minimum resolution specification of intraocular lens implantsusing the modulation transfer function

Minimum resolution specificationof intraocular lens implantsusing the modulation transfer function

Laurence W. Grossman and Robert W. Faaland

We investigated the use of modulation transfer function (MTF) measurements to provide a standard testof minimum optical quality of intraocular lenses. We used a water cell with plane entrance and exitwindows. This geometry is independent of lens material but relatively simple to implement. Weinvestigated the choice of aperture stop, and 3.0 mm was deemed a suitable choice of stop diameter.Minimum acceptable performance must be specified if this technique is to be adopted as a standardmethod. The MTF of an ideal lens defocused 1/2 wave is suggested as a possible reference. Strehlratios, although desirable because they can be measured directly without determining MTF's, were foundto be unsuitable. These ratios tend to emphasize the high-frequency response, and the observed ratiosare typically too low to provide assurance that the low-frequency response is as high as desired. MTFintegrals or contrast at spatial frequencies of particular interest were found to be useful benchmarks ofacceptable optical quality.

Key words: Intraocular lens, intraocular lens testing, optical quality, image quality, resolution,modulation transfer function.

Introduction

Semiquantitative test methods have traditionally beenused to specify the minimum acceptable resolution ofintraocular lenses (IOL's).1 This testing involvesevaluation of the finest bar pattern spacing of animage generated using the IOL. For the sake ofsimplicity, this test has been done in air rather thanin the aqueous environment of the IOL's intendeduse. This testing has permitted the industry toproduce a remarkably reliable product.2 3 However,this type of testing is not without problems.- 6

First, since the test looks only at a limiting resolu-tion, it leaves open the possibility of a lens with anacceptable limiting resolution but overall poor con-trast. A lens with a high degree of flare would be anexample of such a situation. The need for tests thatlook at the overall bandpass characteristics of the lenshas long been recognized in optics.

Second, although in the past all lenses were madeof a single material, poly(methyl methacrylate)

The authors are with the Center for Devices and RadiologicalHealth, Food and Drug Administration, HFZ-134, Rockville, Mary-land 20857.

Received 18 August 19920003-6935/93/193497-07$06.00/0.© 1993 Optical Society of America.

(PMMA), IOL's made from silicone are commerciallyavailable today and water-containing gel materialsare under study. These newer materials have indi-ces of refraction closer to that of the surrounding insitu aqueous medium. Therefore higher curvaturesmust be used to achieve the same refractive power.These higher curvatures result in much more spheri-cal aberration when tested in isolation in air. Also,for water-containing gel lenses the state of hydrationis difficult to control during testing in air.

Modulation transfer function (MTF) measure-ments have been widely used in the optics industry asa means of better characterizing image quality of animaging system. This functional response can bemeasured directly or it can be inferred from othermeasures such as wave-front interferometry. 5 MTFperformance can be calculated through ray-tracemethods. Therefore in principle one can relate mea-sured results to that predicted for a perfectly madelens.

A natural alternative to testing an IOL in isolationwould be to test the lens in a model eye.6 This is atechnically demanding test. One must be carefulthat the lens or lens system serving as the corneaprovides the desired refraction without introducinginterfering aberrations. Additionally, as IOL's aremanufactured in a range of powers, there is no single

1 July 1993 / Vol. 32, No. 19 / APPLIED OPTICS 3497

choice of corneal lens refraction that would mimic thein situ geometry of all IOL's.

This work examines the feasibility of using a lessdemanding IOL MTF test geometry consisting of awater cell with plane entrance and exit windows.This geometry can accommodate any material thatmight be compatible with the intended use of the lensbut avoids the complications associated with thequality and placement of the corneal lens.

The vast majority of IOL's implanted are madefrom PMMA having in situ powers in the range from15 to 25 D and are either biconvex or planoconvex inshape. However, there exists a need to provide arange of powers that runs from at least 5 to 35 D.Meniscus lenses are also available to provide a spacebetween the lens and the posterior capsule.5 7 Thismay reduce the likelihood of pitting during Nd:YAGlaser treatment for posterior capsule opacification.Flexible lenses such as silicone have been introducedin order to reduce the incision size. A successful testprotocol must accommodate these variations.

We examined the MTF response of IOL's in a watercell to provide information on measurement repeat-ability, as well as trends that are due to lens power,lens shape, or choice of material. We also examinedbenchmarks that might be incorporated into a stan-dard requirement for minimum performance.

Method

IOL's were tested in groups according to powers andstyles. Three groups of planoconvex lenses weretested: 10, 20, and 30 D. PMMA meniscus, PMMAbiconvex, and silicone biconvex lenses, all nominally20 D, were also tested. Each lens group comprised aminimum of six lenses. In order to minimize poten-tial artifacts that are due to the fabrication technique,each lens in a group was obtained from a differentmanufacturer except when limited by availability.Each of the tested lenses passed industry standardtests for optical quality. The majority of the testedlenses were obtained as part of an earlier study of theoptical quality of IOL's3 and were obtained by U.S.Food and Drug Administration inspectors from ran-dom samples of stocks released for shipment.

The six meniscus IOL's came from five manufactur-ers and the six silicone IOL's came from threemanufacturers. The ratio of front surface curvatureto rear surface curvature for the meniscus lensesranged from 1.5 to 2. The PMMA biconvex IOL'sranged in shape from nearly equibiconvex to nearlyplanoconvex.

Measurement reproducibility was investigated bymeasuring an additional series of eight IOL's a totalof seven times each. Each measurement involvedmounting and dismounting the lens from the watercell. These lenses ranged in in situ power from 14 to26D.

IOL's were tested in a water cell with optically flatentrance and exit windows. The entrance and exitwindows were located approximately 3 mm in front ofand 10 mm behind the IOL, respectively. In this cell

a 20-D IOL has an effective focal length of approxi-mately 50 mm.

IOL optic diameters are typically approximately 6mm. Resolution testing is typically done with acentered 3-mm aperture.' Pupil sizes following im-planatation vary from individual to individual andwith lighting conditions. Values of as much as 5 mmhave been reported.8 9 In this investigation two aper-tures were examined, the traditional value of 3 mm,and, in part because of a desire to test more of theoptical surface, a larger value of 4.5 mm.10 Theaperture stop was immediately in front of the IOL.Measurements were conducted with the most convexside toward the incident light to minimize the effectsof spherical aberration on the final result.

Lenses were tested on a commercially availableMTF test bench. This system images a one-dimen-sional slit at infinite conjugation through the IOLwater cell. A 10x objective relays the resultingspread function image to a linear diode array detector.The measured signal is Fourier transformed withcorrections for dark current and slit width to yield theMTF.

Point-by-point comparisons of measured and tar-get MTF's may place high demands on the accuracy ofthe measurement. The differences between mea-sured and allowed values, particularly at the lowestfrequencies of interest, may become small and mayexceed the measurement system's ability to accu-rately distinguish. Other ways of using the MTFresults were therefore investigated.

Three benchmarks of optical quality were gener-ated from the MTF measurements. These wereStrehl ratio, the area under the MTF curve, and theMTF response (contrast) at 30 cycles/deg. The Strehlratio is the maximum intensity of a point-spreadfunction referenced to the maximum intensity of adiffraction-limited equivalent system.1"12 The Strehlratios were estimated by assuming radial symmetryand summing the volume of the discrete conicalsections defined by linear interpolation of the MTFcurve. The MTF integral was calculated by the

0.8

U.1-

0.6

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0

0 20 40 60 80 100Spatial Frequency (cycles per degree)

Fig. 1. Seven MTF measurements repeated on the same IOL.The diffraction-limited response of an ideal lens is also shown as adashed line.

3498 APPLIED OPTICS / Vol. 32, No. 19 / 1 July 1993

Table 1. Summary of Repeatability Measurements

Relative RelativePower Strehl MTF Contrastin Situ Number of Ratio Area (30 cycles/deg)

Lens (D) Observations % s.d. % s.d. % s.d.

C1 15.7 8 2.5 2.1 2.4C2 15.7 8 2.9 2.4 3.0C3 14.4 7 3.3 3.1 4.3C4 16.2 7 1.8 1.5 1.9C5 24.6 7 5.8 4.9 10.6C6 21.2 7 3.9 3.1 2.5C7 24.4 7 5.5 3.7 3.9C8 25.5 7 9.7 5.7 6.7

Mean 4.4 3.3 3.3

trapezoidal rule. The MTF integral and the relativecontrast values were both normalized to that ex-pected for a diffraction-limited lens.

Results

Seven individual measurements of a 25 D IOL in thewater cell are shown in Fig. 1. This result is typicalof those observed for the entire group of eight lenses

U.I-

0.8

0.6

0.4

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0

PMMA, 10 D, planoconvex, 3.0 mm aperture

lens a--*-lens b

lens c\-. -lens d

lens elens f

.\ > x\\\ . -- lens g-.- e.......... .N. >. - Rayleigh limit

...... .

, _.................N

. I.

used for these repeatability tests. Table 1 summa-rizes these repeatability measurements. Standarddeviations (S.d.'s) are listed for each of the threebenchmarks calculated on each trial, that is, Strehlratio, MTF integral, and contrast at 30 cycles/deg.The mean standard deviation over the entire group ofeight lenses was found to be less than 5% for each ofthe three benchmarks.

MTF measurements for 10-, 20-, and 30-D planocon-vex PMMA IOL's are shown in Figs. 24. Eachfigure contains the individual MTF measurementsfor both 3.0- and 4.5-mm apertures. The diffraction-limited MTF of an ideal lens of identical wavelengthand aperture is also shown and identified as theRayleigh limit in the figure legends.

When measured with a 3-mm aperture, each of theplanoconvex lenses exhibited a diffraction-limited cut-off frequency, in agreement with Holladay et al.13The shapes of the MTF curves were more variablethan had been observed during the repeatabilitytests. At 10 and 20 D the better results wereessentially diffraction limited.

Increasing the refractive power or increasing theaperture stop to 4.5 mm significantly reduced theobserved MTF's. As this effect was observed for all

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0.6U.

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- lens a-lens b.-''-'\C ' ' '''''' l'''' . '' ....... ....... ..........-......-'-- lens c- lens d

; . ....... -------------- ------ ........................ -lens e

lens f. .t~> .\ - Rayleigh limit

s~~~ Ne. . . . . . ........ ............... . .............. .............. . ...............

0 20 40 60 80Spatial Frequency (cycles per degree)

0 20Spatial

40 60 80 100Frequency (cycles per degree)

0.8

0.6

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Fig.2. MTF measurements of seven PMMAplanoconvex IOL's of10 diopter nominal refractive power in situ using 3.0- and 4.5-mmapertures.

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0



Fig. 3. MTF measurements of six PMMA planoconvex IOL's of20-D nominal refractive power in situ using 3.0- and 4.5-mmapertures.


100

PMMA, 20 D, Bconvex, 3.0 mm aperture

0.8

0.6IL

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0

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0


100


Fig. 4. MTF measurements of eight PMMA planoconvex IOL's of30-D nominal refractive power in situ using 3.0- and 4.5-mmapertures. An additional MTF, labeled lens g, is also shown.

This lens is actually meniscus in shape.

lenses, it is assumed to be attributable to sphericalaberration inherent to the lens shape, not to anymanufacturing defect.

One lens in the 30-D group (Fig. 4) had an MTFthat was significantly worse than the others in thatgroup. This lens is actually a meniscus shape, notplanoconvex. It was the only meniscus lens obtainedin this power range and is shown for convenience.As it was the only lens of its kind, no further analysiswas performed on this curve. The results for thislens are not included in the averages for the 30-Dplanoconvex group.

PMMA biconvex, meniscus, and silicone biconvexMTF results at 20 D (Figs. 5-7) were largely consis-tent within each group but with varying degrees ofdeparture from a diffraction-limited response fromgroup to group. With the one exception mentionedin the previous paragraph, lenses measured with a3-mm aperture exhibited a diffraction-limited cutofffrequency, in agreement with previous reports.'3 1

4

The PMMA meniscus shape and the silicone lensmaterial had the least ideal responses, consistentwith the greater curvatures of their surfaces.

Table 2 lists means and standard deviations of the

0.8

0.6U.I.

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0.8

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0.4

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0

100


Fig. 5. MTF measurements of six PMMA biconvex IOL's of 20-D

nominal refractive power in situ using 3.0- and 4.5-mm apertures.

three benchmarks of quality calculated for each of thepower and shape groups. The small number oflenses in each power and shape group limit thestatistical power of these results, but a typical valuefor a standard deviation of any of the benchmarkswould be of the order of 15%.

Discussion

Calculated MTF's for an ideal lens with 3-mm aper-ture, green light, and various amounts of defocus areshown in Fig. 8.15 The units of defocus are wave-lengths of optical path difference. Lord Rayleigh'soriginal resolution limit compares well with a 1/4wave defocus error in a diffraction-limited lens.This amount of defocus is not normally considered bya human observer to be significant." A minimumacceptable MTF based upon this amount of aberra-tion would be unnecessarily demanding.

Increasing the defocus to 3/4 wave produces anMTF with a cutoff frequency slightly less than 30cycles/deg. Normal visual acuity requires resolu-tion to 30 cycles/deg. Most patients have normalcorrected visual acuity following cataract surgery.It is not unusual for a pseudophakic person to havebetter than average acuity. In order to preserve thispossibility a resolution requirement better than 3/4


Silicone, 20 D, Biconvex, 3.0 mm aperture

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100

Fig. 6. MTF measurements of six PMMA meniscus IOL's of 20-Dnominal refractive power in situ using 3.0- and 4.5-mm apertures.

wave is required; therefore 1/2 wave seems to be anarbitrary but reasonable target MTF of minimumacceptability. Out to 40 cycles/deg, this targetMTF is similar to the results previously reported forthe human eye with a 2.0-mm pupil.'6"17

Strehl ratios and MTF integrals do not directlyspecify the contrast of the frequencies of interest.However, if held to sufficiently high levels, theyprovide a reasonable assurance that adequate con-trast will be achieved. The benchmark of contrast at30 cycles/deg was picked, as this is the frequencylimit required for normal 20/20 visual acuity.

An advantage of Strehl ratios is that they can bedetermined directly without the need for MTF mea-surement. Today's video technology makes an inex-pensive fast measurement a real possibility, as theStrehl ratio is directly related to focal spot peakintensity.' 2

The Strehl ratio, the MTF integral, and the relativecontrast at 30 cycles/deg for the 1/2 wave defocusedideal lens with the above assumptions are approxi-mately 0.30, 0.55, and 0.34, respectively. Referringto the summary of results in Table 2, these values aresomewhat less demanding than 2 standard deviationsbelow the mean for all the 3-mm aperture tableentries.

Silicone, 20 D, Bconvex, 4.5 mm aperture

20 40 60 80Spatial Frequency (cycles per degree)

100

Fig. 7. MTF measurements of six silicone biconvex IOL's of 20-Dnominal refractive power in situ using 3.0- and 4.5-mm apertures.

The 1/2 wave defocus target MTF is a more difficultrequirement to meet when the aperture is increasedto 4.5 mm. The Strehl ratio and MTF integraltarget values would not change. The relative con-trast target at 30 cycles/deg increases to 0.6.Most of the measured lenses of 20 D or more wouldnot meet any of the benchmarks for this target MTF.

_- ]a\ f . - -RAYLEIGH0.8 -t____ _; - 1/4 WAVE0.8

1/2 WAVE--- 3/4 WAVE

0.6 - ' \ Ax \ - -1 WAVEU.

2-

0.4

0.2

0


Fig. 8. Calculated MTF's for an ideal lens with a 3-mm apertureand 550-nm light for various degrees of defocus. Data are takenfrom the tables of Levi and Austing.15


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PMMA, 20 D, Meniscus, 4.5 mm aperture


Table 2. Summary of Strehl Ratio, MTF Area, and Relative Contrast at 30 Cycles/deg

Strehl Ratio MTF Area Integral 30-cycle/deg ContrastSample

Size Mean s.d. Mean s.d. Mean s.d.

3.0-mm aperturePlanoconvex, 10 D 7 0.83 0.11 0.86 0.08 0.81 0.12Planoconvex, 20 D 6 0.65 0.12 0.76 0.09 0.69 0.11Planoconvex, 30 D 8 0.60 0.07 0.70 0.06 0.61 0.08

Biconvex, 20 D 6 0.83 0.06 0.89 0.05 0.86 0.07Meniscus, 20 D 6 0.67 0.08 0.76 0.09 0.68 0.10Silicone, 20 D 6 0.74 0.13 0.80 0.10 0.71 0.12

4.5-mm aperturePlanoconvex, 10 D 7 0.55 0.16 0.70 0.12 0.68 0.15Planoconvex, 20 D 6 0.32 0.04 0.45 0.04 0.41 0.08Planoconvex, 30 D 8 0.18 0.10 0.31 0.11 0.27 0.12

Biconvex, 20 D 6 0.54 0.10 0.66 0.07 0.64 0.07Meniscus, 20 D 6 0.17 0.03 0.30 0.04 0.24 0.07Silicone, 20 D 6 0.23 0.05 0.36 0.04 0.36 0.19

The most heavily utilized portion of the IOL optictypically will be the central 2-3-mm zone. Any testof minimum quality must be sensitive to problems inthis portion of the lens. A test using a 4.5-mmaperture must therefore be more sensitive than a testusing only a 3-mm aperture, as the fraction of theaperture affected is less. Yet the observed MTF'sare so low that they are probably much less sensitiveto central defects than the smaller 3-mm aperture.Thus a 4.5-mm aperture geometry seems to be at adisadvantage for this type of test.

An additional factor working against the use of a4.5-mm aperture is the strong dependence of all threeof the summary benchmarks tested upon refractivepower. Attempts to allow for the poor response ofthe higher-power lenses would render the test nonuse-ful for lower power and midpower lenses. This isalmost certainly due to the influence of sphericalaberration resulting from the increased curvatures atthe higher powers.

Because the Strehl ratio is a two-dimensional con-struct, much greater weight is placed on the higherfrequencies of a measured MTF than the lowerfrequencies. Normal visual acuity requires resolu-tion to only 30 cycles/deg, about a third of thediffraction limit of a 3-mm aperture. Therefore thisconstruct is useful only if the calculated Strehl ratio isclose enough to unity that it is unlikely that the lessemphasized low frequencies will be lower than de-sired.

For 4.5-mm apertures this is clearly not the case.With an aperture this size, Strehl ratios tended to bewell below 0.5. Small changes in the high-frequencycontent of a measured MTF could easily mask largerand much more important changes in the low-frequency contrast.

If one imposes the additional requirement that thebenchmark for minimum acceptable quality be insome sense a useful foundation for characterizationof multifocal lenses currently undergoing clinical

trials, then the Strehl ratio would definitely be anunfavorable candidate, as the expected ratios willdefinitely be far from unity.

Even for the 3-mm aperture a single minimumrequirement is probably not workable for all stylesand refractive powers expected to be in distribution.The reduced MTF performance at the higher curva-tures of the meniscus and silicone lenses, the resultfor the single meniscus lens at 30 D, and the trends ofthe planoconvex lenses with increasing refractivepower suggest that an MTF-based construct mustmake some allowance for the shape of the lens.

Ray-trace modeling could provide a reasonablebenchmark for comparing measured results thataccount for lens curvature. Figure 8 contains acalculated line labeled Rayleigh (2x). This is thediffraction-limited curve calculated at twice the fre-quency of the abscissa. This curve resembles the1/2 wave defocus curve up to the 30 cycles/deg limitof interest. Ray-trace-derived MTF's could be substi-tuted for the diffraction-limited response in situa-tions where spherical aberration substantially affectsthe measured result. A minimum acceptable targetMTF could then be derived by a similar resealing ofthe abscissa or possibly by direct calculation of a 1/2wave defocus response.

There is probably a limit to what can be achievedwith this approach. The modeled function will notcompletely remove the masking effect of sphericalaberration on one's ability to detect other aberrations.As the ray-trace-derived MTF approaches that deemedthe minimum acceptable without spherical aberra-tion the sensitivity of the test would be expected to bereduced. Yet so long as the correction is not ex-treme, this seems like a pragmatic solution.

Conclusions

MTF measurements using a water cell with planeentrance and exit windows provided useful informa-tion about the optical quality of IOL's. This geome-


try is independent of lens material but relativelysimple to implement.

We investigated aperture stops of 3.0 and 4.5 mm.For most refractive powers of interest, the 4.5-mmaperture yielded results strongly dependent on lenspower and shape. These 4.5-mm results also tendedto be far from that of an ideal lens. Sphericalaberration is the likely source of these problems.The 3.0-mm aperture was therefore deemed a moresuitable choice of stop diameter.

Three benchmarks computed from the measuredMTF's were investigated. Strehl ratios, althoughdesirable because they can be measured directlywithout determining MTF's, were found to be unsuit-able as these ratios tend to emphasize the higherfrequencies and the observed ratios are typically toolow to provide assurance that the low-frequencyresponse is as high as desired.

Minimum acceptable performance criteria must bespecified if this technique is to be adopted as astandard method. A curve produced by 1/2 wave ofdefocus is suggested as a possible reference. Alterna-tively a curve produced by a perfectly made lens atfocus and then rescaled along the abscissa to 2 x is apossibility. These two curves have similar shapesout to approximately 40 cycles/deg under the condi-tions of interest.

An accounting for the effects of spherical aberra-tion will be necessary at the higher powers and highercurvatures. Without such an accounting a uniformrequirement of minimum acceptable quality will ei-ther become too restrictive for these higher curva-tures or become too loose for the lower powers andlower curvatures.

The possibility of using ray-trace methods to pro-vide benchmarks for IOL designs affected by spheri-cal aberrations is a topic for follow-up studies. Theability to test a lens against its design seems highlydesirable. The choice of whether to use simulatedcorneal refraction could be based upon a determina-tion of whether that particular geometry minimizesinterfering aberrations.

The authors thank members of the ANSI Z80.7IOL optical quality working group for many usefuldiscussions and suggestions. The assistance of MikeSimpson, formerly of 3M Corporation, Donn Silber-mann of IOLAB Corporation, Val Portney of AllerganMedical Optics, Don Calogero of the Office of DeviceEvaluation, Food and Drug Administration, and Ed

Thall of University of Arizona was particularly appre-ciated.

References1. American National Standards Institute, American National

Standard for Ophthalmics-Intraocular Lenses-Optical andPhysical Requirements (American National Standards Insti-tute, New York, 1984).

2. W. J. Stark, D. M. Worthen, J. T. Holladay, P. E. Bath, M. E.Jacobs, G. C. Murray, E. T. McGhee, M. W. Talbott, M. D.Shipp, N. E. Thomas, R. W. Barnes, D. W. C. Brown, J. N.Buxton, R. D. Reinecke, C. S. Lao, and S. Fisher, "The FDAreport on intraocular lenses," Ophthalmology 90, 311-317(1983).

3. L. W. Grossman, D. A. Igel, and R. W. Faaland, "Survey of theoptical quality of intraocular lens implants," J. CataractRefract. Surg. 17, 168-174 (1991).

4. L. W. Grossman and W. B. Knight, "Resolution testing ofintraocular lens implants," J. Cataract Refract. Surg. 17,84-90 (1991).

5. M. J. Simpson, "Optical quality of intraocular lenses," J.Cataract Refract. Surg. 18, 86-94 (1992).

6. V. Portney, "Optical testing and inspection methodology formodern intraocular lenses," J. Cataract Refract. Surg. 18,607-613 (1992).

7. J. T. Holladay, "Evaluating the intraocular lens optic," Surv.Ophthalmol. 30, 385-390 (1986).

8. M. Nakazawa and K. Ohtzuki, "Apparent accommodation inpseudophakic eyes after implantation of posterior chamberintraocular lenses," Am. J. Ophthamol. 96, 435-438 (1983).

9. D. J. Nadler, N. S. Jaffe, H. M. Clayman, M. S. Jaffe, and S. M.Luscombe, "Glare disability in eyes with intraocular lenses,"Am. J. Ophthalmol. 97,43-47 (1984).

10. R. W. Faaland, L. W. Grossman, and D. A. Igel, "Opticalquality testing of monofocal intraocular lens implants with a 3mm and 4 mm aperture," J. Cataract Refract. Surg. 17,485-490 (1991).

11. W. J. Smith, Modern Optical Engineering (McGraw-Hill, NewYork, 1966) pp. 311-321.

12. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford,1975).

13. J. T. Holladay, A. C. Ting, C. J. Koester, V. Portney, and T. R.Willis, "Intraocular lens resolution in air and water," J.Cataract Refract. Surg. 13, 511-517 (1987).

14. J. T. Holladay, A. C. Ting, C. J. Koester, V. Portney, and T. R.Willis, "Silicone intraocular lens resolution in air and water,"J. Cataract Refract. Surg. 14, 657-659 (1988).

15. L. Levi and R. H. Austing, "Tables of the modulation transferfunction of a defocused perfect lens," Appl. Opt. 5, 967-974(1968).

16. F. W. Campbell and R. W. Gubisch, "Optical quality of thehuman eye," J. Physiol. 183, 558-578 (1966).

17. A. van Meeteren, "Calculations on the optical modulationtransfer function of the human eye for white light," Opt. Acta21, 395-412 (1974).


minimum resolution specification of intraocular lens implantsusing the modulation transfer function

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