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Journal of Cultural Heritage 15 (2014) 391–402

Available online at

www.sciencedirect.com

Original article

Locating contact areas and estimating contact forces between the“Mona Lisa” wooden panel and its frame

Giacomo Goli a,∗, Paolo Dionisi-Vicib, Luca Uzielli a

a GESAAF, University of Florence, ViaS. Bonaventura, 13,50145 Firenze, Italyb Department of ScientificResearch, TheMetropolitanMuseumof Art, Fifth Avenue, 1000, 10028 NewYork, USA

a r t i c l e i n f o

Article history:

Received 14 May 2013Accepted 26 August 2013

Available online 23 September 2013

Keywords:

Mona Lisa

Painted panels

Mechanical constraints

Contact pressure

Contact forces

a b s t r a c t

Since 2004 an international research group of Wood Technologists has been given bythe Louvre Museum

the task of analysing the hygro-mechanical state of the Poplar (Populus alba L.) panel on which Leonardo

da Vinci painted his“Mona Lisa”, namely verifying the appropriateness of the thermo-hygrometric condi-

tions in its exhibiting showcase, where the microclimate is actively controlled, and assessing the potential

consequences of any hypothetical fluctuation. In order to acquire data about the mechanical behaviour

of the panel, and to feed and calibrate appropriate simulation models, the team has not only set up a con-

tinuous monitoring by means of automatic equipment, but has also performed manual measurements on

the occasion of the annual openings of the showcase where the masterpiece is conserved and exhibited.

This paper reports about techniques used for estimating the forces acting between the wooden panel

and itsframe (the châssis-cadre), and their location, such data being of primary importance for evaluating

the panel’s internal stresses. The contact forces have been calculated on the basis of the local contact

pressures, imprinted on a pressure-sensitive foil as a range of saturation values of the colour developed

in the contact areas. The forces calculated as above have also been compared with the contact forces

between the panel’s back face and the crossbeams pressing it against the châssis-cadre, which have been

measured by means of a load cell. As could be expected, the results from so different techniques do not

strictly coincide; however the agreement is fairly good.

© 2013 Elsevier Masson SAS. All rights reserved.

1. Research aims

The research presented in this paper aims to provide realis-

tic information about magnitude and location of the forces acting

between the wooden panel on which Leonardo da Vinci’s “Mona

Lisa” is painted, its crossbeams and its frame. Such data are of

primary importance for analysing the mechanical situation of the

panel and calibrating an appropriate simulation model of deforma-

tions and stresses produced by the environmental fluctuations, in

order to evaluate and optimize any measure, which could improve

its conservation.

2. Introduction

2.1. A short description of the Mona Lisa panel’s structure and

geometry

Approximately five centuries ago, Leonardo da Vinci painted his

world-known Mona Lisa on a panel made of a one-piece tangential

∗ Corresponding author. Tel.: +393290656674; fax: +39055319179.

E-mail addresses: [email protected] (G. Goli),

[email protected] (P. Dionisi-Vici), [email protected] (L. Uzielli).

boardof Poplar(PopulusalbaL.)∼79×53cm,∼13mmthick,which

arrived at our age almost unaltered except minor interventions (for

further details see [1]).

Only the front face is painted, whereas thepanel’soriginal wood

surface shows up on the back face.

The panel features a complex double curvature, developed

throughout the centuries under the effect of the mechanical con-

straints and the environmental variations to which it has been

exposed, and also influenced by the∼11cm-long crack, running

parallel to the grain through the panel’s whole thickness, starting

from the upper edge, and reaching the lady’s forehead, above her

right eye.

The panel is inserted in a frame (châssis-cadre) made of Oakwood, and is slightly forced against the 7.5mm wide rim of the

frame by means of four Sycamore ( Acer pseudoplatanus L.) wood

crossbeams, whichare fixed by screwsto the châssis-cadreand hold

the panel flatter than it would be if unconstrained. Due to the lon-

gitudinal curvature of the panel usually only twoof the crossbeams

(the top and the bottom one) press against it, occasionally a third

one can be in contact with the panel.

Panel and châssis-cadre are inserted in a larger wooden gilded

frame, the only visible by the public.

An exploded drawing of the assembly (painted panel, châssis-

cadre, crossbeams, frame), made in 2004 by the restorers in charge

1296-2074/$ – seefrontmatter © 2013 Elsevier MassonSAS. All rightsreserved.

http://dx.doi.org/10.1016/j.culher.2013.08.003

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392 G. Goli et al. / Journal of Cultural Heritage 15 (2014)391–402

Fig. 1. An exploded drawing of the assembly: painted panel (1), châssis-cadrewith crossbeams(2),gilded frame (3). The fissure is in the upper part ofthe panel.

Drawing byD.Jaunard andP.Mandron, 2004 modified.

of the wooden support, is shown on Fig. 1; due to successive inter-

ventions, the cross-sections of the present crossbeams are slightly

different from those shown in the drawing.

The panel is maintained into a climate-controlled display

case, which gets opened yearly to check the conditions of the

painting.

2.2. The main studies carried out to analyze the mechanical

situation of the panel

Since 2004 an international team of scientists has been given

by the Louvre Museum the task of analysing the hygro-mechanicalstate of the Poplar panel. The questions asked by the Museum’s

Curators were basically to evaluate the climatic specifications for

the display case, assess the risk of crackpropagation, suggest possi-

ble modifications to the framing system, and suggest any measure,

which could improve the conservation conditions or the annual

check-up procedure. An in-depth study of the panel, including its

wooden support and the systemof cracks in the paint layers, is pre-

sented in [2] and [3]. An analysis of the risk of propagation of the

fissure laying in the upper part of the panel is reported in [4].

In order to have a better understanding of the physical and

mechanical behaviour of thepanel, specific simulation models were

developed and validated against measurements and monitoring of

its actual behaviour.

The measurements include:

• the forces exerted by the upper crossbeam on the upper part of

the panel, being automatically measured at 20minutes intervals

by a monitoring equipment purposely developed and adapted

(see [5]);• the forces exerted on the contact points between the panel and

the crossbeams, manually measured every year on the occasion

of the annual opening of the showcase;• three transversal profiles of the panel, measured manually every

year by means of a precision comparator on few selected points;• the shape of thepanel’sconvexity, alsomeasuredyearlyby means

of optical techniques: in particular the 3D surface inside and out-

side its frame was reconstructed by the means of stereo imaging

and light projection systems (see [6] and [7]).

A FEM model based on heat & mass transfer + hygro-mechanical

behaviour was also implemented, and calibrated by means of the

collected data (see [8] and [9]).

Work is still on going, and further data keep being collected,

both with the same techniques and with new or improved ones.

2.3. The objectives of this paper

If the panel’s shape were perfectly cylindrical, it would touch

the châssis-cadre only in the central parts of its upper and lower

rims. On the contrary, the complex shape of the panel makes the

contact zones quite irregular and difficult to be identified.

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G. Goli et al. / Journal of Cultural Heritage 15 (2014)391–402 393

Fig. 2. a: schematic diagram indicating the zones of the rim, where the pressure-sensitive foils was applied for the measurements; b: the right upper corner (seen from

behind) of the châssis-cadre, with the pressure-sensitive foils applied on the rim; here the châssis-cadre is dark, and the whitish pressure-sensitive foils strip is wider than

the rim, which canbe seen with some difficultythrough thetranslucent film; thepurple marks on thecorner have been obtained by applying pressure on pressure-sensitive

foils with a ballpoint, in order to make easy thesuccessive identification of thestrip’s location.

Previous direct observations indicated thatcontact areasare not

onlydistributedalongtheupperandlowerrimsofthe châssis-cadre,

but also a third contact area exists on the left (seen from behind)

rim, not far from the upper side (as shown on Fig. 2).

However, despite several attempts, no accurate evaluation of

the location of contact areas, let alone of contact pressures, could

be performedbefore thisstudy;difficulties originated notonly fromthe extreme care required in any handling or manipulation of the

artwork itself, but also from the presence of the “barbe” (crest on

the edge of the colour layer) running all around the perimeter of

the painting itself (see [1]).

Since theactual contact areas between thepanel’sfrontfaceand

the châssis-cadre cannot be anticipated a priori, the measurements

performed until now only allowed to roughly estimate, by means

of equilibrium calculations, just the magnitude and action line of

the resulting forces acting between panel, crossbeams and frame,

but not their actual distribution.

However, the FEM model mentioned above is quite sensitive

to the magnitude and distribution of such forces, therefore a new

seriesof measurementswas planned inorderto provide more com-

plete anddetailed ones, being of primary importance in order to be

used as input in the model, for better evaluating the panel’s actual

internal stresses.

This paper reports about such additional measurements, which

have been performed by means of a commercially available

pressure-sensitive multilayer foil. The contact forces have been

computed on the basis of the local contact pressures, imprinted

on the pressure-sensitive foil as a range of colour densities devel-oped in the contact areas. The results have finally been compared,

by equilibrium calculations, with the results of the manual mea-

surements of forces.

3. Materials and methods

3.1. The reference system

In order to properly identify the points were the forces are

applied as well as for computations, the following convenient ref-

erence system was adopted (see Fig. 5):

• the originof axes is located at the internal upper left corner (seen

from behind) of the panel, approximately coinciding with the

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Fig. 3. Theimproved procedure, during thesecond measuring campaign (2012). a: the pressure-sensitive foils was applied on limited zones of the châssis-cadre rim; b: the

châssis-cadrewas maintained vertical and the crossbeams were held tight directly by hand.

completely clamped against the châssis-cadre. In fact it could be

that the contact areas and pressures changed along time in such

a way that some maximum values took place at some intermedi-

atephase duringthe process of clamping thecrossbeams.However

in the described context such possibility appears unlikely, and in

any case it would have been impossible to analyse the evolution of

areas and pressures along time; therefore such possibility will not

be considered here.

3.5. Measuringmanually the forces between crossbeams and

back face of the panel

The forces exerted by the crossbeams on the panel have been

measured every year since 2005 by means of a procedure and a

device presented in [5]. Some further details are given in the fol-

lowing. The device is composed of an uni-axial load cell equipped

with a support that canbe temporarily fixed to the châssis-cadreby

means of a small clamp; the load cell measures forces applied to its

front end along the direction of a threaded rod, which can be used

to adjust the height of the contact point; a steel ball and a washer

ensure a centred contact between rod and panel, and a convenient

distribution of the contact pressure on the panel (see Fig. 5b). To

perform the measurement of the force acting on the contact area

between the panel and the end of a given crossbeam, the rod’s end

is driven in contact with the panel’s back, as near as possible to theselected area; to ensure the firmness of the contact, the rod gets

moved forward until the load cell reads a limited force. The end

of the crossbar gets then unscrewed, so that the whole load gets

transferred from the crossbeam to the load cell, without any dis-

placement of the panel. The load cell capacity was 100N and the

accuracy 0.03%.

Such measurement is performedat all thecontactpoints, which

aretypically Locations1, 2, 7, 8 (see Fig.5a), since due tothe convex

shape of the panel normallyno contact takes place in Locations3, 4,

5, 6; however in 2012, possibly due to a minor modification made

on one of the panel’s contact points, contact took place at Location

4 as well.

Note. The measuring system described above is potentially

affected by several inaccuracies, including:

• the uncertain location of the actual contact zones between the

crossbeams and the backside of the panel;• the distancebetweenthe locations where theforces wereactually

measured, and the actual contact zones mentioned above;• thepossibleinfluence of thecontactforce between rodand panel,

and of relaxation phenomena.

In the present context such inaccuracies could not be pre-

vented noranalysedin greater depth; theywill thereforebe lumped

together, and estimated as a global inaccuracy of approximately

10%, quite larger than the one of the load cell alone.

4. Results

4.1. Contact areas and pressure values for the individual areas

The contact marks obtained from the second measurement

campaign were clearly visible and definitely produced by a per-

pendicular force, without any lateral sliding. Therefore, we may

assume that no double or false marks were present.

The contact marks are in most cases located near the edges of

the rims; this is clearly a consequence of the convex shape of the

panel, which can seldom rest flat against the whole rim.

Also, the marks are numerous, discontinuous and quite small,

which highlights the obvious unevenness of the contacting sur-faces; such unevenness can be attributed to several factors,

including effects of processing methods or tools, and of the

macrostructure of wood.

The contact areas and pressure values rounded up to steps of

0.1MPa are shown on Fig. 6.

4.2. Forces, and their action lines

Having thus determined the individual areas and the respective

pressures acting on them (assumed to be all perpendicular to the

average plane of the châssis-cadre), the resulting force was com-

puted for each area, for each rim of the châssis-cadre, and for the

whole of it,by simple vectorsumming; theresults are shown in the

following. Fig.7 shows howthe contact forcesare distributed along

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Fig. 4. Outline of the procedure adopted for deriving the relationship between the colour densities recorded on the pressure-sensitive foils strips and the corresponding

pressure values. a: colourdensity references fromthe pressure-sensitive foilstechnical data sheet; b: desaturated colourdensity references fromthe pressure-sensitive foils

technical data sheet;d: an impressedpressure-sensitive foils strip;e: a selected part from theimpressed pressure-sensitive foils strip;f: theimagein (e)afterdesaturation;

g: contact areas manually determined and selected; h: for each area the mean grey value determined; i: pressure values identified foreach individual area, according to its

mean grey value; l: each area coloured according to theestimated pressure.

the rims of the châssis-cadre; eachrim was divided in 10 segments,

and the total force acting on each segment was computed, shown

in a table andgraphically represented by the colourof thesegment.

Fig. 8 shows the locations of the points where the resultingforces could be considered to be applied. Such locations were com-

puted bymeans of the ImageJ software, as the centre of mass of the

contact areas, each area being weighted by the grey-scale level of

the desaturated scan after image inversion.

Table 1 summarizes the total forces acting on the individual

rims, and on the châssis-cadre as a whole, resulting from measure-

ment made with PSF method.

Table 2 summarizes the forcesbetween thepaneland thecross-

beams, measured manually (according to the method described in

§ 3.5) on the same day, about 1 hour earlier than the PSF measure-ments.

In fact, the moisture content and the moisture gradients of the

panel are likely to change in time, and hence also its distortion

and the contact areas and forces; therefore the results reported

Table 1

Summary of the magnitudes of forces between panel and châssis-cadre, resulting

from measurement made with PSF method. Locations A, B, and C are shown on

Fig. 8.

Location A B C Total force

Identification, seen

from back

(Top,

centre)

(High, l eft) (Bottom,

centre)

Force (N) 24.6 5.8 20.5 50.9

PSF: pressure-sensitive foils.

here are likely to change in time, depending on the surrounding

microclimatic conditions and on their variations.

4.3. Comparison between forces measured with the two methods

In the following, the two force systems will be compared:

• the forces acting between panel and châssis-cadre, measured by

means of the PSF method (see § 3.3), reported in Table 1;

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Fig. 5. a: the new crossbeams installed in 2005 (crossbeams 1 and 4 are wider than the previous ones), and the five locations where the contact force between the panel

and thenearby crossbeamend have been manually measured (although in previous instances thecontact was present in locations1-2-7-8 only, in this case a slightcontact

was detected andmeasuredin location 4 as well). Theoriginof theXY coordinate systemis located on theupper left corner(seenfrom behind) of thepanel, approximatelycoinciding with thecorresponding internal cornerof the châssis-cadre; b: thedeviceused forthe manual measurement of thecontact force in selected locations.

Table 2

Summary of themagnitudes of forces between panel and crossbeams, resulting from measurementsmade with the manual method. Locations1, 2, 4, 7, 8 are numbered as

in [5], and are shown on Fig. 5b.

Location 1 2 4 7 8 Total force

Identification, seen from back (Top, left) (Top, right) (Mid height, right) (Bottom, left) (Bottom, right)

Force (N) 10.0 10.4 14.9 15.9 3.5 54.6

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Fig. 7. Distributionof thecontact forcesalongthe rims of thechâssis-cadre; each rimwas divided in 10 segments,and thetotalforceacting on each segment wascomputed,

shown in the relevant table and graphically represented by the colour of the segment. Each segment of horizontal rims is 53.8mm long, each segment of vertical rim is

65.9 mmlong. Like in previous figures, the view is from the back.

(already discussed in the relevant sections of this paper) will be

considered satisfactory for the purpose of this paper.

Apart from what has been mentioned above, the comparison

cannot be made by just comparing thetotalforces shownin Table 1

and Table 2 because the forces measured with the two methods

have different application points (i.e. Locations A, B and C do not

coincide with Locations 1,2,4,7 and 8), and more complete equilib-

rium conditions need to be verified at any time as follows.

If the panel is physically in equilibrium, the complex of all the

forces and all moments acting on it must be balanced,i.e. their vec-

tor sums must be equal to zero. For the purpose of this analysis, we

analyse the equilibrium in the vertical position, and we neglect the

force of gravity acting on the panel and the vertical forces, which

counteract it, being applied on its lower edge. Therefore we may

consider that when the panel is vertical only the two horizontal

force systems (i.e. the forces between panel and châssis-cadre, and

theforces between panel andcrossbeams)act on it,and must glob-

ally be equal and opposite to each other. In mathematical terms,

equilibrium exists when the following conditions are satisfied (for

the sake of simplicity the panel is here assumed to be flat, with

its central plane parallel to the plane defined by the rims of the

châssis-cadre):

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Fig.8. Locationsof thepointswhere theresultingforcescould be considered to be applied; coordinates, referredto theinternalupper leftcornerof thechâssis-cadre(assumed

to coincide with theupper left cornerof thepanel), were computed by means of theImageJ software.Like in previous figures, theview is from theback, as if thepanelwere

transparent. Thegrey band surrounding the painted area is the unpaintedpart of thepanel.

•

the vector sum of the forces acting perpendicularly to the panelplane equals zero (˙ Z = 0);• the vector sum of the moments about any horizontal axis con-

tained in the central plane equals zero (˙ Mx=0);• the vector sum of the moments about any vertical axis contained

in the central plane equals zero (˙ My=0).

Any deviation from the above equilibrium conditions will show

an unbalance between the two force systems, or rather between

their supposed magnitudes, which wereobtainedby the two differ-

ent measurement methods; and hence any deviation will indicate

a disagreement between the two measurement systems (with the

uncertainties discussed above).

Obviously such analysis cannot indicate by itself if and how

much one of the measurement methods is “better” or more

accurate than theother, allthe more that an additional discrepancyis certainly caused by the above mentioned contact at Location 4

and force of gravity action; however a reasonable agreement will

add value to both of them, and encourage the exploitation of the

one providing, case by case,the information mostuseful andappro-

priate for specific tasks.

As regards condition (a), i.e. equilibrium of total forces act-

ing along the Z axis, the forces measured with the PSF globally

amounted to −50.9N, while the forces measured with the man-

ual system globally amounted to 54.6N. The resulting unbalance

amounts to 3.7N, or 7.3% of the PSF measurement. If we consider

that:

• according to the PSF specifications the measurement accuracy is

10% of the measure itself;

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Table 3

Calculation of moments actingon thepanel after havingchosen referenceaxes (x= 6 mm andy = 229mm) whichprovided largest magnitude of the unbalance,and assuming

the forces measured by the load cell to be located at mid-width of the crossbeam and at 10mm distance from the panel’s edges. This computation intends to quantify the

amountof theunbalanceof themomentsappliedto thepanel bythe forcesmeasured with thetwo measurement methods:(1) thesecond-last row shows thefinal unbalance

values, i.e. thealgebraic sumof allmoments applied to thepanel(boththe ones produced by thecrossbeam forces, measured by theloadcell method, andthe ones produced

by the contact with the châssis-cadre, measured by the PSF method); (2) the last row shows the same final unbalance values, expressed as percentages of the sum of the

absolute valuesof themoments produced by theforces measured by thePSF method.

Moments referred to X’ line (parallel to X axis) Moments referred to Y’ line (parallel to Y axis)

Momentarm [m] Force [N] Moment [N m] Momentarm [m] Force [N] Moment [N m]

Forces exerted by crossbeams, and resulting moments Forces exerted by crossbeams, and resulting moments

Location 1 0.037 10.0 0.37 Location 1 −0.219 10.0 2.19

Location 2 0.037 10.4 0.38 Location 2 0.299 10.4 −3.11


Location 7 0.753 15.9 11.94 Location 7 −0.219 15.9 3.48


Forces calculated by PSF method, and resulting moments Forces calculated by PSF method, and resulting moments

Location A 0.000 24.6 0.00 Location A 0.146 24.6 3.58

Location B 0.225 5.8 −1.30 Location B −0.223 5.8 −1.30

Location C 0.778 20.5 −15.96 Location C 0.000 20.5 0.00

Sum ofall the moments applied[N m] 2.06 Sum of all the moments applied [N m] −0.64

% of sum of PSF moments [%] 12.0 % of sum of PFS moments [%] 13.0

PSF: pressure-sensitive foils.

• in§ 3.5the accuracy of the manual systemwas estimatedaround10%aswell,wemay conclude thatthe twosystems provide forces

along the Z axis having very similar magnitude confirming that

the total forces are comparable.

For conditions (b) and (c) the reference lines in respect to

which the moments should be calculated have been defined by

means of the following procedure. Since the computed moments

are not independent from the assumed reference lines, it would

be meaningless to express the resulting unbalance of moments as

a percentage of the magnitude of a generic resulting moment. In

order to express the unbalance as objectively as possible, refer-

ence lines X’ and Y’, parallel to X and Y axes, were chosen so that

the unbalance was the largest possible. This was done by means

of a trial-and-error procedure applied to the absolute values of the moments computed for the PSF method. The lines resulting

in the largest unbalance resulted as y= 6mm for the line X’ and

x = 229 mm for the line Y’, in the reference system defined in§ 3.1.For the computation of the acting moments the forces measured

with the manual system were considered as acting on the centre of

the crossbeams width, at a distance of 10mm from the panel edge.

Table 3 shows the simple calculations expressing the equilibrium

of the moments.

As can be observed in Table 3, the sum of the moments acting

on the X’ line amounts to 2.06N m (or 12.0% of the moment calcu-

lated by PSF method), and similarly the sum of the moments about

the Y’ line amounts to −0.64N m (or 13.0% of the moment calcu-

lated by PSF method); hence the two methods provide comparable

moments, being very close to the system’s estimated accuracy.

5. Conclusions

The PSF method for measuring the contact areas and contact

pressures between panel and châssis-cadre, and hence computing

magnitude and action lines of the contact forces, has here been

implemented and evaluated. The following conclusions may be

drawn from the reported tests and calculations:

• the production of the contact marks is totally non-invasive, and

can be performed in a reasonably simple way. However, it is

essential to implement appropriate well planned procedures,

namely in order to prevent the formation of “false” marks, pro-

duced by slipping between the contacting surfaces;

• the processing of the imprinted marks in order to derive thepressures, the forces and their action lines is complex and

requires several steps and calculations; the whole procedure can

be performed by means of open-source software, however some

steps could be made quicker and simpler by using specific com-

mercial software;• the reliability of the PSF method has been tested by comparing

its results with those from the manual measurement of forces

acting between panel and crossbeams by means of a load cell.

Obviously such comparison cannot indicate by itself if and how

much each methodprovides “true”results, or oneof the methods

is “better” or more accurate than the other;howeverthe resulting

reasonable agreement supports the validation of both of them,

and encourages the exploitation of the one providing, case by

case, the information most useful and appropriate for specifictasks;

• the results obtained by the PSF method, which provides both

magnitude and location of the contact forces, can be used as

a valuable input in mathematical hygro-mechanical models for

the prediction of the mechanical response of the panel, under

changing micro-environmental conditions.

Acknowledgments

The authors would like to thank the numerous colleagues who

made this paper and the described work possible. Among them,

unfortunatelytoo manyto be allcited, thefollowing onesare specif-

ically mentioned with pleasure and gratefulness:

• Vincent Delieuvin, curator in the department of paintings, Musée

du Louvre, for givingpermission to perform this newkind of test;• Elisabeth Ravaud, from C2RMF, coordinator of the testing sched-

ule, for allocating the necessary time slots;• Daniel Jaunard and Patrick Mandron, restorers of wooden sup-

ports, for their contribution in defining the procedure for

obtaining reliable contact marks and also for providing their

drawing shown on Fig. 1;• Joseph Gril and all the colleagues of the study team, for the sup-

port given in deciding and implementing the described tests;• thecolleagues Linda Cocchi andPaola Mazzanti for their help and

support in preparing the PSF strips and during the manual force

measurements.

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Authors contributions: G.Goli mainly set up and carried out

the tests and analyses with the PSF film; P.Dionisi-Vici mainly

set up and carried out the manual measurement of the forces;

L.Uzielli coordinated the measurement procedures. The three

authors equally contributed to the writing of the paper.

References

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Abrams, Inc., New York, 2006.[2] E. Ravau d, The Mona Lisa’s wooden support, in: J.P. Mohen, M. Menu,

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