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Cleaning processes of encrusted marbles by Nd:YAG lasers operating in free-running and Q-switching...

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Page 1: Cleaning processes of encrusted marbles by Nd:YAG lasers operating in free-running and Q-switching regimes

Cleaning processes of encrusted marblesby Nd:YAG lasers operating in free-running andQ-switching regimes

Salvatore Siano, Fabrizio Margheri, Roberto Pini, Piero Mazzinghi, andRenzo Salimbeni

The removal process of degraded superficial layers from marble samples by Nd:YAG lasers was studiedwhile simulating operative conditions of stone artwork restoration. The effects of laser irradiation at1064 nm with three different pulse durations of 6 ns, 20 ms, and 200 ms were investigated by time-resolvedshadowgraphy and emission spectroscopy of the ejection plume to characterize the specific interactionregimes, with particular concern given to the occurrence of side effects, such as thermal and mechanicaldamages to the substrate, that could affect the laser cleaning procedure. © 1997 Optical Society ofAmerica

Key words: Laser applications, laser cleaning, Nd:YAG, stone restoration.

1. Introduction

The removal of encrustations and degenerated layersfrom stone artworks by means of laser divestmentwas proposed by Asmus et al. in the 70’s,1 though thegeneral idea of using pulsed laser radiation as a lighteraser to remove a high absorbing layer from thesurface of a lower absorption substrate goes back tothe origins of laser technology.2

Probably owing to the large gap between the meth-odologies of laser technology and art restoration andto a natural caution on the part of restorers concern-ing new techniques that could potentially endangerthe integrity of artifacts of high artistic and historicvalue, the effects of laser interaction in this specificfield have not been studied as extensively as in otherapplications of laser ablation. Nevertheless, in re-cent years some important restoration interventionson marble and stone artworks have been performedwith laser assistance, for example, on the portals ofAmiens Cathedral and Notre Dame and on sculp-tures such as Donatello’s San Giovanni from Flo-rence’s Opera del Duomo Museum and the statue of

The authors are with the Istituto di Elettronica Quantistica,Consiglio Nazionale delle Ricerche, Via Panciatichi 56y30, I-50127Firenze, Italy.

Received 13 August 1996; revised manuscript received 10 March1997.

0003-6935y97y277073-07$10.00y0© 1997 Optical Society of America

William Huskisson from the National Museum ofMan Island. These operative tests of laser cleaninghave opened a wide discussion in the art restorationcommunity about the effectiveness and safety of thisnew technique, which is still far from a final valida-tion. Recently, new interdisciplinary forums andmeetings have been established to join together sci-entists involved in both art restoration and lasertechnology.3

Concerning the choice of the laser source for stonecleaning, the requirements of easy handling and port-ability, fiber-optic delivery, high removal efficiencyand selectivity, and finally large commercial diffusionand relatively low cost have favored, so far, Nd:YAGlaser devices. Two operative regimes have been em-ployed up to now: the Q-switching mode, with pulselengths of 5–10 ns and energy as much as 1 Jypulse,and the free-running mode, with pulse durations of0.1–1 ms and energy as much as tens of joules. Inboth cases, important side effects have been evidentduring laser cleaning of stones. Longer pulses caninduce undesired thermal damages such as meltingand vitrification of the substrate.4 On the otherhand, high power short pulses develop strong photo-mechanical effects that can lead to increased surfaceroughness or at least to local fragmentation of thesubstrate.5 This last feature is not surprising. Infact, even though in reports on laser restoration thecleaning process has often been described as a fastvaporization, general studies devoted to other appli-cations of laser ablation have revealed more complex

20 September 1997 y Vol. 36, No. 27 y APPLIED OPTICS 7073

Page 2: Cleaning processes of encrusted marbles by Nd:YAG lasers operating in free-running and Q-switching regimes

thermoacoustic features ~see, for example, Refs. 6 and7!.

An emerging application for laser cleaning thatpresents close relationships with artistic stone resto-ration is the removal of superficial decay due to at-mospheric pollution or of unwanted paints andgraffiti from the walls of modern buildings. Hereefficiency and speed of the cleaning process, morethan the achievement of high precision and control,represent the crucial factors since, usually, large ar-eas are subject to laser treatment. In this respect,Q-switched devices appear to be the best choice.8

In art restoration, although it has already beenshown that the laser cleaning technique can substan-tially reduce the processing time,9 it is more difficultto demonstrate that this procedure always providesremarkable improvements with respect to conven-tional techniques. For example, whether the lasertreatment can improve the quality of the cleaned sur-faces and permits the preservation of the originalpatina of ancient sculptures is still under discus-sion.10 This represents a key factor for both earlyand long-term success of laser restoration, consider-ing that, in addition to artistic and historic implica-tions, the degree of roughness can determine thefuture resistance of stone artworks to environmentalattacks. Furthermore, comparative tests on a largevariety of samples are needed to isolate the condi-tions under which laser cleaning will allow conserva-tive restorations in those cases for which traditionalmethods have been proved to cause damage, as, forexample, in the removal of encrustation from weaksubstrates such as sandstone and corroded mar-ble.9,11

To provide the basis for a quantitative descriptionof the laser cleaning process of encrusted marble, weperformed a preliminary study on the interaction re-gimes induced by Nd:YAG laser pulses of differentdurations, with particular concern given to the pre-vention of undesired side effects. Time-resolvedshadowgraphy provided information on the ejectiondynamics and on the associated thermal and photo-acoustic phenomena. Spectroscopic analysis of theablation plume was also performed to assess the pres-ence of a plasma phase.

2. Materials and Methods

Experiments have been carried out with two distinctNd:YAG laser devices ~1064-nm emission wave-length! that provided three different pulse durations:~1! a commercial laser ~Quanta Ray Model GCR-4!operating in two regimes: normal free-running~NFR! mode with pulses of ;1 J and duration of 200ms FWHM, and Q-switching ~QS! with a pulse energyof 500 mJ and duration of 6 ns FWHM; ~2! a home-made laser operating in a short pulse free-runningmode ~SFR! especially designed for cleaning applica-tions.12 This laser emits pulses of 1-J energy with20-ms duration FWHM ~Fig. 1!, which is approxi-mately the shortest value possible using all-solid-state flash-lamp drivers.

The optical quality of laser emissions was checked

7074 APPLIED OPTICS y Vol. 36, No. 27 y 20 September 1997

with a system for laser beam diagnostics ~Big Sky6.11! that for the two lasers revealed multimode dis-tributions with no evidence of hot spots.

A set of laboratory-produced samples simulatingsuperficial degradation of marble artworks was pre-pared according to a standardized procedure, as peragreement with the restorers of the Opificio dellePietre Dure in Florence, to obtain good repeatabilityof measurements. Each sample was composed of asubstrate of white-gray Carrara marble of 3–5-mmthickness with a first deposit of a 100-mm-thick layerof calcium oxalate, representing the natural patinathat should be safeguarded by the restoration inter-vention.5,10 A second layer of 500-mm-thick blackgypsum ~96% gypsum, 3% carbon black, and 1%quartz powder! was deposited onto the first layer tosimulate the degraded layer to be removed by laserablation. After preparation, the samples were left todry for several days prior to undergoing laser clean-ing tests.

Time-resolved images of the various phases of ma-terial removal were obtained with a pump-and-probediagnostic setup,13 sketched in Fig. 2. The probe

Fig. 1. Typical emission temporal profile of the SFR Nd:YAGlaser.

Fig. 2. Experimental set up for time-resolved shadowgraphy ofthe interaction volume during laser cleaning of encrusted marble.

Page 3: Cleaning processes of encrusted marbles by Nd:YAG lasers operating in free-running and Q-switching regimes

beam from a nitrogen laser ~PRA Model LN 103, 337nm, 0.5-ns pulse duration, 50-mJ pulse energy!, afterspatial filtering and collimation, was sent tangen-tially to the sample surface to probe the air regionwhere laser interaction and material removal oc-curred. The emissions of the probe laser and of theNd:YAG laser were synchronized by a digital delaygenerator that permitted a temporal scan of thewhole event with a time jitter of ;10 ns in the firstfew microseconds. The shadowgraphic patternsproduced by local refractive-index perturbations andejected particulates were detected by a CCD cameradirectly coupled to a frame grabber and stored in apersonal computer for data analysis. A demagnifi-cation optic in front of the camera was sometimesused whenever a perturbation region larger than 5mm in diameter was imaged.

Plume spectroscopy was also performed to assessthe occurrence of a plasma phase during laser-targetinteraction. The radiation emitted from the interac-tion volume was collected by an optical fiber and trans-mitted to the entrance slit of a 0.25-m spectrograph~Jobin-Yvon Model M25!, equipped with a 300-linesymm holographic grating. The spectra detec-tion, recording, and analysis were performed by anoptical multichannel analyzer ~EG&G PARC OMA III

Model 1460!, with a 1024-channel intensified diodearray detector ~Model 1420 G!.

All the measurements were performed on the sec-ond shot of the laser at each location of the sample toavoid surface effects. The time evolution of the per-turbation front was then measured for different shotsand at different locations, moving the sample with amicromanipulator. Owing to the sample homogene-ity, this was found to correlate well with the actualtime evolution of the ablation process.

3. Results

In preliminary trials we measured the laser ablationthresholds of the black gypsum layer with the threeavailable pulse lengths of 6 ns ~QS!, 20 ms ~SFR!, and200 ms ~NFR! that were ;1, 5, and 14 Jycm2, respec-tively.

Further measurements were performed at laserfluence in the ranges of 1–22, 10–32, and 20–130Jycm2, respectively, for the three pulse durations re-ported above. Visual and microscopic observationsrevealed that at fluence levels of 1–3 Jycm2 ~QS!,10–20 Jycm2 ~SFR!, and 30–50 Jycm2 ~NFR!, whichhave been assumed as operative ranges for stonecleaning, the calcium oxalate patina underlying theblack gypsum deposit was not attacked by either ofthe longer laser pulses, though such an attack wasobserved to occur under QS laser irradiation. Thisresult suggests that for the encrusted marble modelwe used in our tests, the QS cleaning process couldnot provide a sufficient degree of selectivity betweenthe deposited layer and the substrate to be safe-guarded, even at a fluence value just above the abla-tion threshold of the deposited layer.

Some examples of the shadowgraphic images dis-playing material removal, as well as laser-induced

acoustic and thermal effects developing in the airregion before the target surface, are shown in Figs.3~a!, 3~b!, and 3~c! for the 6-ns, 20-ms, and 200-mspulse durations, respectively. The QS laser pulsegenerates an intense plasma, as confirmed by thespectroscopic analysis described below. The front ofthis plasma region expands at supersonic speed fromthe target surface and drives the development of ashock wave. The dark shadowgraphic ring corre-sponding to the shock front is typically observable at;1 ms after laser irradiation. A dark cloud expand-ing at lower speed from the target surface is clearlyindicative of the presence of ejected material and sug-gests that material removal involves mostly parti-culates opaque to the probe laser beam. Theseobservations point out the relevant role of the photo-mechanical effect for the 6-ns pulse-induced ablationprocess, as is quantitatively demonstrated in Section4. The complete detachment from the target surfaceof the ablated material cloud when irradiating withQS pulses occurs after ;200 ms @see Fig. 4~a!#.

Conversely, time-resolved imaging of the effects oflonger laser pulses does not show significant photo-mechanical effects. Only weak acoustic waves de-parting from the focal region are barely visible duringthe first microseconds of laser irradiation @see, forexample, the first frame of Fig. 3~b!#; they are relatedto the first intense spikes of the pulse shape. Forboth 20- and 200-ms laser pulses, the sequence offrames shows the formation of a perturbed hot region,whose front expands at constant subsonic speed, asreported in Fig. 5 for the SFR pulse. Then the front

Fig. 3. Sequences of shadowgraphic images showing the evolu-tion of the ablation plume and of the associated acoustic and ther-mal phenomena observed for three different sample irradiationconditions. ~a! QS pulse, 1.7 Jycm2; ~b! SFR pulse, 17 Jycm2; ~c!NFR pulse, 44 Jycm2. Real sizes of the image frames are ~a!10.2 3 14.4 mm2, and @~b! and ~c!# 5 3 5 mm2.

20 September 1997 y Vol. 36, No. 27 y APPLIED OPTICS 7075

Page 4: Cleaning processes of encrusted marbles by Nd:YAG lasers operating in free-running and Q-switching regimes

of the hot region degenerates in turbulent motions.This occurs soon after the end of laser irradiation forthe SFR pulse and during irradiation for the NFRpulse. The turbulence region produces a shadowthat remains visible for as long as 1 ms after irradi-ation @Figs. 4~b! and 4~c!#.

Time-integrated images of the plume emission forthe three different irradiation regimes are reportedin Fig. 6 to give an indication of the size of the wholeheated region in each case.

The spectra obtained from these ablation plumespoints out the presence of plasma for both QS andSFR pulses but not for the NFR pulse. Typical QSand SFR spectra around 400 nm shows intense393.3–396.8-nm lines of Ca II over a continuum @Fig.7~a!#. Also, self-absorption is observable for theseionized lines and for the 422.7-nm Ca I neutral line,revealing a denser plasma in the region close to thetarget with respect to the outer shell. On the otherhand, for NFR pulses, ionized calcium lines are de-tectable only at a fluence higher than 100 Jycm2 @Fig.7~b!#.

4. Analysis and Discussion

The time-resolved shadowgraphy together with theplume spectroscopy evidenced three different re-

Fig. 4. Last phase of the plume evolution for ~a! QS, ~b! SFR, ~c!NFR laser pulses.

Fig. 5. Experimental data and linear fittings of the expansionbehavior of the front of the hot region induced by SFR pulses ofincreasing fluences. Front speeds of 106, 177, 211, and 276 mysresult at laser fluences of 11, 17, 28, and 32 Jycm2, respectively.

7076 APPLIED OPTICS y Vol. 36, No. 27 y 20 September 1997

gimes of laser-target interaction, depending on pulseduration: ~a! blast wave expansion induced by anoptical detonation for QS pulses, ~b! laser-sustainedcombustion for SFR, and ~c! heating and vaporizationfor NFR. These behaviors are analyzed in some de-tail in the following subsections.

Fig. 6. Time-integrated images of the plume detected by a standardCCD camera ~50-ms exposure time!. ~a! QS, ~b! SFR, ~c! NFR pulses.

Fig. 7. Spectra of the plume emission. ~a! QS, 1.7 Jycm2 fluence,showing emission lines of Ca I and Ca II; ~b! NFR at fluences in therange 40–130 Jycm2. In this case, ionized Ca lines appear only atfluences higher than 100 Jycm2.

Page 5: Cleaning processes of encrusted marbles by Nd:YAG lasers operating in free-running and Q-switching regimes

A. QS Interaction

Laser pulses in the nanosecond range can give rise toa so-called optical detonation when the laser inten-sity is high enough to rapidly induce on the targetsurface a plasma that directly absorbs the radiationin a thin layer ~light-absorption wave!. The highlyovercompressed and overheated gas forces a super-sonic expansion of the plasma front, producing anextension of the ionized region ~hydrodynamic re-gime!. An approximate law of motion for the shockfront evolution can be obtained starting from the ex-pression of the detonation speed for a laser pulse withtop hat spatial and temporal shapes14:

cD 5 F2~g2 2 1!ID

r0G1y3

, (1)

where ID is the detonation intensity ~representing inthis case a fraction of laser intensity IL!, r0 ' 1.2 kgm23 is the density of unperturbed air, g ' 1.2 is theadiabatic coefficient for air that can be assumed fortemperatures of thousands of Kelvins.15 The jumpof the gas density on the shock front is ryr0 5 ~g 11!yg ' 11.

The detonation phase will be followed by planarand then spherical decays of the shock. Thus thecomplete time evolution of the front speed is de-scribed by the following approximate expressions:

cf~t! 5 5cD

cDStD

t D1y3

cDtD1y3t1

4y15t23y5

t0 , t # tD

tD , t # t1

t . t1

, (2)

where tD 5 tL 2 t0, tL being the laser pulse duration,t0 the starting time of the normal detonation regime,and t1 the time of switching from planar to sphericaldecay.16 If laser irradiation is provided at a levelthat is much higher than the breakdown threshold ofthe target, one can reasonably assume that tD ' tL,

Fig. 8. Time evolution of the front of the shock wave induced byQS pulses of increasing fluences. Fittings combining planar andspherical expansion geometry have been calculated according to amodel of optical detonation ~see Subsection 4.A!.

whereas in general the real duration of the detona-tion phase should be taken into account.

The relationship between the front speed cf ~t! andthe pressure acting on the target surface at any timeis given by16

ps 5 Sg 1 12g D2gy~g21! r0

g 1 1cf

2. (3)

Figure 8 reports the experimental data of the dis-placement of the shock front versus time for threefluence values of 1.7, 3, and 22 Jycm2 and the corre-sponding fittings obtained from integration of Eq. ~2!.Figures 9~a! and 9~b! report the front speed cf and thepressure at the target surface ps for the same laserfluence. This analysis shows that at fluences of 1–3Jycm2 that are typical values for cleaning applica-tions, the initial pressure is ;10–60 bar, whereas at22 Jycm2 a peak pressure value as high as 410 barcan be produced on the target surface. The durationof pressure pulses is ;20 ns in all cases. It is worthnoting that these pressure peaks can be considered asthe lower limit of the real ones, since the above de-

Fig. 9. ~a! Calculated front speed and ~b! pressure acting on thetarget surface for QS pulses with increasing fluences of 1.7, 3, and22 Jycm2, respectively ~from bottom to top!.

20 September 1997 y Vol. 36, No. 27 y APPLIED OPTICS 7077

Page 6: Cleaning processes of encrusted marbles by Nd:YAG lasers operating in free-running and Q-switching regimes

scription does not include the recoil of material ejec-tion that is due to the plasma-target energy transfer.

B. SFR Interaction

The behavior observed with the SFR pulse suggests adescription of the process in terms of a laser-sustained combustion, where a plasma is initiallygenerated and then is pumped by a laser intensitymuch lower than that required for optical break-down.17 The plasma onset is favored by the highabsorption of the dark layer and by some initialspikes of the laser pulse shape of high instantaneouspower ~see Fig. 1!. In such a condition, only aplasma of low electron density can develop, charac-terized by a low absorption of the incident radiationand subsonic expansion of the front. The tempera-ture inside this plasma region can be very high ~of theorder of 104 K!,14 but the mass density is indeed low.Considering that the laser energy in this case in-creases the enthalpy of the gas H 5 ε 1 pyr ~where εis the specific internal energy! rather than the inter-nal energy and assuming an unperturbed value of H.. H0 from the energy conservation law applied tothe front of the ionization zone, the following expres-sion for the density jump can be obtained:

r

r0<

gnfp~g 2 1!IL

, (4)

where nf is the speed of the hot front.The observed evolution of the front was found to be

linear during laser irradiation ~Fig. 5! with estimatedspeeds in the range 100–300 mys for laser fluences of10–30 Jycm2. Considering that the subsonic speedof the front can be associated with an almost negli-gible overpressure in the hot region with respect tothe outer pressure, one can reasonably assume p ' 1bar. Then Eq. ~4! gives ryr0 ' 0.7–2 3 1022 and theelectron density has to be accordingly low. Such aplasma is quite transparent to the 1064-nm laserradiation, whereas some shielding effects take placein close proximity to the target surface, mostly be-cause of the presence of ejected particles. In sum-mary, it can be argued that plasma formationinduced by SFR pulses does not play a crucial role inlaser-target interaction, as was found to occur in theprevious QS case.

C. NFR Interaction

The observed behavior for the NFR pulse is charac-terized by the presence of turbulent motions from thebeginning of irradiation @Fig. 3~c!#. This case is ex-pected to be similar to the regime induced by cwirradiation. In fact, shadowgraphs of the interac-tion region did not show any ejection of solid materialor acoustic waves expanding from the target surface.This feature confirms that the material removaltakes place by continuous vaporization from the tar-get along the laser-pulse duration.

The model that is often applied to describe theinteraction process in similar irradiation conditionsis the thermal model of a semi-infinite wall that pro-

7078 APPLIED OPTICS y Vol. 36, No. 27 y 20 September 1997

vides the following expression for the temperaturerise at the target surface9,18:

T~0, t! 52AIL

K ÎktL

p, (5)

where A is the target absorbance, IL is the laser in-tensity, K is the thermal conductivity, and k is thethermal diffusivity. The penetrating depth of heatis related to the pulse duration through the equa-tion19:

L 5 Î4ktL. (6)

For NFR pulses one obtains L ' 20–30 mm, to becompared with L ' 5–10 mm for SFR pulses, whichsuggests a larger extension of the thermally damagedzone in the former case, as we typically observed.

5. Conclusions

This experimental study was intended to provide therestorers and scientists involved in conservation ofmarble and stone artworks with quantitative evalu-ations of the laser cleaning process, which could com-plete the picture usually furnished by subjectiveexaminations and postprocess analysis of treatedsamples, such as those that have usually been re-ported to date. The study also helps clarify themechanism of laser-material interaction and sug-gests some criteria to identify the optimum irradia-tion conditions for this specific application.

In particular, we focused our attention on the de-pendence of ablation dynamics induced by Nd:YAGlasers on pulse duration in order to achieve prelimi-nary indications of the optimum temporal range suit-able for stone artwork cleaning. The analysis wasconducted on the basis of time-resolved shadowgra-phy and emission spectroscopy diagnostic techniques.

Strong plasma-mediated photomechanical effectsinduced by QS pulses at typical operative fluencehave been evident. It is reasonable to conclude thatthey are responsible for the roughness of cleaned sur-faces, as reported by various authors. On the otherhand, thermal side effects similar to those caused bycw irradiation are associated with long NFR pulses.A good compromise seems to be represented by SFRirradiation that was observed to induce a laser-sustained combustion regime characterized by aweaker plasma formation that did not cause substan-tial shielding effects to the incoming laser beam anddeveloped lower pressure values compared with QSoperation, with no observable mechanical damage.Moreover, SFR pulsed ablation showed a clear selec-tivity with respect to QS irradiation in the removal ofthe absorbing layer by preserving the underlying pa-tina.

These observations lead us to conclude that, foroptimum irradiation conditions, the pulse durationshould be short enough to induce a pressure transientthat is necessary for fast and efficient material re-moval, but not so short as to induce mechanical dam-age to the substrate. In this respect the SFR laser

Page 7: Cleaning processes of encrusted marbles by Nd:YAG lasers operating in free-running and Q-switching regimes

source we developed and utilized for this study pro-vided a preliminary validation of the possible advan-tages furnished by laser cleaning in the microsecondregime.

The authors thank M. Mazzoni of Istituto di Elet-tronica Quantistica for the use of her laboratory fa-cilities and M. Matteini from the Opificio delle PietreDure in Florence for helpful information about prep-aration of the experimental samples. This researchhas been supported by the Tuscany Regional Govern-ment and by the Special Project Cultural Heritage ofthe Italian National Research Council.

References1. J. F. Asmus, C. G. Murphy, and W. H. Munk, “Studies on the

interaction of laser radiation with art artifacts,” in Develop-ments in Laser Technology II, R. F. Wuerker, ed., Proc. SPIE41, 19–30 ~1973!.

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Congress on Deterioration and Conservation of Stone, J. Del-gado Rodriguez, F. Menriques, and F. Telmo Jeremias, eds.~Laboratorio Nacional de Engenhari Civil, Lisboa, Portugal,1992!; Proceedings of Third International Symposium on theConservation of Monuments in the Mediterranean Basin, V.Fassina, H. Ott, and F. Zerra, eds. ~Soprintendenza Beniartistici e storici di Venezia, Venice, Italy, 1994!; Workshopon Lasers in the Conservation of Artworks ~LACONA! ~Her-aklion, Greece, 1995!; Proceedings of First InternationalCongress on Science and Technology for the Safeguard ofCultural Heritage in the Mediterranean Basin ~to be pub-lished!.

4. M. I. Cooper, D. C. Emmony, and J. H. Larson, “A comparativestudy of the laser cleaning of limestone,” in Proceedings of theSeventh International Congress on Deterioration and Conser-vation of Stone, J. Delgado Rodriguez, F. Menriques, and F.Telmo Jeremias, eds. ~Laboratorio Nacional de EngenhariCivil, Lisboa, Portugal, 1992!, pp. 1307–1311.

5. M. S. D’Urbano, C. Giovannone, P. Governale, A. Pandolfi, U.Santamaria, “A standardized methodology to check the effectsof laser cleaning of stone surfaces,” in Proceedings of ThirdInternational Symposium on the Conservation of Monuments

in the Mediterranean Basin, V. Fassina, H. Ott, and F. Zezza,eds. ~Soprintendenza Beni artistici e storici di Venezia, Venice,Italy, 1994!, pp. 955–962.

6. K. Dorschel and G. Muller, “Photoablation,” in Future Trendsin Biomedical Applications of Lasers, L. A. Svaasand, ed., Proc.SPIE 1525, 253–279 ~1991!.

7. R. O. Esenaliev, A. A. Oraevsky, V. S. Letokhov, A. A. Karabu-tov, and T. V. Malinsky, “Studies of acoustical and shock wavesin the pulsed laser ablation of biotissue,” Lasers Surg. Med. 13,470–484 ~1993!.

8. K. Liu and E. Garmire, “Paint removal using lasers,” Appl.Opt. 34, 4409–4415 ~1995!.

9. J. F. Asmus, “More light for art conservation,” IEEE CircuitsDevices Mag. 6–14 ~March 1986!.

10. M. Matteini and A. Moles, “Le patine di ossalato di calcio suimanufatti di marmo,” in Quaderni dell’Opificio delle PietreDure e Laboratori di Restauro di Firenze, Marble RestorationIssue ~Opus libri, Firenze, Italy, 1986!, pp. 38–45.

11. M. I. Cooper and J. H. Larson, “Laser cleaning of marblesculpture,” in Abstracts of Lasers in the Conservation of Art-works ~Heraklion, Greece, 1995!, p. 6.

12. F. Margheri and P. Mazzinghi, “A short pulse, free runningNd:YAG laser for stone artwork restoration,” Opt. Commun.~to be published!.

13. S. Siano, R. Pini, R. Salimbeni, and M. Vannini, “A diagnosticset-up for time-resolved imaging of laser-induced ablation,”Opt. Laser Eng. 25, 1–12 ~1996!.

14. Yu. P. Raizer, Laser-Induced Discharge Phenomena ~Consult-ants Bureau, Plenum, New York, 1977!.

15. Ya. B. Zel’dovich and Yu. P. Raizer, Physics of Shock Wavesand High-Temperature Hydrodynamic Phenomena ~Academic,New York, 1967!, Vol. 1.

16. A. N. Pirri, “Theory for momentum transfer to a surface witha high-power laser,” Phys. Fluids 16, 1435–1440 ~1973!.

17. Yu. P. Raizer, “Subsonic propagation of a light spark andthreshold conditions for the maintenance of plasma by radia-tion,” Sov. Phys. JETP 31, 1148–1154 ~1970!.

18. M. I. Cooper, D. C. Emmony, and J. H. Larson, “The evaluationof cleaning of stone sculpture,” in Proceedings of the BathMeeting, C. A. Brebbia and R. J. B. Frewer, eds. ~Computa-tional Mechanics, Southampton, U.K., 1993!, pp. 259–266.

19. H. S. Carslaw, Conduction of Heat in Solids, 2nd ed. ~Claren-don Press, Oxford, 1989!, p. 75.

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