Optical profilometry of poly Amethylmethacrylate Bsurfaces after reshaping with a scanningphotorefractive keratectomy ASPRKB system

Fabrice Manns, Pascal Rol, Jean-Marie Parel, Armin Schmid, Jin-Hui Shen,Takaaki Matsui, and Per Soderberg

3338 APPLIED OPTICS @

A prototype frequency-quintupled Nd:YAG laser was used with a scanning system to create, onpoly1methylmethacrylate2 1PMMA2 blocks, ablations corresponding to a correction of 6 diopters of myopiaby photorefractive keratectomy. The topography of the ablated samples was measured with an opticalprofilometer to evaluate the smoothness and accuracy of the ablations. The ablation depth was largerthan expected. With a 50% to 70% spot overlap, large valleylike variations with a maximumpeak-to-peak amplitude of 20 µmwere observed. With an 80% spot overlap, the rms surface roughnesswas 1.3 µm, and the central flattening was 7 diopters. This study shows that optical profilometry canbe used to determine precisely the ablation per pulse and the smoothness and accuracy of surfaceablations. Knowing the exact ablation per pulse is necessary to produce a smooth and accurate cornealsurface by scanning photorefractive keratectomy.Key words: Laser surgery, cornea, profilometry, photorefractive keratectomy. r 1996 Optical

Society of America

1. Introduction

In scanning photorefractive keratectomy 1SPRK2, thecornea is reshaped by moving a laser spot with adiameter smaller than that of the ablated zone.1,2With this technique the laser spot can be moved toany position on the cornea between two laser pulses.SPRK systems can therefore be programmed toproduce the localized and asymmetric ablationsneeded, for instance, to correct irregular astigma-tism after penetrating keratoplasty.

F. Manns and J.-M. Parel are with the Department of Biomedi-cal Engineering and the Bascom Palmer Eye Institute, Universityof Miami, Miami, Florida, 33136. P. Rol is with the Departmentof Ophthalmology, University of Zurich, Zurich, Switzerland. A.Schmid is with the Institute of Forming Technology, Swiss FederalInstitute of Technology, Zurich, Switzerland; and, when this workwas performed, J.-H. Shen, T. Matsui, and P. Soderberg were withthe Bascom Palmer Eye Institute, University of Miami, Miami,Florida 33136. P. Rol is also with the Department of BiomedicalEngineering, University of Miami, Coral Gables, Florida 33124.J.-M. Parel is also with the Universite de Paris, Hopital del

l’Hotel-Dieu, and Unite INSERM, U86 Paris, France.Received 7 November 1995; revised manuscript received 4

March 1996.0003-6935@96@193338-09$10.00@0r 1996 Optical Society of America

Vol. 35, No. 19 @ 1 July 1996

Because the energy per pulse is proportional to thesquare of the spot diameter at a given radiantexposure, SPRK may require a much lower value forthe energy per pulse than the system used in conven-tional excimer laser systems, in which the beam isdelivered through an opening iris diaphragm with amaximum diameter equal to the diameter of theablated zone. With an ablation zone of 5 mm, forexample, the energy per pulse needed for SPRK witha spot size of 0.5 mm is 2 orders of magnitude lessthan that conventionally used. However, as only asmall amount of tissue is removed by each pulse, thelaser must operate at a high repetition rate to correctrefractive errors in a clinically acceptable time.The ablation of a 5-mm zone with a 0.5-mm laserspot requires a repetition rate of at least 100 Hz.The exact correlation between the postoperative

corneal surface roughness and the clinical outcomeof photorefractive keratectomy 1PRK2 is unknown.However, it is generally believed that the cornealsurface after ablation must be smooth for the corneato heal rapidly and with minimal postoperativecomplications.3,4 The smoothness of the surfaceproduced with argon–fluoride excimer laser PRKsystems 1193 nm, 10–30 Hz, 100–250 mJ@cm2, anduniform intensity2 was measured in vitro and in vivoby the use of interferometry or of silicon replicas of

the ablated cornea.5–7 The roughness of the surfaceafter ablation as measured by interferometry was0.1 µm for poly1methylmethacrylate2 1PMMA2 and0.24 µm for the cornea in vitro, with an amplitude of2 µm from the lowest to the highest point. Theroughness of the silicon molds taken in vivo afterphotoablatin of the cornea was between 0.4 and 0.6µm when the repetition rate was less than 30 Hz.In theory, scanning systems can also produce

smooth and accurate ablations if the spot size, theoverlap, and the energy per pulse are appropriatelyselected.8 In this study, the smoothness and accu-racy of ablations of PMMA with a prototype SPRKlaser system emitting at 213 nm were evaluated byoptical profilometry. The data presented are theresults of a preliminary study that was conductedwith a prototype laser, without accurate knowledgeof the ablation rate of PMMA at 213 nm or of thespatial beam characteristics of the laser.

2. Materials and Methods

A. Laser System

A prototype frequency-quintupled, Q-switchedNd:YAG laser system 1l 5 213 nm2 1LaserHarmonic,LaserSight, Inc., Orlando, Fla.2was used. Themea-sured full-width at half maximum pulse durationwas 10 ns, the pulse repetition rate was 10 Hz, andthe measured pulse-to-pulse stability was betterthan 5%. The maximal energy delivered by thislaser was 6 mJ. A delivery system consisting ofseveral lenses was designed to transform the irregu-lar laser beam into a beam with a smooth, quasi-Gaussian intensity distribution on target.The beam was made to converge slightly to obtain

a spot diameter on the target that was estimated tobe 0.5 mm at 1@e2 by measurement of the impact leftby the laser beam on thermal paper. Two computer-controlled galvanometer scanners 1Model G120DT,General Scanning, Watertown, Mass.2 were insertedbetween the optics and focus. We developed ourown computer hardware and software to control theposition andmovements of the scanners. Themaxi-mum energy per pulse at the ablation site as mea-sured with a calibrated energy meter 1Model JD 500,Molectron, Portland, Ore.2 was 3 mJ. The peakradiant exposure on target was 3 J@cm2, assuming aperfectly symmetrical Gaussian intensity distribu-tion with a 0.5-mm diameter at 1@e2. An operationmicroscope allowed us to monitor and record theablations in a coaxial fashion by means of a dichroicmirror. The sample to be ablated was centered andfocused with the help of a cross hair built in oneeyepiece of the operation microscope.

B. Ablation Algorithm

A raster scan with fixed spot positions was used tophotoablate the PMMA blocks. The number ofpulses applied at each position was calculated with aprogram combining the estimated ablation per pulse

and the desired amount of tissue to be removed.8The ablation per pulse entered into the scanningprogram 1Fig. 12was calculated by combination of theablation rate of PMMA at 213 nm 1Ref. 92 and theestimatedGaussian beam intensity distribution 11@e2beam diameter of 0.5 mm2.

C. Ablations

We photoablated flat blocks of PMMA having a rmssurface roughness of less than 0.3 µmbefore ablation.In the first step, for comparing the real ablation perpulse and the ablation per pulse calculated in theprogram, 12 spot ablations 1holes2 were made in asingle PMMA block. We delivered 1, 10, 50, 100,and 500 pulses to the same location with pulseenergies of 0.44, 0.60, and 1.25 mJ, respectively.The energy was varied by the insertion of a combina-tion of calcium fluoride and silica glass slides in thebeam path and was measured with the calibratedenergy meter before and after each ablation.We evaluated the potential smoothness and accu-

racy of scanning PRK by programming the system tocreate, on PMMA, surface ablations corresponding tothe correction of myopia on the cornea. A singleblock of PMMAwith a rms surface roughness of lessthan 0.3 µm before ablation was used. We at-tempted one correction of 6 diopters with values of60%, 70%, and 80% spot overlap and one correctionof 1 and 3 diopters with a 60% spot overlap. Thespot overlap was defined as 1 2 h@d, where h is thedistance between two neighboring positions and d isthe 1@e2 beam diameter. The energy was 1.25 mJfor all surface ablations.

D. Profilometer

The topography of the ablated samples was mea-sured with an optical profilometer that used a focus-detectionmethod10 1Model UB16, UBMMesstechnik,Ettlingen, Germany2. The light emitted by a laserdiode 1l 5 780 nm2 is focused with an objective lenstoward the surface under test. The light reflectedfrom the sample surface is detected by a pair ofphotodiodes connected to a differential amplifier.The focusing objective is translated perpendicularly

Fig. 1. Cross section of the ablation per pulse at 1.25 mJ: Thesolid curve represents the data used in the program to calculatethe laser-pulse map; the dotted curve represents the actualablation per pulse obtained by optical profilometry.

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to the surface until the output of the differentialamplifier is zero. The surface topography is thenacquired when the spot is scanned across the surfaceof the sample. At each point, the position of thesurface with respect to the position at the previouspoint is equal to the distance traveled perpendicu-larly to the surface by the objective. The maximummeasurement range of the UBM profilometer was6500 µm. However, only the range 650 µm wasused so as to obtain a maximal axial resolution of0.05 µm. The lateral resolution of this system was1.5 µm at a maximum measurement speed of 1000points@s.The profilometer scans the surface of the sample in

two perpendicular directions 1vertical and horizontallines2. The ablated samples were placed in theprofilometer so that the measurement axes corre-sponded to the x and y axes of the laser raster scan.In the following discussion, depth profiles measuredalong the horizontal and vertical axes of the pro-filometer are called horizontal cross sections andvertical cross-sections, respectively.

E. Roughness and the Refractive Effect

To determine the roughness of the ablated surfaceand the refractive effect of the ablation, we fitted thecentral zone of a cross section of the surface with asecond-degree polynomial. The rms roughness wasestimated by the rms error between the fit and thecross section. For the correction of myopia, thecorneal ablation depth can be written as11

t1r2 51

2 11

R12

1

R221r2 2

z2

4 2 , 112

where R1 is the initial radius of curvature, R2 is thefinal radius of curvature, r is the radial position, andz is the diameter of the ablation zone. The polyno-mial fit of the cross sections is given by

f 1r2 5 ar2 1 br 1 c 5 a31r 1b

2a22

2 1 b2

4a22c

a24 . 122

Comparing Eqs. 112 and 122 yields

a 51

2 11

R12

1

R22 , 132

where a is the second-degree coefficient of the polyno-mial fit.The scanning system was programmed to produce,

on PMMA, surface ablations identical in depth andshape to the ablations required on cornea for thecorrection of myopia by PRK. The values R2 5 7.85mm and R1 5 6.98 mm were entered into theprogram for a correction of 6 diopters. In this case,the theoretical radius of curvature, in millimeters, ofthe corneal surface after ablation is given by

R2 56.98

1 2 13.96a. 142

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Under the assumption of a corneal refractive index of1.376, the theoretical change in power that theablations would induce on the cornea can be esti-mated in a paraxial approximation by

DD 5 11.376 2 121 1R22

1

R12 5 20.752a. 152

Equations 142 and 152 show that the theoretical refrac-tive effect on the cornea of the PMMA surfaceablations can be estimated by the second-degreecoefficient of the polynomial fit.

3. Results

A. Ablation Profiles

The holes created at 1.25 mJ with one pulse, at 0.60mJ with 1 and 10 pulses, and at 0.44 mJ with 1, 10,and 50 pulses were too shallow and could not bemeasured with the profilometer. The depth of thehole created at 1.25 mJ with 500 pulses was outsidethe high-precision range of the profilometer. Thesolid curve in Fig. 1 is a cross section of the ablationper pulse entered into the program to calculate thelaser-pulse map for the surface ablations. The dot-ted curve is a cross section of the real ablation perpulse at 1.25 mJ, as measured with the profilometer.Figure 2 shows contour plots of the holes created

in PMMA. At 1.25 mJ, the contours are nearlycircular, but they are not concentric. This demon-strates that the ablation per pulse had a slightlyasymmetric Gaussian shape. At 0.60 and 0.44 mJthe contours are elliptic. The ellipticity of the holesis approximately 1.75 at 0.44 mJ, 1.6 at 0.6 mJ, and1.1 at 1.25 mJ. The directions of the major andminor axes of the ellipticity of the holes created at0.6 and 1.25 mJ are approximately 45° and 135°,respectively, with regard to the horizontal direction.Cross sections passing through the point of maxi-

mum depth of the holes created at 0.60 and 1.25 mJshow that the beam intensity distribution is homoge-neous, with no spikes or significant irregularities1Fig. 32. The cross sections have a quasi-Gaussianshape, with a slight asymmetry. The bottom of thehole created at 0.44 mJ with 500 pulses is irregular.The large spike in the profile of this hole is probablyan artifact caused by the presence of dust particleson the PMMAblock during the measurement.The peak ablation rate was calculated by division

of the maximum depth of the holes by the number ofpulses 1Table 12. The low values of the peak ablationrate at 0.44 and 0.6 mJ indicate that these energylevels were close to the ablation threshold. At 1.25mJ, the peak ablation rate was 0.28 µm@pulse.With the argon–fluoride excimer laser 1193 nm2, theablation rate of PMMA is 0.29 µm@pulse when theradiant exposure is approximately 120 mJ@cm2 1Ref.122, which is in the lower range of the radiantexposures used clinically.

B. Surface Ablations

The surface ablations were performed with an en-ergy per pulse of 1.25 mJ. Figures 4–6 show thehorizontal and vertical cross sections passing throughthe center of the surface ablations for a flattening of6 diopters. In each graph the heavy-weight curverepresents the created topography, and the light-weight curve represents the expected ablation profile.The ablation per pulse is shown in Fig. 1.The spikes in the cross sections are measurement

artifacts. In all surface ablations the actual abla-tion depth is larger than the expected ablation

Fig. 2. Contour maps of the holes created with 500 pulses at 0.44and 0.60 mJ and with 100 pulses at 1.25 mJ.

depth. The maximum difference in depth variesbetween 16 and 20 µm. The horizontal cross sec-tions are more irregular than the vertical crosssections. The horizontal cross sections of the abla-tion profiles obtained with 60% and 70% overlapexhibit three large valleylike variations, with amaximum peak-to-peak amplitude varying from 8 to20 µm and a distance between peaks of 1 mm for the60% overlap and 0.8 mm for the 70% overlap. Thevertical cross sections of these surfaces and the crosssections of the surface created with an 80% overlapare more regular.The center of the vertical cross section of the

surface created with an 80% overlap was fitted witha second-degree polynomial 1Fig. 72. The roughnessrms of the vertical cross sections is 1.3 µm, and thetheoretical new radius of curvature calculated withEq. 142 is 8.03 mm, which corresponds to a cornealflattening of 7 diopters. Figure 8 is a three-dimensional representation of the topography of thesurface after ablation, for a flattening of 6 diopterswith an overlap of 80%. Horizontal and verticalcross sections of surface ablations for the correctionsof 1, 3, and 6 diopters of myopia created with a 60%

Fig. 3. Horizontal cross sections of the holes produced at 0.44,0.60, and 1.25 mJ passing through the point of maximum depth.The large spike in the hole created at 0.44 mJ with 500 pulses isan artifact probably caused by dust.

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Table 1. Peak Ablation Rate versus the Energy and the Number of Pulses

Energy 1mJ2

PeakAblation Rate 1µm@pulse2

10 Pulses 50 Pulses 100 Pulses 500 Pulses Average

0.44 Not measurable Not measurable 0.014 0.015 0.0150.60 Not measurable 0.033 0.045 0.046 0.0411.25 0.275 0.294 0.286 Out of range 0.285

overlap are shown in Fig. 9. The spikes in the crosssections are artifacts.

4. Discussion

A. Ablation Profile

The shapes of the holes show that the beam intensitydistribution was smooth but asymmetric. The ellip-ticity of the holes increases when the energy de-creases. As the energy was varied by the insertionof parallel glass slides in the beam path, thesevariations were not due to changes in the spatialcharacteristics of the laser output. The changes inthe shapes of the holes might be related to the formof the ablation-rate curve. The values listed inTable 1 show that the ablation rate is not a linearfunction of the energy. The energy of 0.44 mJ isclose to the ablation threshold, where the ablationrate increases slowly when the energy increases.At 1.25 mJ, the ablation curve is steep. If the beam

Fig. 4. Cross sections of the surface ablation passing through thecenter of the ablated area: attempted flattening, 6 diopters;overlap, 60%; ablation zone, 5 mm. The large spike in the topgraph is an artifact probably caused by dust.

3342 APPLIED OPTICS @ Vol. 35, No. 19 @ 1 July 1996

intensity distribution is circular in the center of thebeam and elliptic in the periphery, the ellipticitycould be amplified when the peak radiant exposurebelongs to the flat portion of the ablation rate andcould be reduced when the peak radiant exposurebelongs to the steep portion of the ablation-ratecurve.The ellipticities and directions of the major and

minor axesmust be taken into account in the calcula-tion of the pulse-distribution map. These new pa-rameterswill probably yield a different and asymmet-ric laser-pulse map. The ablation may induceastigmatism if the ellipticity is ignored.

B. Surface Ablations

In the program that computes the spatial distribu-tion of the pulses, we calculate the amount of tissueremoved by one pulse by combining the ablation rateand the beam intensity distribution.8 The differ-ence in depth between the created and expected

Fig. 5. Cross sections of the surface ablation passing through thecenter of the ablated area: attempted flattening, 6 diopters;overlap, 70%; ablation zone, 5 mm.

ablations and the difference in roughness betweenthe horizontal and vertical cross sections are prob-ably due to the inaccuracy of the ablation rate and ofthe spatial beam characteristics entered into theprogram controlling the ablations.

1. Ablation RateThe relative difference between the expected andactual depth of the surface ablations is approxi-mately 20%. This difference may have been causedin part by errors in the ablation-rate data enteredinto the program that calculates the pulse-distribu-tion map. The ablation rate of PMMA at 213 nmwas taken from previous data obtained by the mea-

Fig. 6. Cross sections of the surface ablation passing through thecenter of the ablated area: attempted flattening, 6 diopters;overlap, 80%; ablation zone, 5 mm.

Fig. 7. Least-squares polynomial fit to the central zone of thevertical cross section of ablation created with an 80% overlap.

surement of the number of pulses required to perfo-rate thin PMMA samples of known thickness.9 Theerror in the ablation-rate data is due to errors in themeasurement of the radiant exposure 1precision valueof approximately 610%2, of the thickness of theablated PMMA block 1precision value of approxi-mately 65%2, and of the number of pulses 1precisionvalue of ,65%2. For creating accurate corrections,the precision of the ablation-rate data should bebetter than 5%, which is difficult to achieve with themethod that we used previously. The ablation-ratedata entered into the program must therefore beadjusted to obtain more accurate ablations.

Fig. 8. Topography of the ablated area created for a correction of6 diopters with an 80% overlap.

Fig. 9. Cross sections of the surface ablation passing through thecenter of the ablated area: attempted flattening, 1, 3, and 6diopters; overlap, 60%; ablation zone, 5 mm. The spikes areartifacts probably caused by dust.

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2. Spatial Beam CharacteristicsThe difference in roughness between the horizontaland vertical cross sections indicates that there was adifference in overlap in the x and y scanning direc-tions. This difference can be caused by discrepan-cies between the actual and the programmed spatialbeam characteristics. The beam intensity distribu-tion was entered into the program as

I1x, y2 5 I0 exp122x2 1 y2

w2 2 , 162

where I0 is the peak radiant exposure, w is the 1@e2beam radius, and x and y are the spatial coordinates.The peak radiant exposure is given by

I0 52E

pw2, 172

where E is the energy per pulse. Equations 162 and172 show that an error in the measurement of thebeam diameter will cause an error in the estimationof the peak radiant exposure. These errors willaffect both the overlap and the depth of the surfaceablations. For instance, if the actual beam diam-eter is 0.6 mm instead of 0.5 mm, the actual overlapis 66%, whereas the expected overlap was 60%.Correspondingly, with an energy of 1.25 mJ, thepeak radiant exposure will be 88 mJ@cm2 instead ofthe expected 127mJ@cm2. This example shows thatthe spatial beam characteristics must be knownquite accurately to create the predicted surface.Measuring the size of the spot created on thermal

paper does not provide the required precision be-cause the exact boundary of the burned surface isdifficult to localize and because the diameter of thissurface does not necessarily correspond to the 1@e2beam diameter. A beam-analysis system capable ofmeasuring small diameters at far-ultraviolet wave-lengths should be used. The three-dimensional to-pography of the hole created in PMMA by one pulsewith a given energy 1Fig. 22 can also be entereddirectly into the program. Figure 1 shows that theablation per pulse used in the program computingthe laser-pulsemap 1calculated by combination of thebeam intensity distribution and the PMMA ablationrate2 is deeper and narrower than the real ablationper pulse.

3. Smoothness and PredictabilityThe data presented are the results of a preliminarystudy that was conducted with a prototype laser,without accurate knowledge of the ablation rate ofPMMAat 213 nm or of the spatial beam characteris-tics of the laser. Mechanical vibrations in the sys-tem or the animals1,13 and jitters of the scanners areadditional factors that might interfere with ablation.The surfaces created were deeper and rougher thanexpected. Even so, at 80%, for a flattening of 6diopters, the rms roughness of the vertical cross

3344 APPLIED OPTICS @ Vol. 35, No. 19 @ 1 July 1996

section was only 1.3 µm, and the central flatteningcalculated with Eq. 152was 7 diopters.After adjustment of the ablation-rate data and of

the beam characteristics entered into the programthat calculates the laser-pulse map, the smoothnessand predictability of the ablations should improvesignificantly. According to the theoretical study,8the roughness of the surface after ablation is propor-tional to the central ablation depth. With an abla-tion depth of 65 µm, the predicted rms roughness is0.4 µm. However, in practice, the surface will berougher than that predicted by the model because oflocal inhomogeneities in the ablated sample, deposi-tion of ablation debris on the surface, and energyfluctuations.The smoothness of the corneal surface after abla-

tion may also be improved by modification of thescanning technique. A raster scan with fixed spotpositions was used to photoablate the PMMAblocks.Using variable spot positions or moving the beam ina random fashion might help to eliminate the smallsurface irregularities 1Fig. 62.

4. Clinical SignificanceBecause of the structural differences between PMMAand corneal tissue and because of the presence ofclinical factors during corneal ablation, the results ofcorneal ablation may not necessarily correlate wellwith the results of PMMAablation. The laser proto-type and the scanning system were used in a studyon rabbits,1,13 with the same parameters 160% and80% overlap, 0.5-mm spot, 6-diopter flattening, en-ergy of 1 mJ2. The shape of the corneal surface inthe acute histologic sections was comparable qualita-tively to the shape of the PMMA surfaces measuredby profilometry. With an 80% overlap, small varia-tions with a maximum peak-to-peak amplitude of 4µm were observed in the histology sections 1Fig. 102.With a 60% overlap the roughness of the cornealsurface was variable: In some sections large saw-tooth variations were observed, whereas in othersections the surface was similar to that created with

Fig. 10. Acute histology section of a rabbit cornea ablated withan 80% overlap 1Hematoxyline and Eosin stains; magnification32502.

an 80% overlap. This observation also matches theresults of the profilometry study 1Fig. 42.The PMMA surfaces created with the prototype

SPRK system and measured by profilometry arerougher than the surfaces created on PMMA withconventional argon–fluoride excimer laser PRK sys-tems that use an opening diaphragm or an ablatablemask and measured by scanning electron micros-copy.14 It is difficult to evaluate how much thisdifferencewill affect the epithelial and stromalwoundhealing and the stability of the refractive outcome.In an early study of excimer laser PRK on mon-

keys with a prototype delivery system that used theopening diaphragm, Marshall and colleagues15 cre-ated a surface with large steps separated by approxi-mately 0.5 mm. The irregularity of the surface didnot seem to affect the healing process, except inthose areas where beam irregularities or eye move-ments created large local variations of the ablationdepth.Hanna and colleagues16 also observed a normal

healing process in monkeys after excimer laser PRKwith a scanning-slit delivery system. This systemcreated a corneal surface with periodic undulationshaving a maximum amplitude of 2 µm and a mini-mum period of 20 µm.17More recently, Obata and colleagues18 used rabbits

to test a scanning excimer laser PRK system inwhich a rectangular beam is scanned across thecorneal surface in six different directions. A wave-like pattern with a peak-to-peak amplitude of 10–20µm was visible at the periphery of the ablation zonein the acute histology sections. Even so, the heal-ing process was comparable to that observed in otherstudies. The authors did not evaluate the accuracyof the corrections.Because of the measurement time, optical pro-

filometry using a focus-detection method cannot beapplied directly to in vivo measurements of thecorneal surface after PRK. The accuracy of theablations and the corneal surface roughness could beevaluated clinically if a silicon replica of the cornealsurface were made and the topography of the rep-lica5,7 were measured or if low-coherence interferom-etry were used along with image-processing tech-niques.19

5. Conclusion

This study shows that the ablation rate and spatialbeam characteristics must be known precisely andthat the parameters of the scanning system must beadequately selected to produce smooth and predict-able ablations with PRK systems. The measure-ments also demonstrate that optical profilometrycan be used to determine precisely the ablation rateof PMMA, as well as the smoothness and accuracy ofsurface ablations. The results show that develop-ing a system for SPRK with a quasi-Gaussian beamis more difficult than developing a conventional PRKsystem with a flat-top beam. Indeed, when theintensity distribution is Gaussian, the ablation rate

must be known precisely for radiant exposures rang-ing from the ablation threshold to the peak radiantexposure and the spatial beam characteristics mustbe measured with high precision. On the otherhand, with a flat-top intensity distribution, the beamdiameter and the ablation depth per pulse at theselected radiant exposure are the only parameters.

This work was supported in part by the EnterpriseFlorida Innovation Partnership, the Florida LionsEye Bank, and Research to Prevent Blindness, NewYork, New York. We are grateful to U. Feuer of theInstitute of Forming Technology, Swiss Federal Insti-tute of Technology, Zurich, Switzerland, for support-ing the profilometer measurements and to MichelleSavoldelli of the University of Paris, Hopital del’Hotel-Dieu and Unite INSERM, U86 Paris, France,for preparing the histology sections.

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