adaptive optics and vision

7/28/2019 Adaptive Optics and Vision

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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.)

Journal of Modern Optics 3429


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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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