Lecture 23, 24 - Wavefront abberations of the eye

Question 1

Main factors affecting quality of retinal image:

Answer 1

• Diffraction
• Defocus
• Aberrations
• Scatter

Question 2

What are aberrations?

Answer 2

• Important as they reduce the retinal image quality of the eye and therefore reduce visual acuity
• During subjective refraction optometrists are correcting a combination of defocus and aberrations. However they are unable to correct aberrations completely with spherical and astigmatic lenses.

Question 3

What are the two types of abberations:

Answer 3

• Chromatic
• Monochromatic

Question 4

Define Ray and Wavefront

Answer 4

• Ray
Lines normal to the wavefront at every point on the intersection
• Wavefront
A surface over which an optical disturbance has a constant phase

Question 5

Chromatic aberrations cause:

Answer 5

• Results from the fact that the refractive index of materials change with the wavelength of light

Question 6

Chromatic aberration

Answer 6

• The velocity of light in a medium (hence the refractive index) varies with its wavelength.
• Thus the image of a source of white light (consisting of a wide range of wavelengths) is extended along the optical axis.
• The refractive index of blue light is higher than red light, making a lens more powerful when blue light is travelling through it

• Short wavelengths come to focus before longer wavelengths

Question 7

Two types of chromatic abberation

Answer 7

• Longitudinal
- describes the fact that the blue image will be formed in front of the red

• Transverse
- describes the lateral displacement of the red and blue light

Question 8

Chromatic aberration cause

Answer 8

• Results from the fact that the refractive index of materials change with the wavelength of light

• Result: Coloured fringes around objects

Question 9

Chromatic aberration: How much?

Answer 9

More than 1.5 dioptres from one extreme of the visible spectrum to the other.

Question 10

Chromatic aberration: Why don’t we notice coloured fringes?

Answer 10

• The eye is much less sensitive to wavelengths towards the ends of the spectrum - fringes will be relatively dim
• ? Neural filtering, lens filtering
• CA may cause some image degradation but correcting it is impractical

Question 11

Monochromatic aberrations cause:

Answer 11

• Paraxial rays are rays that are near the axis
• Therefore the sine of the angle and the angle expressed in radians is very similar
• However the eye is not a paraxial optical system and a more accurate relationship is needed to define the aberrations

Question 12

Five monochromatic aberrations are:

Answer 12

• Spherical Aberration
• Coma
• Oblique Astigmatism
• Curvature
• Distortion

Question 13

Contour plots:

Answer 13

• The wavefront aberration or error is the distance between the actual and reference wavefronts as a function of position in the pupil
• This is typically shown as a contour map
• The contours join points in the exit pupil where the wavefront aberration has the same value
• Closely packed contours suggest large amounts of aberration and a poor image
• No contour = ideal non aberrated system

Question 14

Spherical aberration:

Answer 14

• Rays entering through the periphery of the pupil are refracted more than the paraxial rays
• Only monochromatic aberration which occurs when both the object and image points lie on the optical axis of a centred system
• In the eye positive SA occurs when marginal rays intersect the optical axis in front of the paraxial rays
• Positive SA is commonly found in the eye

Question 15

Spherical aberration cause:

Answer 15

This causes some “blurring” of the image

Spherical aberration in the eye is only about 0.6D for a 5mm pupil as a result of:

• Aspherical cornea
• Refractive index gradient of the crystalline lens

Question 16

How is spherical aberrations reduced?

Answer 16

• The effects of spherical aberration are further reduced by the Stiles-Crawford effect
• Light entering through the centre of the pupil is more likely to be absorbed by a photoreceptor than light entering through the periphery

Question 17

The Stiles-Crawford effect:

Answer 17

• Cones act like waveguides (see pic)
• Cones are “aimed” at the centre of the pupil - less likely to absorb light coming from the periphery of the pupil

Question 18

Describe “Coma” aberration

Answer 18

• Occurs only for off-axis object points in a centred optical system
• Produces a characteristic comet shaped image
• The tail of the comet points towards the optical axis in negative coma (away in positive)
• The length of the tail increases as the object and image points go further off axis

Question 19

Results from Coma

Answer 19

• Results from the displacement of rays passing through different parts of the annulus
• Rays travelling through peripheral parts of the lens form a ring image that is displaced in comparison to the paraxial image
• Ring images get larger as the radius increases

Question 20

Coma affects depending on axis?

Answer 20

• As an off-axis aberration coma would not be expected to influence foveal visual performance to any great extent
• But the eye is not perfectly centred and therefore coma can occur along the visual axis of some individuals

Question 21

Oblique astigmatism:

Answer 21

• Arises from off-axis object points
• Caused by differences in the refractive power in the saggital and tangential planes of an optical system

Question 22

Field curvature:

Answer 22

• Arises because the in-focus image of an optical system does not usually lie on a plane
• It usually lie on a curve (the Petzyal surface)
• Further from the lens axis in the object plane (eg B) the distance from the object to the first principal point of the lens increases
• Image distance also gets shorter in +ve lenses and in the eye
• The wavefront aberration for any image point corresponds to a simple shift in focus to give a circular wavefront contour
• Field curvature is compensated to some extent in the eye as the retina is also curved

Question 23

Distortion:

Answer 23

• Results from differences in magnification with variations in the distance from the optical axis
• Pincushion= magnification increases with distance from axis
• Barrel= magnification decreases with distance from axis
• For any image point a lateral displacement corresponds to a simple tilt of a flat wavefront
• results in a wavefront map that show equispaced straight line contours parallel to the saggital section and a tilted isometric view
• Not usually considered to be a problem in the eye (visual system can adapt to this)

Question 24

Terminology used to assess optical quality

Answer 24

• Point spread function (PSF)
• Modulation transfer function (MTF)
• Phase transfer function (PTF)
• Optical transfer function (OTF)

Question 25

Point spread function:

Answer 25

• Is the light distribution in the image of a point at or close to the paraxial image plane
• This distribution depends on both the level of aberration in the beam and diffraction (both are dependent upon the wavelength of light)
• General Rule: the smaller the PSF width the better the image quality
• Line spread function is similar but is a line instead of a point

Question 26

Point spread function: with pupil diameter

Answer 26

• In the case of diffraction: the PS decreases in width with an increase in size of the pupil
• But the PSF will increase in diameter with increasing pupil size due to aberrations
• Therefore there is an optimum pupil width where the PS is minimum (2-6mm)
• The shape and size of the PSF will vary with the type of aberrations present

Question 27

Modulation transfer function (MTF)

Answer 27

• MT is related to the PSF
• Describes the loss of contrast suffered when an image is cast of a sinusoidal grating object
• The ratio of image contrast to object contrast captures the blurring effects of optical imperfections
• The variation of this ratio with spatial frequency and orientation of the grating object is called the MTF

Question 28

Methods of measuring abberations:

Answer 28

• A number of methods have been employed since the 19th century to measure aberrations
• We will discuss four of the most common methods

• Examples include
- Tscherning Aberroscope
- Hartmann shack wavefront sensor
- Ray tracing
- Retinoscopy principle

Question 29

Tscherning abberoscope

Answer 29

• A grid of laser spots is used to form an image on the retina
• The grid travels through the optics of the eye and the end point image will be distorted due to the aberrations
• The deviation of each spot from its perfect position is measured and processed to give the wavefront aberration

Question 30

Hartmann shack wavefront sensor:

Answer 30

• Currently the most popular method

• Unlike aberroscope and ray tracing techniques in that it is essentially a ray trace from a retinal point out of the eye

• a narrow beam from a laser is imaged by the eye and the light passed back from the fundus travels through a wavefront sensor consisting of many microlenses (lenslets) to the CCD camera

• These lenslets focus the rays into spots which define the wavefront pattern

• The amount that the lenslet image is displaced from the ideal image position indicates the level of aberration

Question 31

Principles of the Shack-Hartmann Wavefront sensor:

Answer 31

• The local slope (or the first derivative) of the wavefront is determined at each lenslet location

• The corresponding wavefront is determined by a least squares fitting of the slopes to the derivative of a polynomial selected to fit the wavefront

• Zernike polynomial is the most commonly used

Question 32

Retinoscopy Principle

Answer 32

• An infra-red slit scans through the pupil measuring the refractive power of the eye
• The wavefront is calculated by determining the changes in refractive power across the area of the pupil

Question 33

What are Zernike polynomials

Answer 33

• set of basic shapes that are used to fit the wavefront
• analogous to the parabolic x2 shape that can be used to fit 2D data

Question 34

How bad is the eye? Static abberations

Answer 34

• For the most part, aberrations in the eye are random. When you average enough eyes together, most terms are no different from zero. The only high order aberrations that is non-zero is spherical aberration, which averages to a small positive value.
• Overall, the eye’s high order aberrations reduce with pupil size. The dashed line indicates the effective diffraction limit, according to Marachel’s criterion.

Question 35

What can change wave aberrations in the eye?

Answer 35

• Dynamic Changes in the wave aberrations are caused by
- accommodation
- eye movement
- eye translation
- tear film

Question 36

Clinical instruments to measure aberration:

Answer 36

• Tscherning based: Allegretto (Wavelight laser)
•Hartmann Shack: Zywave (Bausch and Lomb)
•Ray Tracing; Tracey (Tracey technologies)
• Retinoscopy: OPD/ARK-1000 (Nidek)

Question 37

Differences in measurements of instruments caused by…

Answer 37

• Comparison between instruments has revealed a poor level of agreement between higher order aberration measures

Could be due to differences in
•accommodation control
• Method of measurement
•Differences in the maths

Question 38

Why measure abberations?

Answer 38

• Imaging the internal eye structures
• Analysis and correction of visual performance

Question 39

Analysis and correction of visual performance:

Answer 39

• Aberrations can reduce the visual performance of the eye
• Correction of aberrations will therefore have the potential to improve visual performance
• Refractive surgery, intraocular lenses and contact have all been developed to try to correct aberrations

Question 40

Intra-ocular lenses

Answer 40

• IOLs are implanted as a replacement to the crystalline lens following cataract surgery
• They can potentially produce high levels of wavefront aberration (especially SA)
• This again creates problems such as reduced visual performance especially at night
• Measurement of wavefront aberrations prior to surgery will help in the development and design of IOLs that reduce wavefront aberration levels

Question 41

Contact lenses:

Answer 41

• Contact lenses produce reasonably predictable wavefront aberrations
• Visual performance can be improved when lens design is modified to reduce wavefront aberration
• Disadvantage of contact lenses is that they are likely to rotate on the eye
• The rotation can limit the accuracy of the wavefront correction
• Contact lenses do have the advantage of being reversible and easily modified

Question 42

Can we create supernormal vision using adaptive optics?

Answer 42

• Contrast sensitivity has already been shown to be enhanced 6 fold
• Visual acuity limits have been increased from 6/4 to 6/2
• The retinal image of a point object is 8 times brighter when corrected
• The theoretical limit on image quality for the eye equals an acuity of ~ 6/1

Question 43

• Basic science imaging applications
• Pre-clinical applications

Answer 43

Basic science imaging applications
- reveal properties of single cells in living eyes
- correlate properties of cellular structure in living eyes with visual performance
- nonlinear imaging of structure and function

Pre-clinical applications
- faciliate longitudinal tests on animal models
- test outcomes of drugs and treatments for eye disease
- correlate phenotypes with genotypes

Question 44

• Clinical imaging applications

Answer 44

• provide early diagnosis for retinal or other systemic diseases
• better understand the etiology of retinal disease for which little is known
• discover more sensitive biomarkers for retinal disease
• track progression of eye disease
• measure response at cellular level to therapies that treat disease
• preselect patients or diseases that may benefit best from therapies or treatments

Question 45

Functional imaging applications

Answer 45

• facilitate better relationships between structure and function
• reveal properties of cell networks in living eyes (ie retinal circuitry)

Question 46

• Vision applications
• Dynamic applications

Answer 46

• Vision applications
Vision Applications
- pre-test the benefits of aberration correction on vision develop optimal aberration profiles for long depth of focus test possible signals that drive accommodation and/or eye growth
- reveal the optical retinal and neural limits of human vision
• Dynamic applications
- measure properties of blood flow in small capillaries
- measure scattering changes in response ot light stimulation
- measure eye motion with high accuracy and frequency

Question 47

• Light delivery applications

Answer 47

• track and stimulate single cells or networks of cells for electrophysiology expts
• microperimetry
• targeted laser treatment (photocoagulation, or uncaging drugs)
• track eye movement responses to stimulation
• study role of eye movements for vision

Question 48

Imaging the internal eye structures

Answer 48

• Taking account of the ocular aberrations allows clinical instruments to gain better resolution when examining the internal structures of the eye
• This ability to compensate for optical aberrations has an important role in research and in the early detection of various ocular pathologies