Wavefront Aberrations and Spectacle Lenses Part
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dispensingoptics 4 January 2010
Wavefront aberrations and spectacle lenses
In response to requests for more challenging CET, part one Darryl Meister ABOM, explains the fundamentals of wavefront aberrations and image quality in part one of this two-part series
CompetencIes covered: Optical appliances Target group: Dispensing opticians, optometrists
Although evaluating the ‘wavefront’ point can be represented theoretically corresponding wavefront as both aberrations of a lens or optical system using rays emanating outward from propagate away from the object or has become commonplace in fields the object or waves emanating toward the image. such as astronomy, in which adaptive outward that are perpendicular to optical systems minimise the wavefront those rays. Just as rays of light diverge Aberrations are focusing errors that aberrations of telescopes caused by from an object point, waves of light prohibit proper image formation. There atmospheric turbulence, there is spread out like ripples of water are several ways to characterise the increasing interest in the ophthalmic travelling away from a stone that has aberrations produced by a lens or applications of this technology. This been dropped into a pond. At any optical system. In geometrical optics, interest has been driven in no small given distance from the original object ray tracing is often utilised to calculate part by recent advances in laser point, a wavefront exists that the path of a bundle of rays from an refractive surgery that in theory could represents the envelope bounding object point as the rays are refracted allow surgeons to reduce the ‘high- waves of light that have travelled an at the various surfaces of each lens or order’ wavefront aberrations of the equal distance from the object. optical element. Aberrations are then eye, in addition to the traditional determined by calculating the spherical and cylindrical refractive As the distance from the object distance of these refracted rays from errors, using a procedure known as increases, the curvature of these the intended focal point. Alternatively, wavefront-guided ablation. Eliminating wavefronts becomes progressively the deformation of the corresponding the high-order aberrations of the eye flatter, eventually appearing flat wavefront of light as it passes through may allow us to achieve supernormal beyond ‘optical infinity’. The object the optical system may be also vision, with better than ‘normal’ visual point serves as the common centre of determined. acuity and contrast sensitivity1. curvature of these wavefronts (Figure 1). Conversely, light converging to a point In a perfect optical system, spherical Wavefront aberrations focus can be described using wavefronts of light from an object The propagation of ‘light’ has been spherical wavefronts that become point should converge to a single described as a rapid movement of progressively smaller, converging to an point focus at the desired image energy particles (photons) that travel infinitely small image point. Further, a location, such as the retina of the eye. in a wave-like manner. The ray of light from the same object point In the presence of optical aberrations, propagation of light from an object remains perpendicular to the however, these wavefronts become
This article has been approved for 1 CET point by the GOC. It is open to all FBDO members, including associate member optometrists. Insert your answers to the six multiple choice questions (MCQs) on the answer sheet inserted in this issue and return by 11 February 2010 to ABDO CET, Courtyard Suite 6, Braxted Park, Great Braxted, Witham CM8 3GA OR fax to 01621 890203, or complete online at www.abdo.org.uk. Notification of your mark and the correct answers will be sent to you. If you complete online, please ensure that your email address and GOC number are up-to-date. The pass mark is 60 per cent. The answers will appear in our March 2010 issue. C-12500 1 January 2010.qxd:1 11/12/09 09:38 Page 5
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either too steep, too flat, or distorted IDEAL WAVEFRONT Y
(Figure 2) T from their ideal shape . I N I
RAY F N I Accordingly, rays of light corresponding T
WAVE A SINGLE
W
A T
N POINT to these wavefronts are spread out or V I
E O
P FOCUS F
R T
smeared at the plane of the desired O C E N J
T B focus by these aberrations, instead of O intersecting at a single, sharp point.
ABERRATED WAVEFRONT Y
Wavefront aberrations represent a T I N I F N
convenient way to characterise I
T
A SPREAD
T
complex optical errors in focus N OF I O
P FOCUS
produced by an optical system. At T DISTANCE FROM OBJECT TO IMAGE POINT C E J B
any point across the aperture of the EQUALS RADIUS OF WAVEFRONT CURVATURE O optical system, such as the pupil of the ERROR eye, the wavefront error is the effective optical separation, or Figure 1: A wavefront represents the envelope Figure 2: In the presence of optical aberrations, difference in optical path length, that bounds waves of light at a given distance wavefronts of light do not converge to a sharp from an object point or an image point point focus at the desired image plane between the actual aberrated wavefront and the ideal reference wavefront. These errors are usually these fundamental shapes or modes Zernike aberration modes are expressed in micrometres or microns (Figure 3). commonly represented using a double ( m), which are equal to one- indexing scheme: thµousandth of a millimetre (0.001mm). Further, each Zernike mode is m n associated with a particular type of Z For a given object point, the overall optical error, or wavefront aberration, where n is a whole number indicating shape of the wavefront aberration allowing the wavefront errors to be the radial order and m is a positive or after it has been refracted by the described as a combination of negative integer indicating the optical system can be modelled and quantities of more basic optical meridional frequency of the mode. For quantified mathematically, if a aberrations that are also more familiar instance, the polynomial function of 1 sufficient number of wavefront error to eye care professionals. Each Zernike the Zernike mode expressed as Z3 , measurements are taken across the mode includes two components: varies as a cubic function away the aperture of the system. The shape of 1. The radial order component centre of the pupil (n = 3) and varies an aberrated wavefront can be indicates the exponential variation of sinusoidally one time around the modelled from wavefront error the polynomial function away from circumference of the pupil (m = 1). measurements by ‘fitting’—or closely the centre of the pupil—or how many approximating—the measurements peaks and troughs occur away from Zernike aberration modes are with a series of polynomials. Using the centre. commonly grouped by their radial mathematical curve fitting techniques, 2. The meridional frequency order (n), which indicates how much the measurement data is ‘expanded’ component indicates the number of the contribution of a given range of or expressed as a sum of terms of sinusoidal repetitions of the function modes to the overall shape of the polynomial functions. Increasing the around the meridians of the pupil—or wavefront depends upon pupil size. number of terms used in these how often the peaks and troughs Each radial order contains one or polynomials results in successively repeat around the circumference. Continued overleaf more accurate approximations of the original wavefront. The most common polynomial series in ophthalmic use is TH the Zernike polynomial series, which 0 Z 0 has been shown to characterise the 0 PISTON optical aberrations of the eye effectively2. 1ST Z -1 Z 1 Zernike polynomial series 1 1 VERTICAL TILT HORIZONTAL TILT R
The Zernike polynomial series is used to E D R R TRADITIONAL E O
breakdown or decompose complex ND D
L EYEGLASS 2 R A O I PRESCRIPTION
D -2 0 2 wavefronts into a collection of W A Z 2 Z 2 Z 2 O L R polynomial basis functions called OBLIQUE ASTIGMATISM DEFOCUS WTR/ATR ASTIGMATISM R E
modes. These basis functions allow the D R O
shape of even complex wavefronts to RD H
3 G I H be broken down, or decomposed, Z -3 Z -1 Z 1 Z 3 Figure 3: Displaying the 3 3 3 3 into an assortment of more basic OBLIQUE TREFOILVERTICAL COMA HORIZONTAL COMA WTR/ATR TREFOIL Zernike polynomial component shapes. Just as you can functions by their reconstruct a model of a house by radial order produces 4TH a pyramid of -4 -2 0 2 4 combining various simple shapes, such Z 4 Z 4 Z 4 Z 4 Z 4 as triangles and rectangles, you can aberration modes OBLIQUE QUATREFOILOBLIQUE SECONDARY ASTIG SPHERICAL ABERRATION WTR/ATR SECONDARY ASTIG NORMAL QUATREFOIL (modes to the fourth MERIDIONAL FREQUENCY also reconstruct a given wavefront order have been -4-3 -2 -1 0 +1 +2 +3 +4 from an appropriate combination of shown) 1 January 2010.qxd:1 11/12/09 09:38 Page 6
dispensingoptics 6 January 2010
with polynomial terms of lower or equal order to minimize the variance of the Zernike polynomial. These ABERRATED WAVEFRONT WTR/ATR TREFOIL VERTICAL COMA SPHERICAL ABERRATION features result in some useful properties3: • The contribution of an individual Zernike aberration mode to the total =++ wavefront error is given by the magnitude of its corresponding YXX Y YXX Y coefficient. • The variance of each aberration RMS ERROR = √3 µM C 3 = 1 µM C -1 = 1 µM C 0 = 1 µM 3 3 4 mode is given by the square of its corresponding coefficient. • The total variance of the wavefront is equal to the sum of the variances of Figure 4: Even complex wavefront shapes can be ‘decomposed’ into a combination of more the individual aberration modes. fundamental aberrations • The addition of more Zernike aberration modes can only increase more aberration modes, each with a The outer two second-order modes the total wavefront error. -2 2 specific meridional frequency (m). The (Z2 and Z2 ), referred to as astigmatism, • Adding higher-order Zernike radial orders of the Zernike polynomial have the shape of a capstan toric aberration modes will not alter the series increase indefinitely. The number surface and correspond to the lower-order modes. of modes within each radial order also cylinder power error of the wavefront. • Eliminating wavefront aberrations up increases as the radial order increases This capstan shape has positive to a given radial order will minimise the from the addition of modes with refractive power through one principal total error of the aberrated wavefront successively higher meridional meridian and negative refractive up to that order. frequencies, resulting in a pyramid of power of the same magnitude aberration modes when the Zernike through the other meridian, resulting in Wavefront aberrations polynomial series is represented a spherical equivalent—or average and image quality graphically (Figure 3). power—equal to zero, similar to a In the absence of optical aberrations, Jackson cross-cylinder. A cylinder axis the image quality of an optical system The Zernike polynomial basis function is not specified separately, so two is limited by diffraction, which is the varies as a function of the sine of the cylinder components—indicating the subtle bending or spreading of light at angle formed by each meridian of the amount of cylinder power present at the edge of an aperture. Instead of pupil when m is negative and as a either axis 45 or axis 135 and at either reproducing a point of light from an function of the cosine of the angle axis 180 (with-the-rule) or axis 90 object as an equally sharp and when m is positive. Consequently, (against-the-rule)—are required to equally intense image point, modes in the same radial order with define the power and orientation of diffraction results in a slight diffusion of meridional frequencies that are equal the cylinder power. The total cylinder the focus. When the aperture is -m in value but opposite in sign (Zn and power is equal to the vector sum of circular, as is the case with the pupil of +m Zn ) represent the same shape but are these two components. the eye, diffraction produces a rotated with respect to each other. circular pattern known as Airy pattern, This allows aberration modes with Each Zernike aberration mode also which is characterised by a central m vertical and horizontal components has a coefficient Cn associated with disk of maximum of image intensity, Stepper UK (such as prism) or oblique and with- it, which indicates the amount of that surrounded by rings of significantly Eyewear Fashion That Fits the-rule/against-the-rule components particular Zernike aberration mode lower intensity (Figure 5). Diffraction (such as astigmatism) to be present in the actual wavefront at a varies inversely with pupil size, Olivia wears frame style Si 234 increasing as the pupil size becomes represented unambiguously. Modes given aperture or pupil size. Essentially, For more information call 01732 375975 with a meridional frequency of zero each coefficient serves as a scaling smaller. (m = 0) have polynomial functions that factor that sets the size—or heights of do not vary around the circumference the peaks and troughs—of the Visual acuity is the most common of the pupil, resulting in a rotationally polynomial function of the subjective measure of image quality in symmetrical shape. corresponding Zernike aberration eye care. Visual acuity represents the mode. This ‘decomposes’ a complex resolving power of the eye or the Of particular interest are the three wavefront shape into specific ability to discriminate two object Zernike aberration modes of the quantities of individual aberration points as separate. Visual acuity is second radial order (n = 2), known modes (Figure 4). These coefficients often expressed as a Snellen fraction, collectively as the second-order are ordinarily determined by fitting the which is the ratio of the distance at aberrations. This radial order wavefront error measurements with which a person can discern two small corresponds to the traditional each Zernike polynomial using a least- objects as separate—such as the curvature or vergence of the squares method. strokes of a Snellen optotype letter—to 0 wavefront. The centre mode (Z2 ), the distance at which the separation referred to as defocus, has the shape Zernike polynomial functions are of the two objects subtends an angle of a paraboloid and corresponds with orthogonal—or independent of each of one minute of arc at the eye. This the average sphere power error of the other—over a circular pupil. Each angle represents the minimum angle wavefront. Zernike polynomial is also 'balanced' Continued overleaf 1 January 2010.qxd:1 11/12/09 09:38 Page 8
dispensingoptics 8 January 2010
POINT SPREAD FUNCTION DIFFRACTION-LIMITED PSF ABERRATED IMAGE PSF AIRY DISK 100% 100% 100% PSFDL PSFAI
Y Y STREHL RATIO = Y T T T I I I PSFDL S S S N N N PSF E E E AI T T T N N N I I I
E E E G G G A A A M M M I I I
DIFFRACTION-LIMITED 0% 0% 0% IMAGE OF OBJECT POINT IMAGE PLANE IMAGE PLANE IMAGE PLANE
Figure 5: Diffraction of light at a circular aperture from a single object point Figure 6: Graphs of the point spread functions of a diffraction-limited optical produces an Airy pattern (shown here enlarged) with a central disc of system and an optical system with significant optical aberrations show the maximum image intensity surrounded by rings of lower intensity distribution of image intensity
of resolution of an eye with ‘normal’ the distribution of image intensity from increases. Consequently, the MTF visual acuity. Because the observer a single object point across the function typically decreases as the usually attempts to identify intended image plane of an optical spatial frequency increases (Figure 7). progressively smaller optotypes at a system. Optical aberrations and The high frequency cut-off represents fixed testing distance, most commonly diffraction degrade the image of an the maximum spatial frequency that at 6 metres, this testing distance object point, resulting in a smeared or can be resolved by the optical system. represents the numerator of the diffuse point spread function (Figure Snellen fraction. 6). The total image of a finite object Wavefront aberrations of the eye represents the convolution of the point In vision science, the radial orders of It is also possible to measure the image spread function of the optical system the Zernike polynomial series are quality of an optical system such as for each point on the object, so that routinely categorised as either ‘low- the eye objectively once the each point on the image reflects the order aberrations’ or ‘high-order wavefront aberrations have been aberrated point spread of the aberrations.’ Low-order aberrations determined4. There are three corresponding point on the original are Zernike modes of the ‘second particularly common objective object. order’ or lower (n ≤ 2). High-order measures of image quality: aberrations are Zernike modes of the • Root-mean-square error (or RMS) The Strehl ratio indicates the ratio of ‘third order’ or higher (n ≥ 3): • Strehl ratio of the point spread the peak intensity of the aberrated • Low-order aberrations include 0 function (or PSF) point spread function to the peak defocus (Z2 ) and oblique and with- • Modulation transfer function (or MTF) intensity of a diffraction-limited point the-rule/against-the-rule astigmatism +2 2 spread function. The Strehl ratio ranges (Z2 and Z2 ), which are associated The root-mean-square error indicates from 0 to 100%, with a value of 100% with the sphere power and cylinder the variance of the aberrated indicating a diffraction-limited optical power of the eye or optical lens, wavefront produced by an optical system free from aberrations. Optical respectively. system from the ideal wavefront over aberrations cause a diffusion of the • High-order aberrations include -1 some reference plane. The RMS error is image of an object point, resulting in a vertical and horizontal coma (Z3 and 1 equivalent to the standard deviation less compact point spread function Z3 ), oblique and with-the-rule/against- -3 3 of the wavefront error measurements with a lower peak and, consequently, the-rule trefoil (Z3 and Z3 ), spherical 0 over a regular grid of points. The RMS a lower Strehl ratio compared to a aberration (Z4 ), and so on. error of an aberrated wavefront is also diffraction-limited system. • While the first-order aberrations of -1 easily calculated from the coefficients vertical and horizontal prism (Z1 and 1 of the Zernike aberration modes. The The modulation transfer function Z1 ) are also technically low-order contribution of one or more aberration indicates the capacity of an optical aberrations, these Zernike modes as modes to the total RMS error is given system to reproduce the contrast well as the zeroth-order piston mode 0 by the vector magnitude of their modulation of a repeating sine wave (Z0 ) are usually ignored in corresponding aberration coefficients: test pattern as the spatial frequency of measurements of image focus quality. the pattern—or the number of cycles m 2 RMS = ∑(Cn ) per unit of distance—increases. Although Zernike radial orders √ Modulation refers to the contrast of a continue indefinitely, the wavefront m where each Cn represents the test pattern, which is the ratio of the aberrations in normal human eyes are coefficient of a particular Zernike difference between the maximum usually described adequately by the aberration mode. The RMS error of the and minimum luminance levels of the first six or seven Zernike orders. Low- wavefront up to a given radial order pattern to the average luminance order aberrations characterise the can be determined from the level. Higher spatial frequencies are gross deviation of an aberrated magnitudes of the Zernike coefficients associated with finer detail. wavefront from the ideal shape in each of the radial orders up to and Aberrations prevent an optical system required to produce a point focus at including the specified radial order. from maintaining high image contrast the desired location. These aberrations The point spread function indicates as the spatial frequency of the object are usually the most detrimental to the 1 January 2010.qxd:1 11/12/09 09:38 Page 9
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SMALL (3 MM) PUPIL SIZE LARGE (6 MM) PUPIL SIZE ORIGINAL OBJECT MODULATION ABERRATED IMAGE MODULATION S MAX MAX U L C U E M C O N I F N A E A N I N LENSLET FOCUS ABERRATIONS OF EYE D
C M E U R DISPLACED ON CCD DISTORT WAVEFRONT L E
MIN MIN D R
FREQUENCY = 2 CYCLES FREQUENCY = 2 CYCLES O - W O L R O R R E POINT ON MAX MAX RETINA A L U E M M C O
N CCD LENSLET I N A C A
N I
N SENSOR ARRAY R C M E E U L D R
MIN MIN O -
FREQUENCY = 4 CYCLES FREQUENCY = 4 CYCLES H G I H
MAX MAX L U E Figure 8: Low-order aberrations degrade image Figure 9: Many commercial aberrometers use a M C N I N A A N I N quality significantly, even at smaller pupil sizes, wavefront sensor that is based on the Shack- C M E U L whereas high-order aberrations more detrimental Hartmann principle, which measures the MIN MIN FREQUENCY = 6 CYCLES FREQUENCY = 6 CYCLES at larger pupil sizes deflections caused by the distorted wavefront through an array of small lenslets the nearest one-quarter diopter (0.25 D). Zernike aberration mode to the High-order aberrations generally decline second-order defocus mode. This with radial order and vary significantly from allows one to express any aberration Figure 7: The modulation (or contrast) reproduced person to person. Moreover, high-order mode as a ‘spherical equivalent’ SE in by an optical system typically decreases as the spatial frequency of the original test pattern aberrations can fluctuate over time or with dioptres using the following equation: increases due to wavefront aberrations and variations in accommodation. diffraction -4√ 3 m Because of the increasing pupil SE = 2 Cn quality of vision for normal eyes. Low- dependence of the aberration modes ρ order aberrations are traditionally in the higher radial orders, high-order m corrected with prescription spectacle aberrations become more detrimental where Cn is the aberration coefficient lenses or contact lenses. to vision quality at low-luminance of the Zernike mode of interest in levels when the pupil size is large microns and is the radius of the pupil m High-order aberrations characterise (Figure 8). High-order aberrations can at which the ρcoefficient Cn was the more subtle deviations of an reduce image quality by further determined in millimetres. aberrated wavefront from the ideal reducing image contrast and by shape. In most eyes, high-order causing ‘halos’ and similar effects, The effects of the various Zernike aberrations are generally small particularly around bright lights at modes on vision quality differ; compared to the low-order night. High-order aberrations can also therefore, the results of this equation aberrations. Generally, these exacerbate night myopia. Further, should be interpreted with caution. aberrations have less impact on vision because maximum vision quality is Zernike aberration modes with larger quality in normal eyes, although eyes essential while operating a motor meridional frequencies, which are with certain ocular conditions, such as vehicle in order to ensure adequate located farther from the centre of the keratoconus, may exhibit significant reaction time, especially at night, Zernike pyramid, often have less high-order aberrations. This can result excess high-order aberrations can impact on vision quality than modes in ‘irregular astigmatism’ and similar significantly influence visual with smaller frequencies. Additionally, anomalies of ocular refraction. performance and even safety. Zernike modes with the same Otherwise, high-order aberrations are meridional frequency in different radial usually not visually meaningful until the Refractionists are generally familiar orders can interact with each other to lower-order aberrations of defocus with the effects of low-order wavefront improve or degrade vision quality7. and astigmatism have been aberrations on vision quality. The substantially corrected. second-order Zernike defocus and Using spherical and cylindrical lenses, astigmatism aberrations caused by the a refractionist determines an Population studies have shown that uncorrected refractive errors of the approximate correction for the low-order aberrations typically account eye result in blurred vision and second-order aberrations of the eye for over 90% of the total wavefront reduced vision acuity, which varies during the ocular refraction, including error; roughly 80% is due to defocus, with the magnitude of the refractive any defocus and astigmatism. This alone. These studies have also shown error. Only the second-order Zernike refraction is influenced, however, by that the RMS wavefront error for the aberration modes have coefficients the high-order aberrations of the eye. high-order Zernike aberration modes is that relate directly to common Objective refractions based on approximately 0.30 to 0.35 microns on dioptric powers. It is more difficult to wavefront measurements should take average for a 6mm pupil size, which is interpret the effects of higher-order into account the complex interaction equivalent to 0.25 to 0.30 D of second- aberration modes on vision. Assuming between the high- and low-order order Zernike defocus5,6. High-order that Zernike aberration modes with aberrations that ultimately leads to the aberrations are often smaller than the equal RMS wavefront errors degrade subjective judgment of best focus. In residual defocus and astigmatism vision quality equally, however, it order to measure the high-order remaining after the eye is corrected to becomes possible to relate any Continued overleaf 1 January 2010.qxd:1 11/12/09 09:38 Page 10
dispensingoptics 10 January 2010
aberrations of the eye, a special of this point source then serves as the measured and used to model the device utilising a wavefron sensor is object point for the device. Light from wavefront errors of the eye (Figure 9). required, which is commonly referred this retinal object point passes through to as an aberrometer. Just as a an array of small lenslets after leaving Key points corneal topographer provides more the eye. These lenslets sample the • Wavefront aberrations represent information about the shape of the optics of the eye over the entire pupil. one of several possible ways to cornea than a conventional Each lenslet then brings light to a focus characterise the focusing errors of an keratometer, an aberrometer provides on a CCD sensor. Ideally, light from the optical system. more information about the optics of retina should produce a plane (flat) • The Zernike polynomial series serves the eye than a conventional wavefront after passing back through as a particularly convenient autorefractor. the optics of the eye when representation of wavefront accommodation is relaxed. Any aberrations with several useful Many aberrometers rely on the Shack- differences between the ideal plane properties. Hartmann principle. A point source of wavefront and the actual wavefront • Low-order wavefront aberrations are light from the aberrometer— exiting the eye will cause the light associated with the traditional sphere representing a distant object—is passing through a given lenslet to and cylinder powers of lenses and are projected onto the retina. The image deviate. The deviation of each focus is typically the most detrimental to vision quality. • High-order wavefront aberrations are more detrimental to vision quality at larger pupil sizes or when the lower Multiple choice questions (MCQs): order aberrations have been eliminated. Wavefront aberrations and spectacle lenses: part one References 1. MacRae S (2000) Supernormal vision, hypervision, and customised 1. Which statement concerning corneal ablation. J Cataract Refract wavefront errors is not true? aberrated wavefront produced by an Surg 26(2), 154-157. a. The wavefront error is equal to the optical system from the ideal 2. Thibos L, Hong X, Bradley A, and distance of the refracted ray from wavefront over some reference plane? Cheng X (2002) Statistical variation of the intended focal point a. Root-mean-square error aberration structure and image quality b. Wavefront error measurements are b. Point spread function in a normal population of healthy usually taken across the aperture of c. Strehl ratio eyes. J Opt Soc Am A 19(12), 2329- an optical system d. Modulation transfer function 2348. c. Wavefront error measurements can 3. Atchison D (2005) Recent advances be used to predict image quality 5. Which instrument is likely to give the in the measurement of d. The error is the difference in optical most information about the optics of monochromatic aberrations of human path length between the actual the eye? eyes. Clin Exp Optom 88(1), 5-27. aberrated wavefront and the ideal a. Keratometer b. Aberrometer 4. Marsack J, Thibos L, and Applegate reference wavefront c. Autorefractor d. Focimeter R (2004) Metrics of optical quality derived from wave aberrations predict 2. Which relationship is not a common 6. Which statement about high-order visual performance. J Vis 4(8), 322-328. objective measure of image quality? aberrations is not true? 5. Porter J, Guirao A, Cox I, and a. Modulation transfer function a. In most eyes high-order aberrations Williams D (2001) Monochromatic b. Visual acuity are generally large compared to aberrations of the human eye in a c. Root-mean-square error the low-order aberrations large sample population. J Opt Soc d. Strehl ratio b. Excess high-order aberrations can Am A 18(8), 1793-1803. significantly influence visual 6. Castejón-Mochón J, López-Gil N, 3. Which Zernike aberration order does performance and even safety when Benito A, Artal P (2002) Ocular wave- a refractionist determine during the driving at night front aberration statistics in a normal Vis Res ocular refraction part of an eye c. High-order aberrations include young population. 42(13), 1611- examination? vertical and horizontal coma and 1617. a. Higher order b. Lower order spherical aberration 7. Applegate R, Marsack J, Ramos R, c. First order d. Second order d. High-order aberrations generally and Sarver E (2003). Interactions between aberrations can improve or decline with radial order and reduce visual performance. J 4. Which objective measure of image vary significantly from person to Cataract Refract Surg 29(8), 1487-1495. quality indicates the variance of the person Darryl Meister is the US Technical The deadline for posted or faxed response is 11 February 2010 to the address Marketing Manager for Carl Zeiss on page 4. The module code is C-12500 Vision. He has been an active Online completion - www.abdo.org.uk - after member log-in go to ‘CET member of the optical industry since online’ 1990, and was one of the youngest Occasionally, printing errors are spotted after the journal has gone to print. Notifications can be opticians ever to earn the ABO's viewed at www.abdo.org.uk
dispensingoptics 4 February 2010
Wavefront aberrations and spectacle lenses
Darryl Meister ABOM, explains the applications of part two spectacle lenses for the correction of wavefront aberrations in part two of this two-part series
CompetencIes covered: Optical appliances Target group: Dispensing opticians, optometrists
The first installment of this two-part Wavefront aberrations of spectacle derived from a ‘small angle’ series reviewed the fundamental lenses approximation of Snell’s law of optical and mathematical principles The specified ‘power’ of an refraction for small angles of associated with wavefront aberrations ophthalmic lens is actually based incidence. For relatively small angles, and image quality, with an emphasis upon a mathematical approximation the sine function of the angle is nearly on the Zernike polynomial series. The that is generally only accurate within equal to the angle, itself, in radians, so second part now examines the the paraxial region of the lens, or the that sin i ≈ i when i is small. This small- application of wavefront technology region of the lens within the immediate angle approximation quickly loses to the eye and corrective spectacle vicinity of the optical axis. Calculations accuracy, however, for object points lenses. Several spectacle lens of lens power for fabrication purposes located at significant distances from manufacturers are now marketing lens are typically based upon this the optical axis of the lens, resulting in designs that minimise the effects of approximation. For instance, the focal both low-order and high-order ‘high-order’ wavefront aberrations. power along the optical axis of a ‘thin’ wavefront aberrations. Consequently, These spectacle lenses generally fall lens is given by the Lensmaker’s the Lensmaker’s equation does not into one of two categories that offer equation: adequately describe the refraction of distinctly different potential visual light at significant viewing angles or at n- -n benefits: F = 1 + 1 significant distances from the optical 1. Spectacle lenses that are claimed r1 r2 centre of the lens. to reduce the high-order aberrations of the spectacle lens, most commonly where r1 is the radius of the front Many eye care professionals are in progressive lenses, and surface in metres, r2 is the radius of the familiar with the traditional optical 2. Spectacle lenses that are claimed back surface, and n is the refractive aberrations that can degrade vision to reduce the effects of high-order index of the lens material. quality through conventional ocular aberrations of the wearer’s eye. This relatively simple equation is spectacle lenses, which were first
This article has been approved for 1 CET point by the GOC. It is open to all FBDO members, including associate member optometrists. Insert your answers to the six multiple choice questions (MCQs) on the answer sheet inserted in this issue and return by 18 March 2010 to ABDO CET, Courtyard Suite 6, Braxted Park, Great Braxted, Witham CM8 3GA OR fax to 01621 890203, or complete online at www.abdo.org.uk. Notification of your mark and the correct answers will be sent to you. If you complete online, please ensure that your email address and GOC number are up-to-date. The pass mark is 60 per cent. The answers will appear in our April 2010 issue. C-12501 2 February 2010.qxd:1 21/1/10 14:17 Page 5
Continuing Education and Training
described in detail by Ludwig von the rotation of the line of sight behind Y T I N I
Seidel for rotationally symmetrical the lens. F IMAGE N I POINT T A optical systems (Figure 1). The
T SPREAD N I O P
aberrated wavefront produced by the The low-order wavefront aberrations T C E
Seidel aberrations of an optical system associated with curvature of the field J B O
S I
for a given object point or viewing and radial astigmatism are typically X A - F F
angle can also be broken down or the most detrimental to vision quality in O decomposed into a series of Zernike conventional single vision and bifocal CURVATURE OF THE FIELD aberration modes. There are five lenses. These aberrations are generally Y
T HORIZONTAL I N I
primary Seidel optical aberrations: reduced or eliminated over a F VERTICAL IMAGE N I POINT T
curvature of the field A 1. Seidel occurs sufficiently wide field of view through
T SPREAD N I O
when a bundle of light rays refracted either judicious base (front) curve P
T C E
through the periphery of a lens is selection or the use of an aspheric lens J B O
S I
brought to a point focus outside of the design. When a spectacle lens X A - F F
intended image plane; this aberration conforms to proper optical design O is primarily characterised by the principles, low-order wavefront RADIAL ASTIGMATISM 0 Zernike defocus mode (Z2 ). aberrations are negligible. Y T I N 2. Seidel radial astigmatism occurs I IMAGE F N I
POINT T
when a bundle of light rays refracted The position of the fitted spectacle A SPREAD T N I
obliquely through a lens produces an lens may also introduce a form of O P
T C E
astigmatic focus instead of a single radial astigmatism, resulting in J B O
S point focus; this aberration is primarily unwanted prescription changes that I X A - N
characterised by the Zernike degrade vision quality. An increase in O -2 2 2 2 astigmatism modes (Z and Z ), sphere power and induced cylinder SPHERICAL ABERRATION although Zernike defocus may also be power occur when a spectacle lens is Y T I N introduced. tilted, producing a wavefront I F IMAGE N I POINT spherical aberration T 3. Seidel occurs aberration that is characterised by the A
T SPREAD N I
when the outer rays in a bundle of Zernike defocus and astigmatism O P
T C E
light rays are refracted more or less modes. These power errors vary as a J B O
S than the inner, paraxial rays near the function of the power of the lens and I X A - F
optical axis; this aberration is primarily the amount of tilt. With stronger F O characterised by the Zernike spherical prescriptions, the low-order wavefront COMA 0 aberration mode (Z4 ). aberrations produced by changes in 4. Seidel coma occurs when the outer the position of wear of the spectacle Figure 1: The primary Seidel aberrations that rays of in a bundle of light rays lens can be significantly greater in affect image clarity include curvature of the field, radial astigmatism, spherical aberration, and refracted obliquely through a lens are magnitude than the uncorrected high- coma refracted more than the inner rays; this order aberrations of either the eye or aberration is primarily characterised by the lens. changed from positive to negative or -1 1 the Zernike coma modes (Z3 and Z3 ). vice versa. The Zernike oblique -2 5. Seidel distortion occurs when the For either pantoscopic tilt or face-form astigmatism mode (C2 ) is zero in this magnification of images of extended wrap of a thin spherical lens of power simplified case. objects increases or decreases away F, the coefficients for the Zernike from the optical axis of a lens; this defocus and with-the-rule astigmatism Spectacle lenses may also introduce 0 2 aberration is primarily characterised by modes (C2 and C2 ) are given by: high-order wavefront aberrations, such -1 1 the Zernike prism modes (Z1 and Z1 ), 2 as spherical aberration and coma, H sin although distortion will be ignored in F = F 1+ 2nθ particularly in stronger prescription this context because it does not ( ) powers. Spherical aberration is due to influence image clarity. FH an effective increase in refractive Fv = 2 cos power away from the optical axis of a The Seidel aberration function has θ lens, causing rays of light in the field-dependent terms that vary with 0 Fv+FH 2 C2 = periphery to focus more closely to the the angle of view, typically increasing -8√3 ρ lens than light rays near the optical as the angle of view increases. Zernike axis. Coma is due to a variation in 2 Fv-FH 2 aberration polynomials, on the other 2 refractive power that affects C = √ hand, are calculated along a single 4 6 ρ extended object points located away angle of view. Consequently, in order where FH is the power through the from the optical axis of the lens. to characterise the wavefront horizontal meridian of the lens, Fv is the Fortunately, the relatively small pupil aberrations of a lens or optical system power through the vertical meridian, n aperture of the eye ‘stops down’, or over an extended field of view using is the refractive index of the material, limits the area of the lens used for the Zernike polynomial series, Zernike is the radius of the pupil in millimetres, ρ focusing light from any given object aberration modes must be calculated and is the angle of lens tilt. For face- point across the field of view, which 2 at multiple angles of view to represent form θwrap, the sign of C2 should be Continued overleaf 2 February 2010.qxd:1 21/1/10 14:17 Page 6
dispensingoptics 6 February 2010
-3 -1 -3 3 3 3 SPHERICAL ABERRATION (Z ). The coefficients C and C of PERMITTED BY PUPIL Y T I
N these two Zernike aberration modes I F N I
T A
depend upon the rate of change in T N I SURFACE ASTIGMATISM LOW-ORDER ABERRATIONS O P addition power along the progressive T +25 +25 C
E 1
J +20 +20 B O +15 +15 corridor : +10 +10 +5 +5 LENS WITH SPHERICAL ABERRATION, LARGE PUPIL -1 3 3 0 0 3 A 1 A –5 –5 SPHERICAL ABERRATION C = δ = BLOCKED BY PUPIL –10 –10 √ ρ √ ( )ρ
Y 24 24 h
T 2 2
I –15 –15 N I
F –20 –20 N I
T –25 –25 -3 A A 3 1 A 3 T µ
N SURFACE ASTIGMATISM (D) RMS WAVEFRONT ERROR ( M) 3 I C = = O δ P
T √ √
C ρ ( )ρ 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 24 24 h E 2 2 J B O
LENS WITH SPHERICAL ABERRATION, SMALL PUPIL where is the radius of the pupil in millimetrρes and A is the rate of δ Figure 2: The small pupil aperture of the eye Figure 3: The low-order wavefront aberrations of a change in addition power in dioptres effectively limits the amount of spherical progressive lens are due primarily to unwanted per millimetre, which is the equal to aberration and coma introduced by spectacle surface astigmatism in the ‘blending’ regions of A lenses the lens, as demonstrated by contour plots of the ratio of the addition power to surface astigmatism and RMS wavefront errors for the corridor length h, or A = A/h. reduces the effects of these two a 6mm pupil at each point over the lens δ aberrations considerably (Figure 2). The progression of addition power quantities of Zernike oblique and with- essentially acts as a coma-like -2 Properly designed single vision and the-rule astigmatism modes (Z2 and wavefront aberration along the 2 bifocal lenses typically produce only Z2 ), which contribute significantly to progressive corridor, while the negligible amounts of low-order and the overall shape of the aberrated astigmatism-free nature of the corridor high-order aberrations in most wavefront. The low-order wavefront is achieved by a trefoil-like wavefront prescription powers. The optical aberrations of a progressive lens are aberration over the same region. limitations of progressive lenses, on the due primarily to this unwanted Further, these aberrations are other hand, introduce meaningful astigmatism (Figure 3). The distribution proportional to the rate of change in levels of both low-order and higher- of addition power over the lens addition power ( A) along the δ order aberrations. In any case, surface can also result in blur from progressive corridor of the surface. minimising the wavefront aberrations insufficient or excess plus power for a Additionally, these equations for the produced by a spectacle lens will not given viewing distance when the third-order Zernike coefficients provide the wearer with better than his object of regard is either too close or demonstrate the pupil size 3 or her best corrected visual acuity. too far away. The contribution of this dependence ( ) of the third-order ρ power error to the aberrated wavefront aberrations produced by Wavefront aberrations of wavefront is characterised by the progressive lenses, which vary as the 0 progressive lenses Zernike defocus mode (Z2 ). third power of the pupil size. Progressive lenses produce significant second-order wavefront aberrations, Furthermore, the smooth change in Traditional coma is due to an particularly in the lateral ‘blending’ addition power and surface asymmetric variation in refractive regions of the lens. Providing a astigmatism over the progressive lens power and magnification across the progressive change in addition power introduces non-negligible levels of lens for object points away from the requires a surface that varies smoothly high-order wavefront aberrations that optical axis. The change in addition in curvature. The mathematical are characterised by the Zernike power across a progressive lens constraints of producing a smooth wavefront aberration modes surface produces a very similar effect. change in curvature along the associated with variations in curvature, As the line of sight passes down the progressive corridor, however, result in particularly the modes of the third progressive corridor of the lens, the surface astigmatism, or a difference in radial order, coma and trefoil*. In fact, power at the upper margin of the curvature at any given point, away it can be demonstrated pupil differs from the power at the from the progressive corridor of the mathematically that the refracting lower margin by an amount roughly lens. Minkwitz showed mathematically action of a simple progressive lens equal to the product of the pupil that, in the vicinity of the progressive surface, with circular cross-sections diameter and the rate of change in corridor at least, the unwanted and a linear progression of addition addition power at that particular surface astigmatism lateral to the power, can be reproduced by location. In fact, coma is directly progressive corridor increases twice as combining an equal quantity of proportional to the rate of change in -1 rapidly as the change in addition vertical coma (Z3 ) and oblique trefoil mean addition power at any point power along the corridor. across the lens surface (Figure 4). * Mathematically, curvature is associated with the second derivatives of a surface, whereas a Although the Zernike coma and trefoil The unwanted cylinder power variation in curvature is associated with the third produced by the refraction of light derivatives of the surface; Zernike third-order aberration modes remain constant through the surface astigmatism of a aberrations modes exist when a refracted over the progressive region of the wavefront has non-zero third derivatives. Continued overleaf progressive lens introduces significant 2 February 2010.qxd:1 21/1/10 14:17 Page 8
dispensingoptics 8 February 2010
SURFACE ASTIGMATISM HIGH-ORDER ABERRATIONS PROGRESSIVE A HIGH-ORDER PROGRESSIVE B HIGH-ORDER +25 +25 +25 +25 8
7 POWER VARIES +20 +20 +20 +20 6 INCREASE IN +15 RAPID CHANGES IN +15 GREATER LEVELS OF +15 +15 SURFACE POWER OVER PUPIL SURFACE CURVATURES HIGH-ORDER ABERRATIONS +10 +10 +10 +10 +0 .50 +5 +5 +5 +5 0 0 0 0 0 +1.00
8 .0 1
+ 0
7 .0 +1.50 –5 –5 –5 –5 1 6 + +1.50 +2.00 –10 –10 –10 –10 –15 –15 –15 –15
6 MM –20 –20 –20 –20
8 –25 –25 –25 –25
7 ADDITION POWER PLOT 6 SURFACE ASTIGMATISM (D) RMS WAVEFRONT ERROR (µM) RMS WAVEFRONT ERROR (µM) RMS WAVEFRONT ERROR (µM)
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Figure 4: The progression of addition power across Figure 5: High-order aberrations are greatest over Figure 6: Well-designed progressive lenses often a progressive lens surface causes the power to regions of the lens in which the addition power exhibit similar levels of high-order aberrations as vary over the finite diameter of the wearer’s pupil, and astigmatism are changing rapidly demonstrated by plots of RMS wavefront errors introducing a coma-like wavefront aberration over each lens surface
simple surface discussed earlier, surface to ‘soften’ the design or distribution of power and unwanted modern progressive lenses employ confining the region to a smaller area astigmatism over the lens design will non-circular cross-sections and to ‘harden’ the design, there are also undoubtedly serve as a greater addition power that varies non-linearly two intimately related approaches to indicator of wearer satisfaction. along the corridor. Nevertheless, the the management of high-order high-order Zernike aberration modes in aberrations. A ‘soft’ lens design with Research has also demonstrated that these lenses will vary with the rate of gradual power changes will typically the impact of high-order lens change in surface power at any point. yield relatively low levels of high-order aberrations on visual acuity in the Coma and trefoil will be highest in aberrations over the entire lens, progressive corridor, where these regions wherein the addition power whereas a ‘hard’ lens design with aberrations are often highest, is and surface astigmatism are changing rapid power changes will yield lower negligible. The caustic focus produced most rapidly (Figure 5). Moreover, levels of high-order aberrations in the in the presence of small amounts of since high-order wavefront aberrations central distance and near viewing high-order lens aberrations may depend upon the rate of change in zones, while creating greater levels at possibly improve the wearer's depth of surface power, these aberrations will the viewing zone boundaries and focus and tolerance to the blur be more significant in progressive within the progressive corridor. In caused by the second-order lenses with shorter corridor lengths or general, minimising high-order aberrations of the lens. In fact, higher addition powers. aberrations in any particular region will aberration coupling between the be at the expense of inducing greater high-order aberrations of the Progressive lens designers have begun levels of high-order aberrations progressive lens and the high-order paying closer attention to high-order elsewhere4. aberrations of the eye can sometimes wavefront aberrations, and in some yield better visual acuity than cases even developing progressive Although high-order aberrations may obtained with the naked eye6. lens designs with reduced high-order result in a reduction in image quality Nevertheless, the high-order aberrations2. Unfortunately, you and a loss of contrast, low-order lens aberrations produced by a progressive cannot eliminate the high-order aberrations generally account for the lens will have at least some impact on aberrations produced by a progressive greatest impact on vision quality with the wearer’s vision, and therefore lens surface, just as you cannot progressive lenses. The maximum RMS represent a meaningful quantity to eliminate unwanted surface wavefront error for the low-order evaluate during the optical design astigmatism. In fact, for modern, well- aberrations is up to ten times greater process. designed progressive lens designs at than the maximum error for the high- least, the average levels of high-order order aberrations (Figure 7). In Correcting the wavefront aberrations calculated globally over particular, unwanted astigmatism aberrations of the eye each lens surface are often similar in dominates much of the lens. Further, in Spectacle and contact lenses are magnitude (Figure 6)3. Nevertheless, contrast to the low-order aberrations, generally prescribed to correct the you can judiciously manage both the clinical research has demonstrated low-order aberrations of the eye, low-order and high-order aberrations that the high-order aberrations of corresponding to the Zernike defocus of a progressive lens. progressive lenses are seldom any and astigmatism modes. If the low- greater in magnitude than the natural order aberrations of eye have been Just as there are two general high-order aberrations of a typical corrected with lenses, vision quality approaches to the management of wearer’s eyes5. Consequently, for the becomes limited by any residual high- low-order astigmatism and defocus, correction of presbyopia with order aberrations, such as spherical by either distributing the ‘blending’ progressive lenses, which suffer from aberration and coma, particularly at region over a larger area of the significant low-order aberrations, the larger pupil sizes. Visual acuity for 2 February 2010.qxd:1 21/1/10 14:17 Page 9
Continuing Education and Training
NO CORRECTION LOW ONLY CORRECTION HIGH & LOW CORRECTION LOW-ORDER ABERRATIONS HIGH-ORDER ABERRATIONS +25 +25
+20 +20 N O I
+15 +15 T A
+10 +10 L U M
+5 +5 I S 0 0 N O
–5 –5 I S I
–10 –10 V –15 –15 –20 –20 –25 –25 RMS WAVEFRONT ERROR (µM) RMS WAVEFRONT ERROR (µM) R O R 1 1 1 1 7 7 7 7 4 4 4 4 2 2 5 5 8 8 0 0 . . . . 3 3 6 9 6 9 R 0 0 ...... 1 1 3 3 1 1 1 1 0 1 0 1 E 2 2 3 3 0 0 2 2 3 3 4 4 0 0 2 2
E Figure 8: Once the low- V A
W order aberrations of
G N
I the eye have been N I
A corrected, which are M Y X Y X Y X E
R typically more Figure 7: Low-order aberrations due to unwanted detrimental, visual surface astigmatism are significantly greater in performance magnitude than high-order aberrations over most becomes limited by of the progressive lens surface high-order aberrations
‘normal’ individuals, without significant to improve visual performance, at In fact, just a few millimetres of ocular pathology, ranges from 6/6 to least compared to post-operative movement of the line of sight from the 6/5 under typical testing conditions results obtained using traditional centre of an ideal wavefront when the low-order aberrations have methods, by modifying the ablation correction will introduce new, lower- been corrected with lenses. If both the profile based upon the high-order order wavefront errors that are low-order and high-order aberrations aberrations of the eye. Because of actually greater in magnitude than of the eye are eliminated, however, variations in wound healing and other the higher-order aberrations initially super vision may be obtained with factors influencing surgical outcomes, eliminated, and these errors will improved contrast sensitivity and however, it is difficult to correct progressively worsen with increasing supernormal visual acuity that is completely the subtle high-order movement8. Since the human eye noticeably better than 6/6 (Figure 8). aberrations of the eye through surgery. remains in a constant state of Often, patients do not experience a movement, correcting the high-order Once the low-order and high-order notable improvement in visual acuity aberrations of the eye with a aberrations of the eye have been compared to their best spectacle spectacle lens actually results in completely eliminated, diffraction correction prior to refractive surgery7. poorer vision quality over most of the becomes the limiting factor in image wearer’s field of view. Thus, the resolution at small pupil sizes. It is also possible to incorporate a sensitivity of these aberrations to Rayleigh’s criterion states that, in order correction for certain high-order normal gaze changes places drastic to distinguish two objects points as aberrations into soft contact lens limits on the visual benefits of separate, sufficient distance must designs, since it is possible to cause correcting the high-order aberrations separate the central Airy patterns of these lenses to remain relatively fixed of the eye with a spectacle lens. the two image points. At larger pupil with respect to the optics of the eye sizes, the resolution of the human eye by minimising rotational and Although there are significant optical becomes limited by the anatomical translational movements about the limitations associated with eliminating density of the retinal photoreceptors, cornea. Unfortunately, spectacle the high-order aberrations of the eye or the number of cones over a given lenses cannot eliminate the high-order with a spectacle lens, it is possible to region of the retina, which is a aberrations of the eye without determine better ‘low-order’ ‘sampling frequency’ limitation known introducing additional, lower-order spectacle corrections by considering as the Nyquist limit. Additionally, the aberrations as the eye rotates from the the influence of high-order aberrations chromatic aberration of the eye for centre of the lens. For instance, on vision. The optimum prescription is different wavelengths of light serves as correcting second-order aberrations influenced by not only the low-order another optical limitation. Therefore, results in induced first-order prism as sphere and cylinder refractive errors, due to the optical and physiological the eye moves from the centre of the but also by the higher-order limitations of the human eye, even a correction (that is, Prentice’s rule), aberrations of the eye at a given pupil perfectly corrected eye free from while correcting third-order aberrations size. optical aberrations can only achieve results in induced second-order 6/3 to 6/4 visual acuity. astigmatism and defocus errors.* Determining the endpoint of refraction by taking into account the effects of Nevertheless, there exists potential for high-order aberrations on blur may * This effect can be appreciated by adding a an improved visual outcome. horizontal or vertical offset to the terms of a result in more accurate low-order ‘Wavefront-guided’ corneal ablation is Zernike basis function, and then expanding the spectacle refractions that deliver new binomials, so that a term such as 2x2 in a quickly becoming the new standard 2 2 Zernike polynomial becomes 2(x + x) = 2x + optimum vision over a broader range of care in refractive surgery. 4x x + 2 x2 in the presence of a horΔizontal offset of luminance levels or viewing Wavefront-guided ablation promises ( Δx), nowΔ with lower-order 4x x and 2 x2 terms. Continued overleaf Δ Δ Δ 2 February 2010.qxd:1 21/1/10 14:17 Page 10
dispensingoptics 10 February 2010
the presence of significant high-order comfortable binocular vision. PUPIL BLOCKS HIGH- ORDER ABERRATIONS
Y aberrations such as spherical T I N I F N I
aberration. The Jackson cross-cylinder Furthermore, with the advent of free- T A
T N I technique may fail to converge to the form surfacing technology, lens O P
T C
E ideal cylinder power correction in the surfacing no longer needs to be J B O presence of high-order aberrations or constrained by the rounding errors of ORIGINAL PERFORMANCE WITH SMALL PUPIL the inability of the patient to hard lap tooling. Free-form surfacing
REFRACTION AFFECTED determine the relative legibility of technology enables laboratories to BY H-O ABERRATIONS Y T I
N Snellen chart letters that have been fabricate lenses that precisely I F N I
T
A distorted in shape or caused to ‘ghost’ replicate prescription powers in one-
T N I O P
by cylinder power. hundredth dioptre (0.01 D) increments. T C E J B
O When a wavefront-guided spectacle In addition to the potential variability prescription is fabricated to more ORIGINAL PERFORMANCE WITH LARGE PUPIL of subjective refraction, the use of precise optical tolerances, the result is REFRACTION OPTIMIZED FOR H-O ABERRATIONS lenses in one-quarter dioptre (0.25D) a truly optimum low-order vision Y T I N I F increments during the refraction correction that provides improved N I
T A
T
N procedure places a limitation on the contrast sensitivity and visual acuity I O P
T
C measurement precision of the final under a wider range of luminance E J
B 13 O prescription powers, resulting in levels or viewing conditions . MODIFICATION MODIFIED PERFORMANCE WITH LARGE PUPIL rounding errors of up to ±0.125D. Someday, this technology may very Traditional lens surfacing relies on hard well supplant the current model of lap tooling to produce the prescription eyewear delivery by establishing a Figure 9: Wavefront-guided prescriptions can fine- tune the low-order spectacle refraction to ensure surface, which is typically limited in new standard of care for prescribing maximum vision quality across a range of pupil precision to ±0.0625D. The and fabricating spectacle corrections. sizes propagation of rounding errors from refraction and surfacing can Key points conditions. Using wavefront data contribute up to 0.2D of unwanted • Spectacle lenses cannot correct the captured by an aberrometer, a power error. high-order aberrations of the eye wavefront-guided or wavefront- without introducing even greater optimised spectacle refraction can be Because aberrometers capture aberrations away from the centre of determined objectively by calculating extensive data regarding the the lens. the prescription powers that maximise wavefront aberrations of the eye over • Properly designed single vision and some predefined measure of retinal the entire pupil, it becomes possible to bifocal lenses generally suffer from vision quality9. Conventional modify the traditional low-order only negligible low-order and high- autorefractors have not replaced spectacle refraction by taking into order aberrations. subjective refraction as the best account the effects of high-order • Changing addition power and method to determine the final low- aberrations on retinal image quality, to unwanted astigmatism over order spectacle prescription powers. the nearest one-hundredth dioptre progressive lenses introduces Furthermore, the accuracy of the (0.01D). Software employing significant low-order and high-order forced-choice method typically optimisation algorithms can calculate aberrations. utilised during subjective refraction to the spectacle refraction that delivers • Spectacle prescriptions can be determine the final spectacle the best retinal image quality at a enhanced using both low-order and correction for an eyeglass wearer given pupil size or range of pupil sizes high-order aberration measurement suffers from the inherent variability of without the limitations imposed by data from an aberrometer to subjective responses10,11. conventional autorefractors or even maximise vision quality over a broad subjective refraction (Figure 9). range of pupil sizes. The patient may use different perceptual criteria—such as sharpness, Consequently, when combined with References contrast, or legibility—when choosing sophisticated computer programs that 1. Blendowske R, Villegas E, and Artal the ‘best focus’, which may maximise vision quality based upon P (2006) An Analytical Model correspond to differing lens powers. the wavefront aberration data of the Describing Aberrations in the The depth of focus of the eye may eyes, aberrometry can potentially Progression Corridor of Progressive make it difficult for the patient to deliver more accurate and reliable Addition Lenses. Optom Vis Sci 83(9), discriminate reliably between small vision corrections compared to 666-671. changes in vision quality when traditional subjective refraction12. It is 2. Wehner E, Welk A, Haimerl W, presented with multiple lenses for even possible to reconcile the Altheimer H, and Esser G (2006) comparison. Although the effect is wavefront-guided refraction against Spectacle Lens with Small Higher ameliorated somewhat by the the manifest subjective refraction in Order Aberrations. US Patent 7,063,421. directional sensitivity of the retina, order to preserve any deliberate 3. Villegas E and Artal P (2004) known as the Stiles Crawford effect, changes to the ocular refraction Comparison of aberrations in different the spherical equivalent of the meant to balance the stimulus to types of progressive power lenses. refraction may vary with pupil size in accommodation or otherwise ensure Continued overleaf 2 February 2010.qxd:1 21/1/10 14:17 Page 12
dispensingoptics 12 February 2010
Ophthal Physiol Opt 24(5), 419-426. Surg 32(4), 577-583. Optom Vis Sci 75(8), 617-622. 4. Meister D and Fisher S (2008) 8. Guirao A, Williams D, and Cox I 12. Cheng X, Bradley A, and Thibos L Progress in the spectacle correction of (2001) Effect of rotation and translation (2004) ‘Predicting subjective judgment presbyopia. Part 2: modern progressive on the expected benefit of an ideal of best focus with objective image lens technologies. Clin Exp Optom method to correct the eye’s higher quality metrics’. J Vis 44, 310-321. 91(3), 251-264. order aberrations. J Opt Soc Am A 13. Guillen J and Kratzer T (2009) 5. Villegas E and Artal P (2003) 18(5), 1003-1015. Apparatus and method for Spatially Resolved Wavefront 9. Thibos N, Hong X, Bradley A, and determining an eyeglass prescription Aberrations of Ophthalmic Progressive- Applegate R (2004) ‘Accuracy and for a vision defect of the eye. US Powered Lenses in Normal Viewing precision of objective refraction from Patent Application 2009/0015787. Conditions. Optom Vis Sci 80(2), 109- wavefront aberrations’. J Vis 4(4), 329- 112. 351. Darryl Meister is the US Technical 6. Villegas E and Artal P (2006) Visual 10. Leinonen J, Laakkonen E, and Marketing Manager for Carl Zeiss Acuity and Optical Parametres in Laatikainen L (2006) Repeatability Vision and an ABO Certified Master Progressive-Power Lenses. Optom Vis (test-retest variability) of refractive error Optician. He has been an active Sci 83(9), 672-681. measurement in clinical settings. Acta member of the optical industry since 7. Tuan K (2006) ‘Visual experience Ophthal Scand 84, 532-536. 1990, and continues to serve as a and patient satisfaction with 11. Bullimore M, Fusaro R, and Adams technical representative to the wavefront-guided laser in situ W (1998) The repeatability of American National Standards Institute I keratomileusis’. J Cataract Refract automated and clinician refraction. and the Vision Council.
Next issue: Stephen Freeman describes the history, technology and applications of current photochromic and polarised lenses
Multiple choice questions (MCQs): Wavefront aberrations and spectacle lenses: part two
1. Which Seidel aberration is primarily b. By confining the ‘blending’ region aberrations upon vision quality with characterised by the Zernike defocus to a smaller area progressive lenses? mode? c. By balancing the high-order a. High-order aberrations have more a. Seidel curvature of the field aberrations with the low-order impact on vision quality than low- b. Seidel radial coma aberrations order c. Seidel spherical aberration d. None of the above; it is impossible b. High-order lens aberrations in are d. Seidel distortion to eliminate all of the high-order noticeably greater than the natural aberrations high-order aberrations of the eye 2. Which two of the Seidel c. High-order aberrations may result in aberrations are both effectively 4. Which person showed a reduction in image quality and a limited by the small size of the pupil of mathematically that, in the vicinity of loss of contrast the eye? the progressive corridor, the d. Low-order aberrations generally a. Radial astigmatism and coma unwanted surface astigmatism lateral have less impact on vision quality b. Spherical aberration and coma to that corridor increases twice as with progressive lenses c. Spherical aberration and distortion rapidly as the change in addition d. Radial astigmatism and spherical along the corridor? 6. Which aberration will most likely be aberration a. Von Seidel induced if the pantoscopic tilt or face b. Minkwitz form angle of a pair of lenses is 3. How is it possible to eliminate the c. Nyquist altered? high-order aberrations on a d. Zernike a. Radial astigmatism progressive lens surface? b. Curvature of the field a. By distributing the ‘blending’ region 5. Which statement is most likely to be c. Distortion of the surface true regarding the impact of d. Spherical aberration
The deadline for posted or faxed response is 18 March 2010 to the address on page 4. The module code is C-12501 Online completion - www.abdo.org.uk - after member log-in go to ‘CET online’ Occasionally, printing errors are spotted after the journal has gone to print. Notifications can be viewed at www.abdo.org.uk