone photoreceptors, which provide us with our
colour vision, are separated by around 2 mm at the fovea [18]. For an eye limited only by
2 3 4 5 6 7 81
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
Pupil diameter (mm)
PSFwidth(m)
Spacing & diameterof foveal cones
Actual diffractionlimit of eye
Figure 4. Variation in the width of the PSF with pupil diameter, for a diffraction-limited eye andwavelength of 550 nm. Increasing pupil diameter decreases the effective width of the PSF and soincreases resolution. (The colour version of this figure is included in the online version of thejournal.)
Minimum separation to be resolvedas two separate sources
PSF width
Figure 3. Rayleigh resolution criterion. In a diffraction-limited system two point sources can beresolved if they are separated by the effective width of their images. (The colour version of this figure
is included in the online version of the journal.)
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diffraction the pupil needs to be greater than around 5.5 mm in diameter for these to be
resolved. However, studies have shown that the eye approaches the diffraction limit for
a pupil diameter of around 3 mm, but beyond this image quality is limited by aberrations
[19]. Hence, in order to image foveal cones reliably in a human eye of typical optical quality,
an AO system is required. Owing to technical limitations AO systems never achieve
a perfect correction and reduce the aberrations to zero. However, a system can be
considered diffraction limited if the Strehl ratio reaches 0.8. This is the ratio of the
aberrated PSF height to the PSF height of an equivalent diffraction-limited eye. The Strehl
ratio of a typical human eye with only defocus and astigmatism corrected can be less than
0.1 [19].
There are two main classes of aberrations: monochromatic and chromatic.
Monochromatic aberrations are considered to be those that occur as a result of rays
having different optical path lengths for different locations in the pupil. This is due to
variations in refractive index and optical irregularities. Although their magnitude can
depend upon wavelength, they are distinct from chromatic aberrations which are evident
in polychromatic light. Chromatic aberrations are due to dispersion, i.e. the dependence ofrefractive index on wavelength. AO manipulates monochromatic aberrations and so the
main focus of this section is on the properties of these types of aberrations. Chromatic
aberrations and their effect on AO will also be discussed briefly.
2.1. Monochromatic aberrations
Monochromatic aberrations are described by the monochromatic wave aberration
function W. This determines the deviation of the actual wavefront from some perfect
wavefront at each point in the pupil. Owing to the inaccessibility of the eyes image space
the aberrations are defined in object space. In this case, for an eye of perfect opticalquality, the emerging wavefront will be plane, and so the geometry of the wave aberration
function is as shown in Figure 5. If the wavefront is phase advanced W is positive, and
negative if it is phase retarded. In order to reduce the optical aberrations in the eye AO acts
on this wavefront.
2.1.1. Zernike polynomials
The aberrated wavefront can be described by a sum of polynomials. The accepted
convention is to use Zernike polynomials as they are orthogonal over the unit circle.
Principal components analysis has demonstrated them to be an efficient basis fordescribing the eyes wave aberration function [20]. There are several variations on the way
in which these polynomials are formulated with regards to the numbering, normalisation,
and angle convention. The convention used in ophthalmic optics is that recommended by
the Optical Society of America Taskforce [21]. The wavefront can be written as
W, X1i0
aiZi, , 2
where is the radial coordinate ranging from 0 to 1, is the azimuthal component
ranging from 0 to 2, and ai is the coefficient of the Zernike polynomial Zi usually
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use in the human eye in 1994, by Liang and colleagues, is considered the cornerstone in the
development of AO for vision science [12]. It was the first simple objective technique
capable of making rapid and precise measurements of the eyes higher-order aberrations.
The sensor consists of an array of lenslets placed in a plane conjugate to the eyes pupil and
a detector at the focal plane of the array. The lenslets are normally square and so
contiguous to maximise efficiency, and the detector is normally a CCD camera. The array
effectively samples the slope of the wavefront at discrete intervals across the entire pupil of
the eye as shown in Figure 10. If the wavefront is plane, as it would be in the case of an
optically perfect eye, a regular array of spots will be formed on the camera. If the
wavefront is aberrated, each spot will be displaced according to the slope of the wavefront
across its corresponding lenslet. By measuring the x and y shift in position of each spot
relative to the positions for an aberration free eye, the wavefront across the pupil can be
determined. The location of the spot is determined by its centroid.
The slope of the wavefront in the x direction across a given lenslet is given by
@W
@xWx
ax
f, 13
f L.A.(a)
Aberration-free eye
Aberrated eye
(b)
Pupil plane CCD plane
Figure 10. Principle of the ShackHartmann sensor. A lenslet array at a plane conjugate to thepupil measures the wavefront slope at discrete locations. (a) For an aberration free eye a regular
array of spots will be formed at the focal plane. (b) An irregular array will be formed for anaberrated eye. (The colour version of this figure is included in the online version of the journal.)
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of pixels. In general the higher the number of actuators/pixels the more spatially intricatethe wavefront that can be corrected for. Hence, in principle, the larger the number of
Zernike modes the device can correct for, provided the device also has a large enough
dynamic range. Dynamic range is determined by the stroke of the corrective device. In the
case of deformable mirrors for example, this is the magnitude of the maximum surface
deflection. Even if the device has a large number of actuators or pixels, if the stroke of the
device is too small much of it will be used up in correcting the lower order modes. Further
requirements are that the device is relatively small, being comparable to the size of the
pupil, so that it can be incorporated into compact systems. Many researchers consider the
corrective element to be the main component that limits the performance of an AO system.
The following section discusses the properties of the main types of correctors that havebeen implemented for AO systems in the eye.
3.2.1. Deformable mirrors
Deformable mirrors are the most common correction devices. They essentially consist of
a mirrored surface whose shape is deformed by actuators. In order to correct for an
aberrated wavefront the mirror deforms into the same shape as the wavefront but with half
the amplitude, as the extra physical path is introduced into both the incident and reflected
path. This is illustrated in Figure 17. Speed is generally not an issue with deformable
mirrors as they can respond with speeds several orders of magnitude faster than the
aberration dynamics.
Deformable mirrors can be broadly categorised into two classes: segmented surface
and continuous surface. Segmented deformable mirrors consist of individual plane mirrors
each attached to a separate actuator as shown in Figure 18. Some devices are piston only
where each segment can only be moved perpendicular to the mirror plane, others can also
be tipped and tilted and so require three actuators per segment. The disadvantages of
segmented mirrors are that there are gaps between the segments. This leads to light loss
and diffraction effects. The percentage of the surface area of the corrector covered by
mirrors is known as the fill factor, which can approach 100%. The segments can be square
or hexagonal. As each segment can be adjusted independently, these mirrors are well suited
Aberrated wave
Plane wave Plane wave
(a)(b)
Figure 16. Principle of wavefront correction by manipulating the optical path length using twomethods. (a) Changing the physical path length using a deformable mirror. (b) Changing the pathlength by altering the refractive index using a liquid crystal device. (The colour version of this figureis included in the online version of the journal.)
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iterations, the flash-lamp is triggered and an image captured. As the lamp takes 510 s to
charge continuous imaging is not possible. Another option for the light source is an SLD
passed through a multimode fibre to reduce its coherence, or a multimode laser diode.
Using these types of sources Rha and colleagues have demonstrated the ability to
continuously capture images of the retina with rates of up to 60 Hz [63]. This real-time
imaging ability allowed them to monitor rapid fluctuations in the reflectance of single
cones. Several other groups also use AO assisted flood illumination ophthalmoscopes, for
example [64,65].
A consideration in retinal imaging is what wavelength to use. From Equation (1) it can
be seen that the width of the PSF decreases with decreasing wavelength. Hence, in principle
resolution is improved. However, there are several issues to consider such as safety and the
availability of a suitable light source. Typical wavelengths used in AO assisted flood
illumination ophthalmoscopy are in the visible region. It has been found that the contrast of
retinal images shows only slight variation in the wavelength range 550750 nm [66]. As the
wavefront source is normally in the infrared region, the chromatic difference in focus is
normally accounted for by translating the CCD camera along the optical axis.
4.1.2. Scanning laser ophthalmoscope
AO can also be combined with a confocal scanning laser ophthalmoscope (cSLO) as
illustrated in Figure 25.
The main advantage of this technique over conventional flood-illumination is its axial
sectioning capabilities. In a cSLO the laser is scanned across the retina and the image is built
up point-by-point. This allows the use of more sensitive point detectors such as
photomultipliers or avalanche photodiodes. Before reaching the detector the light passes
through a small aperture conjugate to the retinal plane being imaged. Owing to this so-called
Laser(wave sensing& retinal imaging)
CCD
X-Yscanning
optics
PMTConfocal pinhole& detector
Figure 25. Principle of the AO assisted confocal laser scanning ophthalmoscope. The wavefrontsensing source is scanned across the retina and is used to build an image point by point. (The colourversion of this figure is included in the online version of the journal.)
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