average optical performance of the human eye as a function of age in a normal population

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Average Optical Performance of the Human Eye as aFunction of Age in a Normal Popu lationAntonio Guirao,x Conception Gonzalez? Manuel Redondo,x Edward Geraghty,2Sverker Norrby,2 and Pablo Artal1

PURPOSE. TO determine the average optical performance of the human eye, in terms of themodulation transfer function (MTF). as a function of age.METHODS. An apparatus was constructed to measure the ocular MTF, based on the recording ofimages of a green, 543-nm laser-point source after reflection in the retina and double pass throughthe ocular media. MTFs were computed from the average of three 4-second-exposure double-passimages recorded by a slow-scan, cooled charge-coupled device camera. The ocular MTF wasmeasured for three artificial pupil diameters (3 nim, 4 mm, and 6 mm) with paralyzed accommo-dation under the best refractive correction in 20 subjects for each of three age categories: youngsubjects aged 20 to 30 years, middle-aged subjects aged 40 to 50 years, and older subjects aged 60to 70 years. The selected subjects passed an ophthalmologic examination, excluding subjects withany form of ocular or retinal disease, spherical or cylindrical refractive errors exceeding 2 D, andcorrected visual acuity lower than I (0.8 in the older age grou p).RESULTS. The average MTF was determined for each age group and pupil d iameter. A two-parameteranalytical expression was proposed to represent the average MTF in each age group for every pupildiameter. The ocular MTFs declined as age increased from young to older groups. The SD of theMTF results within age groups was lower than the differences between the mean for each group.CONCLUSIONS. The average optical performance of the human eye progressively declines with age.These MTF results can serve as a reference for determining mean ocular optics according to age.(Invest Opbthalmol Vis Sci. 1999;4():203-213)

Aging affects different aspects of the visual system inhumans (see references I and 2 for a review). Inparticular, spatial vision deteriorates with age: Thecontrast sensitivity function (CSF) is lower in older subjects,especially at: mid and high spatial frequencies.5 The relativecontribution of optical versus neural factors to this deterio-ration is still a matter of some controversy, although theoptical performance of the eye seems to be reduced onaverage with age. Anal et al.'1 showed thai the mean ocularmodulation transfer function (MTF) in a group of oldersubjects was lower than the average MTF in a group ofyounger subjects. This result, although it was obtained in asmall sample, suggests that ocular aberrations, besides in-traocular scattering, increase with age. Burton et al.,3 bycomparing CSFs obtained with laser interferometry and con-

From the 'Laboratorio de Optica. Dcpartamcnto de Fisica. Univer-sidad de Murcia, Spain; and ^Pharmacia and Upjohn. Groningen. TheNether lands.Presented in part at the annual meeting of the Association forResearch in Vision and Ophthalmology, Fort Lauderdale, Florida, May1997.Supported by Pharmacia and Upjohn, Groningcn, The Nether-lands; and a Direcion General de Investigacion Cientilica y TecnicaSpain Gran t n o. PH94-I 138.Submitted for publication April 7. 1998; revised July 21, 1998;accepted August 21, 1998.Proprietary interest category: C2.Reprint requests: Pablo Artal, Laboratorio de Optica, Departa-me nto d e Fi 'sica. IJniversidad de Murcia. Campus de F spinardo (LdificioC) , 30071 Murcia. Spain.

ventional gratings, also support the idea of a decreasingoptical image quality with age.In this context, an extended and more detailed study ofocular optics according to age contributes to better under-standing of how the eye's optics change with age and definesstandards of the average retinal image quality, representingsubjects of different ages. The definition of an average refer-ence of the optical image quality for different age groups isuseful for ophthalmic optics design and manufacturing. If sub-stantial changes in the ocular performance occur with age, it isunreasonable to use as a reference for older subjects the sameestimates of ocular optics obtained in a young, and usuallysmall, population.The purpose of this study was to evaluate the influence ofage on retinal image quality by determining the average opticalperformance of the human eye, in terms of the MTF, in threegroup s of healthy subjects in different age ranges. To minimizesystematic errors that could affect the results, the experimentswere performed under carefully controlled optical conditionsin even' subject (i.e.. best focus under paralyzed accommoda-tion), withfixed-diameterartificial pupil and co ntrolled relativecentering of the artificial pupil in relation to the natural pupil.The criteria for selection of the subjects for each group werepreviously determined to represent a normal healthy popula-tion. A major problem was defining the conditions of normal-ity/' especially in older subjects.Finally, because previous measurements of the retinal im-age quality were not performed routinely, but only underlaboratory experimental conditions, an initial important part of

this study consisted of developing an adapted version of theInvestigative Ophthalmology & Visual Science:. January lyyy . Vol. 40, No. ICopyright Association lor Kcscarch in Vision and Ophthalmology 2 0 3


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204 Guirao et al. /OKS, January 1999, Vol. 40, No. 1Slow scancooled CCDcamera

cameraobjective

PC computer

computerworkstation(MTF calculations)

\ Green He-Ne Laser)

TV monitor(pupil centeringcontrol)upper level

1. Schematic of the double-pass apparatus (see the Methods section lor details). CCD. charge-coupled device: Mil", modulation transfer function; O". double-pass retinal image; AP, artificial pupil: MD,black diftiiscr: US, beam splitter; I., lens; P, pinhole; M. microscope objective: NDF. neutral-density filter:Pol, polari/er; DM. dichroic mirror; CTL cylindrical trial lens; 1.1:1.) (IR), infrared light-emitting diode; O\point source on retina.

double-pass apparatus to measure the ocular MTF accurately ina relatively large population under conditions that were com-fortable for the subjects.

METHODSSubjectsSixty healthy subjects, distributed in three age groups partici-pated in the study: group A, 20 young subjects (13 women, 7men; age range, 20-30 years; mean age, 24 3 years); groupB. 20 middle-aged subjects (12 women, 8 men; age range,40-50 years; mean age, 46 3 years); group C, 20 oldersubjects (9 women, 1 1 men; age range, 60-70 years; mean age.63 3 years). The subjects were selected after they passed acomplete ophthalmologic examination. We used the the fol-lowing exclusion criteria to limit the study population tohealthy eyes: refractive error (spherical equivalent) more than2 D, keratometric astigmatism more than 1.5 D, correctedvisual acuity lower than 1 (0.8 in subjects in group C), anyprevious surgery on the eye to be tested, amblyopia, any

known ocular or retinal disease (assessed by slit lamp with andwithout retroillumination using standard clinical criteria), andany systemic diseases affecting refractive error (diabetes ordisorders of the nervous system). The study followed the te-nets of the Declaration of Helsinki, and signed informed con-sent was obtained from even' subject after the nature and allpossible consequences of the study had been explained.Double-Pass Apparatus to Measure Ocular MTFThe MTF is widely used for image quality evaluation ofoptical systems.' It yields the relation between the contrastof an object and its associated image at every spatial fre-quency. MTF is probably the most comprehensive functionknown for analyzing the overall optical performance of theeye and can be compared with the commonly used psycho-physical CSF. An objective procedure for measuring ocularMTF is based on recording and processing double-pass ret-inal images of a point sourcethe ophthalmoscopic or dou-ble-pass method.""10

We constructed a double-pass apparatus, similar to thatproposed by Santamaria et al.,' incorporating new and im-


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IOVS, January 1999, Vol. 40, No. 1 Optics of the Aging Eye 205Double-Pass Image(equal pupils) Modulation TransferFunction (MTF) 2D Modulation TransferFunction (MTF) ID

/(x)= PSF(x)PSF(-x) MTF(u) MTF(\u\)

FT(Hx))

20 40 60 80 100Spatial Frequency (c/deg)

FIGURE 2. Diagram of the calculation procedu re. The double-pass image (I[.vJ), recorded with equal pupil diameters, is the autocorrelation of theretinal point-spread function (PSF|.vj), where .r is a two-dimensional spatial coo rdinate. MTF(u) is the square root of the m odulus of the Fouriertransform (FT) of the double-pass image, with a two-dimensional spatial frequency coordinate. The one-dimensional modulation transfer function(MTF) was computed averaging the two-dimensional MTF across all directions (radial average).proved features adapted to routine measurement of ocular MTFin naive subjects. Additional details on the basis, operation, andlimits of the double-pass method are found in several recentarticles." '14 The technique is based on recording images of apoint source projected on the retina after retinal reflection anddouble pass through the ocular media. From these images(double-pass images) the retinal image of the point source, thepoint-spread function (PSF), and ocular MTF are calculated. Aschematic diagram of the apparatus is shown in Figure 1. Thelight source is a 5-mW green (543-nm) He-Ne laser (05 LGR193; Melles Griot, Irvine, CA). This wavelength is approxi-mately centered in the visible spectrum and provides the bestdouble-pass image quality .'s A neutral-density fi lter (NDF) anda linear polarizer (Pol) are placed in front of the laser. Thebeam is spatially filtered (m icroscope ob jective [M] 10X and a25-/im pinhole [P]) and collimated by a 100-mm lens L,. Theartificial entrance pupil (AP,) is conjugated w ith the eye pupilplane. After reflecting in the pellicle beam splitter (BS), thebeam passes the 100-mm lenses L2 and I.v and the eye formsthe image of the point source (O) on the retina (O'). Lenses L,,L2, and L, are achromatic doublets with antireflection coatingsfor the visible spectrum. A second artificial pupil (AP2), placedafter the pellicle, is also conjugated with the eye's pupil planeand acts as the effective exit pupil (when the natural pupil ofthe eye is dilated). A camera objective with 100-mm focallength forms the double-pass retinal image (O") on a slow-scan,scientific-grade, cooled charge-coupled device (CCD) camera(Compuscope CCD 800; Santa Barbara, CA) that integrates thelight coming back from the retina during the exposure time.The retina and the CCD camera's plane are conjugated with amagnification of 6.06. The fieldof view for the 256 X 256-pixelimages is 79.3 minutes of arc, with a sampling rate in thedouble-pass images of 0.31 minutes of arc. This corresponds toa resolution in the Fourier domain of 0.75 cycles/deg. Thisdouble-pass apparatus was specifically designed for this studyin a two-level setup (the shaded area in Fig. 1 shows theelements placed in the upper level of the setup) with mirrorsto direct the beam appropriately in the illumination and re-cording paths (not included for the sake of clarity in Fig. 1).The subject's head was placed on a chin rest mounted on 2-D

positioners allowing the centering of the natural pupil in rela-tion to the artificial pupils.Experimental ProcedureThe subject, positioned on the chin rest with the eye alignedby the experimenter using the control system described later,was instructed to fixate on the point source, convenientlyattenuated by an additional neutral-density filter (not includedin Fig. 1). During the exposure, this neutral-density filter wasremoved, and th e double-pass image was captured by the CCDcamera. For each condition of pupil size or focus, three double-pass retinal images and one background image (with a lighttrap in place of the eye) were recorded. The duration of eachexposu re w as 4 secon ds. Each double-pass image was digitizedwith 256 X 256 pixels and 14 bits/pixel. The exposu re time of4 seconds was chosen to be long enough to break the coher-ence of the incident light and to blur the speck le,1" '^ but shortenough to avoid eye blinks or subject discomfort.The ocular image quality largely depends on three factorsthat must be accurately controlled during the experiments:pupil size, relative centering of the measuring beam and thedilated natural pupil, and the subject's refractive state. In everysubject, double-pass images were collected for three artificialpupil diameters (3 mm, 4 mm, and 6 mm) in thefirst(apertureAP,) and second passes (aperture AP2). The pupil was dilatedand the accommodation paralyzed by instilling two drops of1% cyclopentholate, allowing 5 minutes between drops, andwaiting 30 minutes before beginning the measurements. Insome of the subjects of group C, a drop of 2.5% phenylephrinewas also instilled to dilate the pupil up to 6 mm in diameter.

A subsystem in the setup was used to monitor pupilcentering in relation to the measuring beam. It consisted of aninfrared light-emitting diode (LED) to illuminate the anterioreye, and a CCD video camera (XC-75; Sony, Tokyo, Japan) withthe pro tective infrared filter removed, which formed the imageof the pupil after reflection in a dichroic mirror. The positionof the pupil relative to the m easuring beam is controlled by theexperimenter in a TV monitor. As a practical tool, the cornealreflex was used to follow th e eye movem ents while the double-pass image was captured. Double-pass images collected with


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206 Guirao et al.A F B )


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JOVS, January 1999, Vol. 40, No. 1exposures of 4 seconds" duration obtained on e after theother, clearly exceeding the actual procedure performed.Calculations from Double-Pass ImagesAll the double-pass images were first stored in a personalcomputer and transferred later to a UNIX computer worksta-tion, where the whole image-processing analysis to calculatethe Mil7 was performed. The final double-pass image was theresult of averaging three 4-second exposure images and sub-tracting the background image. The double-pass image was theautocorrelation of the retinal image (PSF),'~ and the MTF wasthe square root of the modulus of the Fourier transform of theaverage double-pass image. Because a low-light-level pedestalappeared in the double-pass images, an appropriate DC peakcorrection in the MTF had to be performed (see reference 13for additional details on this analysis). From the two-dimen-sional MTFs, one-dimensional Mil's were obtained by averag-ing across all directions (example in Fig. 2). The Strehl ratio16characterized optical performance. The ratio is defined as thequotient between the intensity peak in the systems F\SF andthe diffraction-limited PSF, or alternatively, as the quotientbetween the volumes under the 2-D MTFs of the consideredsystem and the diffraction-limited system. As an optical qualityindex, we computed a simplified Strehl parameter: the quo-tient between the area under the measured I-I.) MTF and thearea under the diffraction-limited MTF for the same pupil di-ameter.

RE SUL T SA sample of double-pass images recorded with unequal en-trance (1.5-mm) and exit (4-nim) pupil diameters in the appa-ratus in six young subjects of group A is shown in Figure 3-These images depict the intersubject variability in the retinalimage. Although the average spread of every image is approx-imately similar within the same age range, there are substantialdifferences in the shape of the images, indicating the variabilityof the aberrations among subjects.

The MTFs for every subject of group A for equal 4-mmentrance and exit pupil diameters are shown in Figure 4A, andthe average MTF for that group and error bars representing theSD are shown in Figure 4B. These figures show the variabilityin MTFs among subjects within a single group, in this case theyounger subjects. As an example, with a spatial frequency of 10cycles/cleg the mean modulation is approximately 0.5 0.07(SD). Figure 5 shows the MTFs obtained in every subject wh oparticipated in the study (groups A, B, and C) for the threepupil diameters used. These figures show the actual distribu-tion of MTFs in all the subjects.

The average double-pass images for every age group andpupil diameter are shown in Figure 6. As a result of theaveraging process, these images tended to a radially symmetricshape. A direct comparison of the spread of these double-passimages showed a net decrease of the optical performance withage for every pupil diameter. The relative increase in thespread of the double-pass images was larger with the 3-mmpupil diameter. Within the same age group, the double-passimages became more extended as the pupil diameter in-creased, with the relative increase being smaller in the groupof older subjects. In Figure 7 the average MTFs for even' agegroup and pupil diameter are shown: 3 mm (Fig. 7A), 4 mm

Optics of the Aging Eye 207Group A (4 mm)

A 10 20 30 40 50 60Spatial Frequency (c/deg)

Group A (4 mm) Mean

0 -B 10 20 30 40 50Spatial Frequency (c/deg)

I'IGUKI: 4. (A) Modulation transfer functions (MTFs) for even- subjecttested in group A with a 4-mm pupil diameter. (B) Mean MTF for groupA with 4-mm pupil diameter, with error bars representing the SD.c/deg. cycles per degree.

(Fig. 7B), and 6 mm (Fig. 7C). In Figure 8 the same results areshown but with each panel containing the average MTFs forthe three pupil diameters studied in each age group: A (Fig.8A), B (Fig. 8B), and C (Fig. 8C). These results show thewell-known reduction of the MTF with larger pupil diametersin every group and also a consistent decline of the average MTFin the older groups compared with the MTFs in the youngergroup.

We performed a curve fit to the average MTFs using atwo-parameter analytical expression similar to that proposedby Artal and Navarro1' and provided by:

M(u) = ^ [3 exp(-M/) + cxp(-u/b)] CO

where M(ju) is the one-dimensional MTF, u is the spatial fre-quency (in cycles per degree), and a and b are the twoparameters (in cycles pe r degree). This sum of two exponentialfunctions provides a good fit to the experimental MTF data.


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208 Guirao et al.

3 m m 4 m m1OVS, January 1999, Vol. 40, No. 1

6 mm

C

0 10 20 30 40 50 60 0 10 20 30 40 50 60 0 10 20 30 40 50 60cycles/degree cycles/degree cycles/degreeFuiUKi; 5. Mocliilaiion transfe r functio ns (MTFs) for every subje ct te sted in the thre e age gro ups (A, U, C) with th ree p upil diam eters : 3 mm,mm, and 6 mm.

Parameter a is an approximate estimate of the width at one-third heigh t in the MTF and con seq uen tly can be regarde d as aglobal index of image quality, similar to the Sirehl ratio. Param-eter b in the second weighted exponential is mainly used toimpro ve th e quality of the fit at mid to high spatial fre quencies .It has no direct meaning, in contrast with parameters. In fact,a single-parameter function (for instance, only an exponentialfunction) could also be used to fit the MTFs, although with alower-quality fit. Each MTF for every subject and cond ition wasfitted using equatio n 1. In Table 1 the average values and t heSD of the param eters a an d b are shown for even' MTF in eachof the three age group s and pupil diam eters. Table 1 andequa tion 1 allow easy calculation of the m ean MTF for eachcondition and range of variability. In addition, the values of theSD, especially in parameter , gives an indication of the signif-icance in the differences between age groups and pupil sizes.Based on this parameter, the differences in MTFs among agegroups were statistically significant with a confidence level of99-9%.

The Strehl ratio was computed from the MTFs, as de-scribed in the Methods section, for every subject and pupil

diameter. In Figure 9A, the Strehl ratio as a function of everysubject's age is shown for 3-mm, 4-mm, and 6-mm pupil diam-eters, together with a linear regression to the Strehl ratio valuesfor every subject as a function of age. It shows an approxi-mately linear decline in average from ages 20 to 70 (the slopesand regression coefficients for 3-mm, 4-mm, and 6-mm pupild i ame te r s a re -0 .0046 , -0 .0032 , - 0 . 0 0 1 ; 0.8, 0.83, 0.62,respectively). The average values of Strehl ratio and error barscorresp onding to the SI) for each group and pupil diameter areshown in Figure 9B. These results further show the decline ofthe average retinal image quality with age. The differences inthe average Strehl ratio among age groups are statisticallysignificant within a confidence level of 99.9% (ex cep ting dif-ferences betwee n gr oup A and B with a 6-mm pupil diam eter,which yield a confidence level of 95%).

DISCUSSIONWe performed a detailed study of the average retinal imagequality, using a modified version of the double-pass apparatus,


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IOVS, January 1999, Vol. 40, No. 15 mm 4 mm

Optics of the Aging Eye 2096 mm

Group A

Group B

Group C

FIGURE 6. Average of the double-pass images recorded in the 20 subjects of each group (A, B, C) witheach diameter pupil (3 mm, 4 mm, and 6 mm).

in thre e groups of healthy subjects of different ages. Theapparatus permitted us to obtain the ocular MTF under condi-tions in which focus, pupil size, and centering were controlled.The intersubject variability of the retinal image qualitywithin each age group was studied first. After defocus andastigmatism were carefully corrected in every subject, substan-tial asymmetrical aberrations were found in the fovea, as pre-viously reported.'31 8" 21 These asymmetrical aberrations var-ied greatly from subject to subject. The range of variability inthe overall image quality of MTFs within an age group was alsosignificant, although smaller than that found in other stud-ies ,1 9 2 1 perhaps because of our careful correction of defocusand astigmatism. The intersubject variability was similar in thethree age groups, with the largest variability occurring in theyounger subjects with a 3-mm pupil diameter (note the largestvalue of SD for parameter a for that condition in Table 1). Thisvariability is mainly attributable to the actual differences inocular optics in different subjects. How ever, several sources ofpossible errors in the procedure could have contributed to anincrease in variability: uncorrected amounts of defocus andastigmatism, errors in pupil centering, abnormal eye move-ments during double-pass image recording, or small changes inaccommodation that occur even in the presence of cyctople-gia. These factors were carefully controlled during the collec-tion of the double-pass images, and their impact was thought tobe limited. We also evaluated the variability in the measure-ments in a subject for a given condition. As an example, the SDto estimate the Strehl ratio in a single subject was approxi-

mately 5% of the average Strehl ratio value. For comparison, inthe case in which we found one of the largest variabilities(group A with 3-mm pupil diameter), the mean Strehl ratio was0.4 with an SD of 18%.The average MTFs for the age groups showed a systematicdecline in optical performance with age. This result was ob-tained with ever>' pupil diameter but was more pronouncedwith small and mid-sized pupil diameters. The differences inocular optical performance among age groups were statisticallysignificant, with larger reductions in image quality betweenage groups than those found among subjects of the same agegroup. These results showed an increase in optical aberrationsthat caused a deterioration of retinal image with age. We foundno differences in retinal image quality with age as a function ofthe sex of the subjects.Tn the present study, ocular optical performance declinedapproximately linearly throughout adulthood (Fig. 9A). Otherparameters in the eye also exhibit a linear variation with agefor instance, the amplitude of accommodation' or the thick-ness of the lens.22 Incidentally, the Strehl ratio data, whenregressed, reaches zero at approximately 120 years of age, incommon with other properties of the eye (expect for accom-modation).23 2'' However, this linear reduction in overall opti-cal performance differs from the idea that spatial vision func-tions remain stable up to 50 to 60 years of age and thenundergo a rapid decline,

25Fitting the average MTFs with a simple two-parameterfunction (Eq. 1)was a convenient way to summarize the results


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210 Guiruo et al. IOVS, January 1999, Vol. 40 , No. 1

Pupil diameter: 3 mm

0 10 20 30 40 50 60Spatial Frequency (c/deg)

LL 0.61

Pupil diameter: 4 mm

B 10 20 30 40 50 60Spatial Frequency (c/deg)Pupil diameter: 6 mm

o- 10 20 30 40 50 60Spatial Frequency (c/deg)FIC.UKI; 7. Average modulation transfer functions (M il's) for eachgroup: A (solid line). I) (short dashed line), and C (long dashed line).ai three pupil diameters: (A) 3 mm, (B) 4 mm, (C) 6 mm. c/deg, cyclesper degree.

and show the degree of significance of the differences amongage groups. It also allows incorporation of these results in anyfurther study in which average optical performance as a func-tion of age is required . In particular, these results could be usedas a reference in studies of aging and visual performance or asnew standards for different ophthalmic optics applications inwhich age is considered a relevant factor.Although the reduction in the MTFs obtained from double-pass images as a function of age seemed to be mostly caused by

an increase in optical aberrations, it is important to determinewhether some factor other than aberrations could have af-fected the double-pass measurements with age. One of thosefactors is intraocular scattering, which increases with age.26Scattering produces an approximately uniform halo in theretinal image. Although the relative intensity between the peakin the image and the background was lower in the oldersubjects, we subtracted a constant value from the double-passimage before computing the MTF. Optical aberrations andintraocular scattering affect the retinal image under normal

r -

1- Group A (20-30 years old)3 mm4 mm

10 20 30 40 50 60Spatial Frequency (c/deg)Group B (40-50 years old)

0.8

B 20 30 40 50 60Spatial Frequency (c/deg)Group C (60-70 years old)

3 mm4 mm

- - - - - 6 mm

40 50 60Spatial Frequency (c/deg)FIGURE 8. Average modulation transfer functions (MTFs) plotted to-gether for the same group for each pupil diameter: 3 mm (solid line),A mm (short dashed line), and 6 mm (long dashed line). (A) Group A;(B) group 1$; (C) group C.


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10VS, January 1999, Vol. 40, No. I Optics of the Aging Eye 21 1TABLE 1. Average Values and Standard Deviation of the Two Parameters in the Analytical Expression of the MTF(Eq. 1) for the Three Age Groups and Pupil Diameters

PupilDiameter

Group A Group B Group Cb b

3 mm4 mm6 mm16.12 3.1610.46 2.305.81 1.87

17.50 2.4227.26 1.7621.68 3.7210.52 1.747.15 1.604.72 0.84

21.30 2.3623.58 4.151931 4.655.89 2.104.48 1.123.34 0.77

1926 4.0016.01 4.8614.14 4.67Values are expressed in cycles per degree and are derived using liquation I, with u representing spatial frequency.MTF, modu lation transfer function.

conditions. However, we did not include the effect of scatter-ing in our MTFs because of the procedure we used to computeit. Other investigators have attempted to incorporate the effectof scattering on the MTF by normalizing this function, not to 1,

g03

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6 7(mm)i: 9. (A) Strehl ratio as a funclion of eve n' sub ject 's age at the

three pupil diameters: 3 mm (solid circles'), 4 mm (open squares'), an d6 mm (solid triangles). Lines are the best linear fit. (B) Average Strehlratios for each group and pupil diameter, with error bars representingthe SD.

but to a lower num ber, depending on the level of the scatteringhalo.27 We preferred to follow the traditional approach ofanalyzing aberrations and stray light separately, discountingmost of the effect of scattering in our MTF results by subtrac-tion of the constant value. It should be noted that it is notpossible to separate the exact contribution of aberrations, inparticular higher order aberrations, from the contribution ofscattering. However, in the double-pass retinal images (Fig. 6)the increase in size near the image peak seems mainly to becaused by aberrations of a larger magnitude than by scatter-ing's producing an approximately uniform background. In ad-dition, higher intraocular scattering and reduced transmissionthrough the ocular media produced dimmer double-pass im-ages in the older subjects, for which we compensated in ourexperiment by selecting a different value of neutral-densityfilter for different age groups to keep approximately constan tthe average intensity in the double-pass images across the agegroups.If the properties in the retinal reflection change with age,the double-pass results could be affected differently. Severalstudies have shown that retinal reflection seems to have arelatively unimportant effect on the double-pass estimates ofimage quality,2" particularly in green light.15 These studieswere performed in young subjects, and in consequence, th erecould be additional effects of retinal reflection in the double-pass measurements in older subjects, degrading the MTF. How-ever, other studies in which retinal reflection characteristicswhere analyzed as a funclion of age did not show a significantvariationfor instance, in the retinal reflection directionality29and the Stiles-Crawford effect/" This suggests that the effectof retinal reflection on double-pass measurements is approxi-mately the same at all ages.

The ocular MTF results presented in this study reflectthe overall degradation in optical performance as a functionof age. Additional experiments are required to understandthe underlying causes that produce the reduction in theretinal image quality with age. However, it is useful todiscuss briefly how different changes occurring in the eyecan produce an age-related increment in the amount ofaberrations. The structural changes of the lens with agesuggest an increase of aberrations. Glasser and Campbell31showed that the spherical aberration of isolated crystallinelenses increases with age, and in principle, this could ex-plain an overall reduction of image quality. However thespherical aberration of the lens can be compensated, in part,by corneal aberrations,52 and therefore an increase of aber-rations in the isolated lens does not necessarily imply a


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212 Guirao ct al. IOVS, January 1999, Vol. 40, No. 11

U. 0.8H5 0.6-:

0.4-I0 .2 !

Group A (6.5 mm)Group B (5.5 mm)Group C (4.5 mm)

0 10 20 30 40 50 60Spatial Frequency (c/deg)10. Calculated modulation transfer functions (MIT's) using

Equation I for the three age groups: A (solid line), B (short dashedline), and C (long dashed line) for the average natural pupil diameterof each age at low lum inance levels: 6.5 mm in group A. 55 mm ingro up B, and 4.5 mm in group C.

reduction in the overall MTF. In fact, what is important forfinal retinal image quality is the balance among the aberra-tions of cornea and lens, and with age that balance could bedegraded. The results of MTFs previously measured in oldpatients with monofocal intraocular lens implants*3 maysupport this hypothesis. Those MTFs were similar to thoseobtained in older subjects, even though the optical qualityof the isolated polymethylmethacrylate intraocular lenses*'assessed by theoretical calculations, or at the optical bench,were practically diffraction limited and probably largelyexceed that of the lens. This suggests that an uncorrectedbalance of aberrations may occur after intraocular lens im-plantation . A similar situation, a decoup ling of conical andlenticular aberrations, may also occur in the aging eye.Another two alternatives may explain the reduction in op-tical performance with age in healthy subjects: an averageincrease of corneal aberrations with age and a significantincrease of higher order aberrations (related to intraocularscattering) with age.The reduction in the eye's optical performance with agecould account for a substantial part of the reported decline ofthe CSF with age,* in agreement with the results of other

experiments that found the postoptical CSF. measured by pro-jecting interference fringes on the retina, to be similar inyounger and older subjects.5 Although it is difficult to deter-mine exactly the fraction of the reduction in CSF caused byincreases in optical aberrations, the results in this study indi-cate that it is an important part, on average, under conditionsof optimum focus and fixed pupil diameter.It is important to point out that the average reduction wefound in MTF as a function of age was obtained with artificialpupils. However, in normal viewing with a given luminance,the values of the pupil diameter are on average lower in theolder subjects (senile miosis), meaning that the effect of thepupil size would tend to diminish the differences in the overallimage quality within age groups. This would be especiallyimportant at medium and low luminance levels. As an example,we computed the MTFs using equation 1, by interpolating th evalues in Table I for pupil diameters representing the average

for subjects in the three age groups*5 at low luminance levels.In Figure 10, the resultant MTFs in group A (6.5-mm pupildiameter), group B (55-mm pupil diameter), and group C(4.5-mm pupil diameter) are show n. When the effect of naturalpupil diameter was considered, the differences among agegroups were reduced. We can confirm that the average MTF isapproximately constant in all age groups at: low luminancewith natural pupil. In addition, under normal viewing condi-tions, small refractive errors could also reduce the relativedifferences in MTFs across age groups , because a smaller re-duction is expected in image quality with defocus in systemswith a reduced overall performance. That is to say, possiblesmall refractive errors should reduce the relative MTF by alarger fraction in a younger subject (with better image qualityat best focus) than in an older subject (with worse imagequality). These two factors, senile miosis and a better toleranceto defocus in older subjects, indicate that the differences inimage quality among younger and older subjects found undercontrolled laboratory conditions of lixed pupil diameter andbest focus would become much smaller under normal viewingconditions, especially at low luminances.AcknowledgmentsThe authors thank Daniel Green, University of Michigan, for his criticalreading of the manus cript: Robert A. Wcalc, King's College London , forhis comments on the manuscript; liloy Villegas and Esther Berrio fortheir assistance in parts of the experiments; Ignacio lglcsias for his helpwith software development; and all the subjects for their cooperationin participating in (his study.

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average optical performance of the human eye as a function of age in a normal population

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