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Trusit Dave PhD, BSc, MCOptom, FAAO<br />

Instruments insight<br />

Wavefront aberrometry<br />

Part 1: Current <strong>the</strong>ories and concepts<br />

T<br />

he<br />

visual system is a complex structure, not simply in<br />

terms of its ability to focus light but in terms of its ability to<br />

detect (capture) and interpret <strong>the</strong> image.<br />

Even in a normal eye with zero subjective<br />

refraction, a point object does not form a<br />

point image. This is due to optical<br />

aberrations such as spherical aberration,<br />

coma and o<strong>the</strong>r so-called high order<br />

optical aberrations. Clinically, <strong>the</strong>se can<br />

induce patient symptoms of glare and even<br />

diplopia. The principal site of <strong>the</strong>se<br />

aberrations is <strong>the</strong> cornea; one would<br />

naturally expect this as <strong>the</strong> cornea has <strong>the</strong><br />

highest refractive power and <strong>the</strong>refore any<br />

error in its shape would induce a variety of<br />

aberrations. However, <strong>the</strong> lens and tear<br />

film also contribute to <strong>the</strong> optical<br />

image-forming properties of an eye.<br />

As well as <strong>the</strong> effects of optical<br />

aberrations, ano<strong>the</strong>r factor, diffraction,<br />

induces image blur. Diffraction is <strong>the</strong><br />

deviation of a light path which is<br />

essentially not due to refraction or<br />

reflection. It occurs at a pupil stop and as<br />

<strong>the</strong> eye has a pupil, diffraction will always<br />

exert some effect on image quality.<br />

However, it is well documented that when<br />

<strong>the</strong> pupil size is greater than 4.5mm,<br />

diffraction has little or no effect on <strong>the</strong><br />

retinal image quality, as any image blur<br />

induced by diffraction is within <strong>the</strong><br />

resolving power of <strong>the</strong> retinal cones<br />

(Nyquist’s sampling limit). For <strong>the</strong> human<br />

eye, it has been shown to be around 0.5<br />

minutes of arc or approximately 6/3 1 .<br />

Contrary to diffraction, where image<br />

quality deteriorates with smaller pupils,<br />

high order optical aberrations increase<br />

with pupil size.<br />

Advances in refractive surgery have led<br />

to <strong>the</strong> need for measuring more subtle<br />

errors of optical image degradation.<br />

However, clinicians have long-since<br />

understood <strong>the</strong> need to measure <strong>the</strong>se<br />

optical characteristics in cases where acuity<br />

has not been sufficiently improved using<br />

basic sphero-cylindrical refractive<br />

corrections, such as in keratoconus.<br />

Numerous advances in our ability to<br />

measure corneal topography have provided<br />

a better understanding of surface shape.<br />

However, practitioners require a direct<br />

method of evaluating <strong>the</strong> optical<br />

characteristics of an eye. Quantitative and<br />

qualitative descriptors of <strong>the</strong> optics of an<br />

eye have not been available until <strong>the</strong><br />

development of devices known as<br />

aberrometers.<br />

Many optometrists will have been<br />

involved in refractive surgery<br />

co-management, or examined patients<br />

having undergone a refractive surgical<br />

procedure. More importantly, many<br />

patients are aware of refractive surgical<br />

techniques which potentially result in<br />

‘super vision’ or customised vision<br />

correction. This wavefront-guided<br />

procedure represents an exciting time for<br />

vision correction, with many academic<br />

experts and leading surgeons now<br />

discussing optical properties of eyes in<br />

terms of wavefront aberrations and using<br />

terms like ‘Zernike polynomials’ and ‘RMS<br />

wavefront error’. This two-part article aims<br />

to provide <strong>the</strong> clinician with an<br />

understanding of <strong>the</strong>se terms, and how <strong>the</strong><br />

technology can be used in optometric<br />

practice.<br />

High and low<br />

order aberrations<br />

Routine optometric practice involves<br />

performing a full subjective refraction.<br />

Here <strong>the</strong> sphere, cylinder and axis of<br />

astigmatism are measured. Although we<br />

may feel that this is <strong>the</strong> total refractive<br />

error, we are only correcting two<br />

components of a whole host of refractive<br />

components of <strong>the</strong> optics of an eye.<br />

However, <strong>the</strong>se two components (sphere<br />

and cylinder) constitute by far <strong>the</strong> majority<br />

of <strong>the</strong> optical aberration of an eye.<br />

Never<strong>the</strong>less, we will all have encountered<br />

<strong>the</strong> situation where a patient complains of<br />

poorer vision at night when subjective<br />

refraction is near zero. We often refer to<br />

this as night myopia.<br />

Although night myopia will be one<br />

cause of <strong>the</strong> symptoms – where <strong>the</strong> shift in<br />

wavelength at night induces myopia –<br />

o<strong>the</strong>r monochromatic aberrations, such as<br />

spherical aberration, also play a part as<br />

<strong>the</strong>y increase with pupil size. In <strong>the</strong><br />

majority of normal patients, <strong>the</strong>se high<br />

order aberrations play a minor role,<br />

however, in cases of refractive surgery,<br />

keratoconus and orthokeratology, <strong>the</strong>y can<br />

induce a number of visual disturbances<br />

which can be explained by measurement<br />

of <strong>the</strong> optical aberrations. Therefore, it is<br />

useful to think of subjective refraction as a<br />

procedure used to reduce image blur<br />

optimally using spheres and cylinders<br />

when <strong>the</strong> image is blurred due to<br />

additional factors such as scatter,<br />

diffraction and o<strong>the</strong>r more subtle higher<br />

order aberrations. Fur<strong>the</strong>rmore, subjective<br />

refraction takes into account neural<br />

processing factors which have developed<br />

because of <strong>the</strong> world we live in.<br />

This article will not address <strong>the</strong> effects<br />

of chromatic aberration, where <strong>the</strong><br />

magnitude of refraction varies with<br />

wavelength of light. Discussion will be<br />

limited to monochromatic aberrations<br />

where <strong>the</strong> optical aberrations are<br />

referenced to one wavelength (550nm).<br />

It is important to understand, however,<br />

that optical aberrations will affect all<br />

wavelengths.<br />

Measuring wavefront<br />

aberration<br />

A number of commercial devices are<br />

available to measure ocular aberration.<br />

Most are based on <strong>the</strong> Shack-Hartmann<br />

principle. Before covering <strong>the</strong> basics of this<br />

technique, <strong>the</strong> concept of wavefronts will<br />

be discussed.<br />

Traditionally, we have been taught to<br />

think in terms of light rays for <strong>the</strong> purpose<br />

of ray tracing. However, light rays only<br />

provide information about one point of an<br />

object in image space. To understand how<br />

<strong>the</strong> optics have affected <strong>the</strong> image, we need<br />

to observe and measure <strong>the</strong> bundle of all<br />

light rays exiting <strong>the</strong> eye. This bundle is<br />

often referred to as <strong>the</strong> ‘emergent<br />

wavefront’. In scientific terms, a wavefront<br />

may be defined as “<strong>the</strong> surface over which<br />

an optical disturbance has constant phase”.<br />

Put ano<strong>the</strong>r way, <strong>the</strong> wavefront is <strong>the</strong><br />

surface which joins individual points on<br />

rays which have <strong>the</strong> same optical path<br />

length. The optical path length is simply<br />

<strong>the</strong> distance a ray travels, multiplied by <strong>the</strong><br />

refractive index of <strong>the</strong> material it travels in.<br />

Figures 1a and 1b show a plane and<br />

circular wavefront respectively.<br />

If a point object could be imaged on<br />

<strong>the</strong> retina, <strong>the</strong> emergent wavefront for an<br />

eye with perfect optics would be plane<br />

(Figure 2a). As already discussed, <strong>the</strong><br />

reality is that this rarely occurs. Virtually<br />

all eyes exhibit some level of aberration,<br />

even in <strong>the</strong> absence of conventional<br />

refractive error. As a result, <strong>the</strong> emergent<br />

bundle of light will not be plane, but<br />

ra<strong>the</strong>r it will be deformed. Wavefronts may<br />

adopt any shape. However, in cases of<br />

simple myopia or hyperopia, <strong>the</strong>y will<br />

always be spherical provided <strong>the</strong>re is no<br />

o<strong>the</strong>r ocular aberration (Figure 2b).<br />

An aberrometer measures ocular<br />

aberrations, including low and high order,<br />

by principally measuring <strong>the</strong> wavefront<br />

emerging from <strong>the</strong> eye. There are, however,<br />

a number of different ways to achieve this.<br />

This article only covers <strong>the</strong> most popular<br />

type – <strong>the</strong> Shack-Hartmann aberrometer.<br />

Shack-Hartmann aberrometer<br />

The Shack-Hartmann sensor has been used<br />

extensively in astronomy to correct <strong>the</strong><br />

refractive blur induced by atmospheric<br />

41 | November 19 | 2004 OT

Instruments Insight<br />

Trusit Dave PhD, BSc, MCOptom, FAAO<br />

Figure 1a<br />

Parallel light rays travelling <strong>the</strong> same distance over time. The wavefront<br />

summarising <strong>the</strong> bundle of rays is plane<br />

Figure 1b<br />

Light rays travelling in different directions. The same distance is<br />

travelled over time (same phase), and <strong>the</strong> wavefront summarising<br />

<strong>the</strong> bundle is spherical<br />

Figure 2a<br />

The emergent wavefront of an eye with perfect optics, i.e. no refractive<br />

error and no high order aberrations<br />

Figure 2b<br />

The wavefront in an eye with simple myopia and no o<strong>the</strong>r aberrations.<br />

Here <strong>the</strong> emergent wavefront is perfectly spherical in shape<br />

turbulence. Astronomers developed an<br />

aberrometer to detect <strong>the</strong> aberrations<br />

induced by changes in atmospheric<br />

conditions and <strong>the</strong>n corrected <strong>the</strong>se using<br />

a deformable mirror – an optical<br />

engineering process known as adaptive<br />

optics 2 . This science is now being applied<br />

to <strong>the</strong> eye by virtue of an ocular<br />

aberrometer. The object of <strong>the</strong><br />

Shack-Hartmann aberrometer is to sample<br />

various points on <strong>the</strong> emerging wave<br />

and in doing so, derive <strong>the</strong> shape of <strong>the</strong><br />

Figure 3<br />

A diagrammatic representation of a<br />

Shack-Hartmann plate<br />

wavefront.<br />

Essentially, a Shack-Hartmann plate is a<br />

series of micro lenses arranged in a linear<br />

fashion (Figure 3). These lenslets are<br />

typically 0.25mm in diameter. Each lenslet<br />

focuses a view of <strong>the</strong> point source through<br />

various points of <strong>the</strong> entrance pupil<br />

(Figure 4). In this way, <strong>the</strong> aberrometer<br />

determines <strong>the</strong> shape of <strong>the</strong> wavefront<br />

exiting <strong>the</strong> eye. Although infrared light is<br />

used, <strong>the</strong> aberrations are measured with<br />

respect to peak spectral sensitivity of <strong>the</strong><br />

eye (550nm) by using a correction<br />

algorithm to account for <strong>the</strong> shift in focus<br />

from <strong>the</strong> measurement wavelength to <strong>the</strong><br />

reference wavelength 3 .<br />

Figure 5 shows <strong>the</strong> basic process<br />

involved in capturing <strong>the</strong> wavefront. For a<br />

perfect eye with no aberration, <strong>the</strong><br />

position of <strong>the</strong> spot on <strong>the</strong> CCD sensor<br />

will be at <strong>the</strong> optical axis of each lenslet.<br />

However, <strong>the</strong> reality is that in a normal<br />

eye, <strong>the</strong>re will be some level of aberration<br />

and, as such, <strong>the</strong> image of <strong>the</strong> spot will be<br />

Figure 4<br />

The principle of <strong>the</strong> Shack-Hartmann aberrometer<br />

42 | November 19 | 2004 OT

Instruments insight<br />

displaced from <strong>the</strong> optical axis. A question<br />

commonly asked is: “How is it that <strong>the</strong><br />

infrared laser forming a spot on <strong>the</strong> retina<br />

is not affected by <strong>the</strong> ocular aberrations?”<br />

The answer is that as <strong>the</strong> spot is very small<br />

and enters through <strong>the</strong> centre of <strong>the</strong><br />

entrance pupil to <strong>the</strong> fovea, <strong>the</strong> influence<br />

of <strong>the</strong> ocular aberrations is negligible.<br />

Thus, <strong>the</strong> CCD camera is used to<br />

capture <strong>the</strong> displacement of <strong>the</strong> spot from<br />

<strong>the</strong> optical axis of each lenslet.<br />

Displacements may occur in <strong>the</strong> horizontal<br />

and vertical meridian; Figure 6 shows <strong>the</strong><br />

displacement in <strong>the</strong> y meridian. The slope<br />

of <strong>the</strong> wavefront is easily calculated as <strong>the</strong><br />

displacement/<strong>the</strong> focal length of <strong>the</strong><br />

lenslet. After examining <strong>the</strong> slope at each<br />

micro lenslet in <strong>the</strong> x and y meridia, <strong>the</strong><br />

entire wavefront can be plotted in 3D.<br />

One of <strong>the</strong> objectives in measuring <strong>the</strong><br />

wavefront is to calculate <strong>the</strong> wavefront<br />

error (Figure 7). This describes <strong>the</strong> optical<br />

path difference between <strong>the</strong> measured<br />

wavefront and <strong>the</strong> reference wavefront<br />

(in microns) at <strong>the</strong> entrance pupil. The<br />

wavefront error is derived ma<strong>the</strong>matically<br />

from <strong>the</strong> reconstructed wavefront.<br />

However, <strong>the</strong>se computations result in<br />

many values of wavefront error. They are<br />

<strong>the</strong>refore plotted as a 2D or 3D wavefront<br />

error map for qualitative analysis (Figure<br />

7). These maps are analogous to colour<br />

coded corneal topography maps, where<br />

colours denote varying corneal dioptric<br />

power. In wavefront error maps, each<br />

colour represents a specific degree of<br />

wavefront error in microns. It is important<br />

to note <strong>the</strong> range and interval of <strong>the</strong> scale.<br />

Generally, in order to see as much detail as<br />

possible, choose <strong>the</strong> narrowest scale which<br />

permits <strong>the</strong> maximum number of colour<br />

changes within <strong>the</strong> map. However, when<br />

comparing pre and post treatments, make<br />

sure <strong>the</strong> same scale and step sizes are used<br />

to enable a like-for-like comparison. There<br />

is currently no absolute scale which has<br />

constant range and step size, as in corneal<br />

topography maps.<br />

Zernike polynomials<br />

The wavefront error map only provides<br />

qualitative information about <strong>the</strong><br />

wavefront. The shape of <strong>the</strong> wavefront<br />

takes on many forms and it is difficult for<br />

<strong>the</strong> clinician to evaluate <strong>the</strong> effects of <strong>the</strong><br />

shape on vision. In order to analyse <strong>the</strong><br />

wavefront quantitatively, it needs to be<br />

broken down into terms which are<br />

clinically meaningful. Conventional<br />

refraction breaks <strong>the</strong> wavefront down into<br />

only basic terms – sphere, cylinder and<br />

cylinder axis. A more sophisticated analysis<br />

is required to understand <strong>the</strong> subtle<br />

aberrations. Zernike polynomials are<br />

equations which are used to fit <strong>the</strong><br />

wavefront data in three dimensions. These<br />

polynomials have unique qualities, <strong>the</strong><br />

principal one being that <strong>the</strong>y decompose<br />

<strong>the</strong> shape of <strong>the</strong> wavefront into terms<br />

which describe optical aberrations such as<br />

spherical aberration, coma etc. Figure 8<br />

Figure 5<br />

The process involved in capturing <strong>the</strong> wavefront from <strong>the</strong> entrance pupil. Each lenslet captures a<br />

very small portion of <strong>the</strong> wavefront. The displacement of <strong>the</strong> spot is compared to that of a<br />

perfect wavefront. For a calibrated sensor, a perfect (or plane) wavefront would image <strong>the</strong> laser<br />

spot at <strong>the</strong> optical axis of <strong>the</strong> lenslet<br />

shows <strong>the</strong> Zernike modes commonly used<br />

to describe <strong>the</strong> measured wavefront.<br />

The individual modes, or terms, in <strong>the</strong><br />

polynomial have two variables, ρ (rho)<br />

and θ (<strong>the</strong>ta). ρ is <strong>the</strong> normalised distance<br />

from <strong>the</strong> pupil centre. Normalising ρ<br />

means it has a maximum value at <strong>the</strong> edge<br />

of <strong>the</strong> pupil of one. Therefore, for a 6mm<br />

pupil, a point 3mm from <strong>the</strong> centre would<br />

have a ρ value of 0.5. θ is <strong>the</strong> angular<br />

subtense of <strong>the</strong> imaginary line joining <strong>the</strong><br />

pupil centre and <strong>the</strong> point of interest to<br />

<strong>the</strong> horizontal (Figure 9).<br />

The key point here is that aberrations<br />

are dependent on pupil size. Therefore, all<br />

aberrometry measures must be related to<br />

<strong>the</strong> patient’s pupil diameter. Wavefront<br />

measures must be referenced to a pupil<br />

size.<br />

Each term is sequentially added to<br />

describe <strong>the</strong> entire wavefront. Thus, <strong>the</strong><br />

wavefront may be described as:<br />

W(ρ,θ)=C 1<br />

-1<br />

Z 1<br />

-1<br />

+C 11<br />

Z 11<br />

+C 2<br />

-2<br />

Z 2<br />

-2<br />

+C 20<br />

Z 20<br />

+C 22<br />

Z 2<br />

2<br />

+C 3<br />

-3<br />

Z 3<br />

-3<br />

+C 3<br />

-1<br />

Z 3<br />

-1<br />

+C 31<br />

Z 31<br />

+C 33<br />

Z 33<br />

+C 4<br />

-2<br />

Z 4<br />

-2<br />

etc<br />

Zernike terms are defined using a double<br />

index notation as proposed by <strong>the</strong> Optical<br />

Figure 6<br />

Calculation of <strong>the</strong> slope of <strong>the</strong> wavefront from <strong>the</strong><br />

displacement of <strong>the</strong> image at each individual lenslet<br />

43 | November 19 | 2004 OT

Instruments Insight<br />

Trusit Dave PhD, BSc, MCOptom, FAAO<br />

Figure 7<br />

The wavefront error map shows <strong>the</strong> difference between <strong>the</strong><br />

aberrated and reference (plane) wavefront. Once this information is<br />

processed for all points over <strong>the</strong> pupil, a 2D wavefront error map<br />

can be displayed (right) Figure 8<br />

Society of America 4 . This nomenclature<br />

groups each term according to <strong>the</strong> radial<br />

order (n) and angular frequency (m), thus<br />

each term is written in <strong>the</strong> form Z m n. The<br />

radial order (n) groups Zernike modes in<br />

terms ρ (rho), whereas <strong>the</strong> angular<br />

frequency (m) groups <strong>the</strong> modes in terms<br />

of θ (<strong>the</strong>ta). The coefficient, C, in each<br />

term varies according to <strong>the</strong> number of<br />

modes in <strong>the</strong> Zernike polynomial. C<br />

defines <strong>the</strong> level of a particular mode of<br />

aberration in microns and can have a<br />

positive or negative value.<br />

A list of <strong>the</strong> Zernike terms and <strong>the</strong>ir<br />

optical equivalent up to <strong>the</strong> fourth order is<br />

shown in Table 1. There are, in fact, an<br />

infinite number of Zernike terms which<br />

can be used to fit an individual wavefront.<br />

In practice, however, Zernike terms up to<br />

<strong>the</strong> 4th radial order are measured.<br />

It is worth understanding <strong>the</strong> actual<br />

terms in <strong>the</strong> equation. Let us take <strong>the</strong><br />

example of secondary astigmatism or Z 2 4.<br />

−1<br />

Z1 = 4ρ<br />

sin( θ )<br />

1<br />

Z1 = 4ρ<br />

cos( θ )<br />

−<br />

Z<br />

2 6 2<br />

2<br />

= ρ sin(2θ<br />

)<br />

0<br />

2<br />

Z2 = 3(2ρ<br />

−1)<br />

Z<br />

2 = 6ρ<br />

2 cos(2 θ )<br />

2<br />

Individual modes of Zernike polynomials up to fourth order. ‘n’<br />

represents <strong>the</strong> radial order and ‘m’ <strong>the</strong> angular frequency<br />

Table 1<br />

The double index notation of Zernike term, <strong>the</strong> equation of each mode in <strong>the</strong> Zernike polynomial<br />

and <strong>the</strong> appearance of each mode in a colour-coded wavefront error map<br />

Zernike term WFE Map Optical equivalent<br />

Vertical prism<br />

Horizontal prism<br />

Astigmatism<br />

Defocus<br />

Astigmatism<br />

The Zernike equation is<br />

Z 2 4 = √10(4ρ 4 −3ρ 2 )cos(2θ)<br />

What does<br />

this mean?<br />

As you can see, <strong>the</strong>re are only two<br />

variables in all <strong>the</strong> modes in Table 1.<br />

Broadly speaking, you can categorise each<br />

equation into three areas.<br />

Figure 9<br />

Wavefront error map defining ρ and θ<br />

−<br />

Z<br />

3 8 3<br />

3<br />

= ρ sin(3θ<br />

)<br />

−1<br />

3<br />

Z3 = 8(3ρ<br />

− 2ρ)sin(<br />

θ )<br />

1<br />

3<br />

Z3 = 8(3ρ − 2ρ)<br />

cos( θ )<br />

Z<br />

3 = 8ρ<br />

3 cos(3 θ )<br />

3<br />

−<br />

Z<br />

4 10 4<br />

4<br />

= ρ sin(4θ<br />

)<br />

−2<br />

4 2<br />

Z4 = 10(4ρ<br />

−3ρ<br />

) sin(2θ<br />

)<br />

0<br />

4 2<br />

Z4 = 5(6ρ<br />

− 6ρ<br />

+ 1)<br />

2<br />

4 2<br />

Z4 = 10(4ρ<br />

− 3ρ<br />

)cos(2θ<br />

)<br />

Z<br />

4 = 10ρ<br />

4 cos(4 θ )<br />

4<br />

Trefoil<br />

Coma<br />

Coma<br />

Trefoil<br />

Tetrafoil<br />

Secondary astigmatism<br />

Spherical aberration<br />

Secondary astigmatism<br />

Tetrafoil<br />

44 | November 19 | 2004 OT

Instruments insight<br />

Z 2 4 = √10(4ρ 4 −3ρ 2) cos(2θ)<br />

Normalisation<br />

term<br />

Radial<br />

term<br />

Angular<br />

term<br />

Normalisation of each mode means that<br />

observation of <strong>the</strong> coefficients<br />

immediately gives an indication of <strong>the</strong><br />

level of influence each type of aberration<br />

has on <strong>the</strong> total aberration 5 . The radial<br />

term, in this case of <strong>the</strong> fourth order,<br />

describes <strong>the</strong> variation of <strong>the</strong> wavefront<br />

error with distance from pupil centre. The<br />

largest power ρ is raised to is <strong>the</strong> radial<br />

order, i.e. to <strong>the</strong> power 4. The angular<br />

frequency describes <strong>the</strong> number of repeat<br />

cycles which are made over 360 degrees.<br />

For example, in secondary astigmatism,<br />

<strong>the</strong>re are two repeat cycles over <strong>the</strong><br />

circular pupil, thus <strong>the</strong> radial order is 2.<br />

Also, notice that where <strong>the</strong> radial order is<br />

assigned a negative value, <strong>the</strong> equation<br />

uses <strong>the</strong> sine of θ to describe <strong>the</strong> angular<br />

variation.<br />

The first order term, prism, is not<br />

relevant to <strong>the</strong> wavefront as <strong>the</strong>y represent<br />

tilt and are corrected using a prism. The<br />

second order terms represent low order<br />

aberrations, namely defocus and<br />

astigmatism. Defocus represents <strong>the</strong><br />

spherical component of <strong>the</strong> wavefront.<br />

The astigmatic terms conversely describe<br />

<strong>the</strong> cylinder. Using <strong>the</strong>se three terms, any<br />

sphero-cylindrical lens can be described.<br />

Wavefront maps with defocus and<br />

astigmatism only can be perfectly<br />

corrected using spectacles and contact<br />

lenses. Caution, however, needs to be<br />

exercised when interpreting <strong>the</strong>se terms as<br />

in practice, patient wavefront error maps<br />

have high order terms. As a result, defocus<br />

and astigmatism terms do not represent<br />

<strong>the</strong> sphere and cylinder terms found in<br />

subjective refraction. An estimate of<br />

subjective refraction can be made if only<br />

<strong>the</strong>se three terms are fit to <strong>the</strong> wavefront<br />

data. Second order terms are referred to as<br />

low order aberrations.<br />

Every mode after second order is a high<br />

order aberration. These terms cannot be<br />

measured in conventional refraction or<br />

autorefraction. The only method of<br />

quantifying <strong>the</strong>se terms is by using an<br />

aberrometer. The third order terms<br />

describe coma and trefoil astigmatism.<br />

These terms cannot be corrected using<br />

spectacles, soft or RGP contact lenses.<br />

Attempts have been made to correct<br />

spherical aberration in contact lenses<br />

using aspheric designs. However, this<br />

correction only corrects for lens specific<br />

spherical aberration and not <strong>the</strong> combined<br />

effect of eye and lens. Therefore, <strong>the</strong><br />

optical benefits of such a design may<br />

improve image quality for some patients<br />

but equally <strong>the</strong>re may be some<br />

deterioration in image quality in o<strong>the</strong>r<br />

patients 6 .<br />

Root mean square error<br />

In order to summarise <strong>the</strong> wavefront error,<br />

scientists have tried to develop metrics to<br />

try and best describe <strong>the</strong> wavefront error as<br />

a numeric index. At <strong>the</strong> present time, <strong>the</strong><br />

most widely used metric is <strong>the</strong> root mean<br />

square (RMS) error. All aberrometers<br />

display a RMS error of high and low order<br />

aberrations. This term describes <strong>the</strong><br />

weighted mean of <strong>the</strong> individual Zernike<br />

modes. In o<strong>the</strong>r words, <strong>the</strong> RMS value<br />

describes <strong>the</strong> overall aberration and gives a<br />

‘feel’ of how bad an individual’s<br />

aberrations are. The RMS error is simply:<br />

RMS=√(C2 -2 ) 2 +(C 0 2) 2 +(C 2 2) 2 +(C -3 3) 2 +(C -1 3) 2 ...etc<br />

There are number of disadvantages in<br />

using <strong>the</strong> RMS value. The most significant<br />

is that increases in RMS value do not<br />

necessarily result in decreases in image<br />

quality 5 . For example, if a subject has some<br />

defocus and spherical aberration, <strong>the</strong>n it is<br />

possible that <strong>the</strong> spherical aberration will<br />

help reduce some of <strong>the</strong> image blur<br />

induced on <strong>the</strong> retina. However, because<br />

of <strong>the</strong> way RMS is calculated, <strong>the</strong><br />

cancelling effects of one aberration over<br />

ano<strong>the</strong>r are not considered 7 . As research<br />

continues, better predictors of visual<br />

function will develop 5,8 .<br />

Studies have evaluated normative<br />

values of ocular aberration. Porter et al 9<br />

found a random variation in <strong>the</strong> wavefront<br />

aberration of 109 normal subjects with an<br />

artificial pupil diameter of 5.7mm. Chalita<br />

et al 10 performed aberrometry in 60 eyes<br />

and found mean values of 0.35±0.29<br />

microns for coma; 0.36±0.31 for spherical<br />

aberration; and 0.31±0.14 microns for<br />

o<strong>the</strong>r high order terms for a pupil<br />

diameter of 7mm. It has also been<br />

documented that 91% of <strong>the</strong> RMS<br />

wavefront error can be accounted for by<br />

<strong>the</strong> second order and 99% if Zernike<br />

terms from <strong>the</strong> first four orders are used to<br />

fit <strong>the</strong> wavefront for a pupil diameter of<br />

5mm 11 . Wang and Koch 12 measured ocular<br />

aberrations in subjects screened for<br />

refractive surgery. High order aberrations<br />

were found to have a mean RMS of<br />

0.305±0.095 in 532 eyes across a 6mm<br />

pupil. Spherical aberration was found to<br />

be 0.128±0.074 and coma 0.170±0.089<br />

microns.<br />

Any instrument involved in clinical<br />

measurement must be both accurate and<br />

repeatable. Cheng et al 13 measured <strong>the</strong><br />

accuracy and repeatability of <strong>the</strong> COAS<br />

(Wavefront Sciences) Shack-Hartmann<br />

aberrometer on model eyes. They found<br />

<strong>the</strong> instrument to be both accurate and<br />

repeatable on model eyes. In ano<strong>the</strong>r<br />

study, Cheng et al 14 evaluated <strong>the</strong> variation<br />

of monochromatic aberrometry<br />

measurements over a range of timescales<br />

(five measures in one second without<br />

realignment, five measures in one hour<br />

with realignment at <strong>the</strong> same time over<br />

five days and on five days at monthly<br />

intervals). The authors concluded that<br />

variations in aberrometry maps between<br />

days and months was due to biological<br />

changes to <strong>the</strong> eye, and that this<br />

fluctuation would prevent practitioners<br />

from achieving perfect optical correction,<br />

i.e. an aberration-free eye. Wavefront maps<br />

are also known to vary with<br />

accommodation 15 , tear film quality 16 and<br />

media opacities 17 .<br />

Part 2 of this article, to be<br />

published on December 3, will look<br />

at applications of wavefront<br />

aberrometry in clinical practice.<br />

About <strong>the</strong> author<br />

Dr Trusit Dave is Director of Optimed<br />

(Ophthalmic Medical Instruments),<br />

Clinical Consultant for Topcon GB and a<br />

partner in private practice in Coventry.<br />

References<br />

For a full set of references, email<br />

nicky@optometry.co.uk.<br />

Continuing Education and Training<br />

Systemic Pathology<br />

Orderline: 01252-810939 Fax: 01252-816176<br />

NEW<br />

This book on ‘Systemic Pathology’ is designed to give practitioners and optometric students a<br />

better understanding of <strong>the</strong> principles and practice of clinical medicine and surgery, and in<br />

particular, of <strong>the</strong> fur<strong>the</strong>r management of patients referred by optometrists.<br />

£39.50<br />

45 | November 19 | 2004 OT

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