OPTICAL TECHNIQUES FOR RELIEF STUDY OF MONA LISA'S WOODEN SUPPORT

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1 OPTICAL TECHNIQUES FOR RELIEF STUDY OF MONA LISA'S WOODEN SUPPORT Fabrice Brémand, Pascal Doumalin, Jean-Cristope Dupré, Franck Hesser, and Valéry Valle Laboratoire de Mécanique des Solides, CNRS, UMR 6610, Université de Poitiers SP2MI Bd M. et P. Curie, Téléport 2, BP 30179, Futuroscope Casseneuil cedex, France ABSTRACT Te aim of our study is to obtain a wole field 3D profile of te wood support of te famous painting: Mona Lisa, on front and back faces several times in a day. Tese data allow understanding te mecanical impact of te frame in wic te panel is maintained attaced and can be used to describe te ygromecanical beaviour of te wooden painting. Out of plane displacements and tickness ave been measured and ave been used to validate a numerical simulation of te ygromecanical beaviour of te panel. Two tecniques ave been tested: sadow moiré metod and fringe pattern profilometry. After a previous test realized at te C2RMF (Centre de Recerce et de Restauration des Musées de France) laboratory on a painting of te same period, sadow moiré metod as been cosen. It is more accurate but especially less sensitive to te dark tints, to te canges of contrast and colour of te picture, or its luster. During te testing day, we ave observed te out of plane deformation of te panel. A contraction of te order of 3/10 mm was detected early in te middle rigt part of te panel. Tis deformation is due to te wood s beaviour variations in response to atmosperic conditions of umidity and temperature, wic are not te same in te room as in te case. Te greatest distortion was observed wen removing te frame (±1 mm)., te out of plane displacement and curvatures are maximal near te crack (upper middle left part) and also in te lower part of te panel. Introduction We present in tis paper an original application of te use of optical metods for te study of te famous painting: Mona Lisa. Several laboratories [1] ave participated to tis study in order to evaluate te degradation risk (specially in relation wit te existing crack) and to optimise te conservation conditions (regarding bot te umidity regulation and te design of te frame). Mona Lisa is painted on a poplar support, so our own contribution was to obtain a wole field 3D profile of te panel on front and back face of Mona Lisa. Furtermore, tese values allow understanding te mecanical impact by te frame in wic te panel is maintained attaced and are used to describe te ygromecanical beaviour of te wooden painting by many measurements performed during several ours. Tese experimental data ave been used to realize a numerical model of te panel, and also to validate te numerical simulations of te mecanical beaviour of te panel [1][2]. Te difficulties of tis work are different tan te classical ones in laboratory. For safety problem, we were able to study te painting only a single day. No test can be realized before and after. So large number factors: like brigtness, contrast of te painting and room's ligting in te Louvre museum, are unknown. Te experimental conditions impose tat te measurement tecnique uses a low ligtening of te painting and a minimum apparatus. Te known parameters are te dimensions of te studied zone, relatively large 800x600 mm 2, te attended uncertainty allowing a accurate comparison wit te numerical simulation (about 0.01 mm) and te speed of measurement (several minutes) wic allows studying te ygromecanics beaviour. So, two tecniques ave been cosen: sadow moiré and projection moiré. Te first tecnique is te more precise but more complicated to put into practice (specially te use of a reference grating put on te front of te specimen). It is generally used to study te beaviour of materials under mecanical stresses, but also to determine te form of small objects. Te second tecnique, is less sensitive, but easier to employ, it can be used for large objects. In te present protocol dedicated to Mona Lisa, wic is entirely witout te elp of invasive tecniques, tese two metods were clearly indicated, since tey would not involve pysical contact wit te paint layer.

2 Principle of sadow moiré tecnique (SMT) Te sadow moiré tecnique (SMT) [3][4][5][6] consists in projecting a line grating in front of te object wit te elp of a punctual ligt source, as sown on Figure 1. Superposing te grating and its sadow on te object leads to a moiré penomenon. Moiré fringes correspond to te contour lines of te relief of te object. Te relief Z at te point of x coordinate is determined by te following relation [6]: Z SMT p = k x d x + + Z + Z S O (1) were k is te fringe order or te number of contour lines, d te distance between te ligt source S and te observer O, S te distance between S and te plane of te grating pitc p, o te distance between O and te grating. It makes sense to consider, tat projected and observed beams are collimated. Indeed, tis assumption can be made if te relief Z is small compared to o and s. Furtermore if te distance S is equal to te observation distance o ( = o = S) ten te relief is proportional and linear to contour lines. Tis relief can be determined as a function of te pase ϕ of te grating obtained by a pase sifting process, as sown in te following relations from equation (1): Z SMT ϕ p. = 2π d = ϕ Z 2π (2) were Z, te sensitivity factor, corresponds to te relief between two contour lines. Figure 1 : Principle of projection fringe metod Figure 2 : Set-up of fringe pattern profilometry As a master grating is required in front of te object, tis measuring metod cannot be applied on extra large object. To eliminate geometrical distortions, te relief of a reference plane can be subtracted to te one of te object.

3 Principle of fringe pattern profilometry (FPP) In order to allow te study of larger objects, Durelli [8], Pirroda [9] and Teocaris [10, 11] ave developed te projection moiré metod or fringe pattern profilometry (FPP). Tey ave used te set-up sown on Fig. 2. Te principle of tis metod consists in projecting a fringe pattern first on a reference plane and ten on te studied object [7][8][9][10]. Te first image corresponds to te master grating of sadow moiré. Te second image comes from te grating projected onto te object and corresponds to te sadow of te grating used in sadow moiré. Fringes similar to tose of sadow moiré can appear by adding bot images. Nowadays, tanks to te numeric tool wic is easier to use, bot images are recorded independently and analysed separately by means of pase sifting described in te next paragrap. In sadow moiré, te introduction of pase sifting is quite difficult to carry out (witout modifying contour fringes). However, in projection moiré, we need only to sift te grating in its plane. If te assumption of collimated beams is kept, te relief is ten proportional to te pase difference (φ) between te values obtain on te reference plane (ϕ R) and te second one calculated on te object (ϕ O). Relief is ten determined by te following simplified expression, wic is similar to te sadow moiré relationsip: Z FPP ( ϕo ϕ R ) Pproj φ Pproj. = = 2π tanα 2π d wit d tan α =, p Pproj = and = o = p (3) cos α Anoter solution, wic is not described ere, consists in applying a particular calibration in order to avoid te reference plane [11]. Principle of fringes analysis For bot tecniques, te ligt intensity (I) recorded by te CCD camera can be expressed, at eac pixel (, by I( = I0( + I1( sin( ϕ( ) (4) wit I 0 as te background and I 1 as te amplitude of te fringe pattern. Te accuracy of te relief measurement is function to te pase analysis process. Te more accurate fringe analysis procedures consist in recording several images and introducing a pase sift θ k (eq. 4). I = I ( + I ( sin( ϕ ( + θ ) k ( 0 1 k (5) From at least tree values of θ k, and te corresponding images, one can solve equation 5 [11][12][13]. We ave to use a procedure given a ig accuracy wit a low sensitivity of background and amplitude variation. Tese two last points are very important because te painting as dark or brigt zones. Furtermore, te ligting can not be constant during te test. So we ave cosen a solution allowing to analyse te frequency of a signal and not te intensity, wic allows to minimize tose effects [14][15]. Tis tecnique is reliable and as already been used for moiré and potoelasticity studies [14][16]. It consists in sifting te signal in order to temporally obtain a series of images wit an integer number of period at eac pixel. Te temporal computation of te Fourier transform for eac pixel in te series of images is done in order to extract several armonics. For example, for a sift of one period, te pase can be calculated by: 1 ϕ( = tan 4 1 Im( C Re( C ( ) ( ) (6) Wit C +1 wic represents te first armonic of te complex Fourier spectrum. A pase unwrapping process allows to obtain te continuity of te derivatives of te pase field [17][11]. Tis procedure can be used for SMT or for FPP. For sadow moiré metod, te introduction of pase sifting is obtained by moving te master grating in te z direction. For te second tecnique, it is simply obtained by numerically sifting te projected grating. Previous tests ave been performed to evaluate pase accuracy. Tese tests ave been made on plate of polycarbonate painted in wite. Te obtained accuracy is about 1/200 of wave lengt ( 3 ). Tis value is twice as greater as te one for pase sifting wit 3 images.

4 From equations (2) or (3), we can evaluate uncertainties function to pase values. Te bot expressions are similar; te accuracy is function to te geometric parameters, te period of te grating and te uncertainty on te measured pase. Z SMT p. = 2πd ϕ pproj. = 2πd For a similar device, te differences are due to te period of te grating respectively p and p proj. Experimentally, te pitc for te FPP is five to ten times as bigger as te one for SMT, ten te accuracy decreases in te same way. For example for d and p=1mm, we obtain z FPP 0.1 mm taking into account te accuracy of te pase: z SMT 0.01mm and for p proj=10mm Z FPP φ Figure 3 : Details of recorded image from te FPP and steps for pase calculation (Marco d'oggiono "Mary breastfeeding Jesus ". First Experimental test If SMT gives better accuracy, te specific conditions of te present work does not allow us to coose between FPP and SMT. A first experimental case as been made to definitively adopt te best solution. So a quick experimental test as been realized te day before. Tis study as been performed on a same period painting (beginning of XVI t century),wic is supposed aving te same contrast and brigtness (Figure 3). A profile of a detail is plot on Figure 4. We can see tat SMT gives better results in te ligt zone (factor 2) tan in te dark zone (factor 4).Te RMS error is about 0.03 mm for SMT and 0.11 mm to 0.05 mm for FPP. Tis calculation involves small variations due to te painting and te master grating (reference or projected). Tis test confirms tat SMT is te more efficient metod for tis study.

5 Dark zone Ligt zone relief (mm) coordinates FPP SMT Figure 4 : Comparison of te relief profile obtain by te two tecniques Experimental test procedure Te set-up is sown on Figure 5. Te locations of te grid, te CCD camera and te ligt source ave been coosing related to te conditions of relationsip 2. Te panel as been analysed wit a resolution equal to 600x900 pixels and te pitc of te grid is 1 line/mm. Several measurements ave been realized during te day. Tis made it possible, on one and, to optimize te measuring metod by improving te acquisition conditions and, on te oter, to observe te picture s beaviour wen it was removed from its glass case. Te first (TEST.I) attempt was realized just after te panel was taken from its case, te second (TEST.II) one after a period of two and a alf ours and a series of tests for wic te crossbars wic maintain te panel into te frame were unscrewed, and ten screwed back on. Te tird one was carried out after te panel ad been removed from its frame, and concerned bot te front (TEST.III.f) and back (TEST.III.b) of te panel. Te last attempt (TEST.IV) was performed after te panel ad been refitted into its frame, six ours after te picture was taken from its case. To take account of te manipulations and movements of te painting in assessing te data, a specific procedure was added to our program. Tis consisted of calculating an average plane for te panel, wic was subsequently subtracted from te measurements recorded. Witout positing any ypotesis, a relief relative to tat average plane was obtained at a fixed point on te picture. Te panel s average plane was calculated from its upper and lower edges, were tere is less distortion. Figure 5: Experimental device: 0=4,30 m ; S= 4,30 m; d=2,65 m. Relief measurement A first qualitative examination was quickly performed. By placing te picture beind te reference grid, it was possible to observe te relief directly in te form of contour lines (Figure 6-a). Taking account of te experimental device, we ad about two millimetres between two fringes. We see concentric fringes, wic allowed us to conclude tat te picture is not flat, but bulged on te rigt and side. Te quantitative measurement is obtained by te presented procedure compiled in our software wic calculates te relief for every point. One result is presented on Figure 6-b. Te precision obtained is a function of te contrast of te

6 picture and te state of its surface, wit levels of uncertainty canging from place to place overall, tese being globally 5/100 of a millimetre and ranging between 2/100 mm and 1/10 mm. In order to increase accuracy, a low-pass filter (3x3 pixels) is used. a :Recorded image of te sadow moiré fringes b :Relief (mm) Figure 6 : TEST.I (on te face of te painting) Out of plane displacement By comparing te measured relief during te day, we ave calculated te out of plane displacements of te panel. A contraction of te order of 3/10 of a millimetre was detected early on in te centre rigt part of te panel between TEST.III.f and Test.I (Figure 7-a). Two causes for tis may be advanced, te first related to te unscrewing and screwing back of te crossbars, and te second linked to variations in termoygrometric conditions of its environment, inasmuc as te panel ad been out of its case for two and a alf ours. Te igest displacement was observed on removal from te frame (±0.75 mm) between TEST.III.f and Test.I (Figure 7-b), te deformation and curvatures are largest close to te crack and also in te lower part of te panel. Tis is an indication tat tese bot zones are more strongly affected by bending effect. After te panel ad been refitted into te frame, te out of plane displacements between TEST.IV and Test.I are about 3/10 and +12/10 of a millimetre. Its sape was practically identical to tat obtained after unscrewing and screwing back te crossbars (Figure 7-a). In oter words, te convexity observed at te beginning was maintained. Tese values were used by J. Grill et al to validate teir ygromecanical simulation using a 1D or 2D version of Transpore software [18][2]. Teir algoritm gives predictions for te reaction of a panel portion in te bot extreme situations of free or blocked curvature [1]. Taking as state of reference te second relief (TEST.II) obtained two and a alf ours after te extraction and refitting into te frame, we were able to eliminate effects due to andling and te first variations due to termoygrometric beaviour of te wood. Te convex area is better defined (Figure 8-a). Its maximum follows an inclined axis of 10 compared to vertical and goes troug te split in te panel. From a mecanical point of view, te panel is subject to a combined effect of bending and torsion. In order to visualize te zones of ig curvature, were te stresses are concentrated, te second derivative of te out of plane displacement according to orizontal was calculated given values proportional to te bending moment. Te conclusion is tat stresses are concentrated at te level of te split but also at te bottom of te picture (Figure 8-b). Tickness determination A mapping of tickness was calculated from te relief obtained for te front and back surfaces (TEST.III). Te positioning of te two surfaces was effected in te ligt of depts measured by te Frenc Centre for Museum Researc and Restoration at te four corners of te picture. From tis map, a computer model representing te picture s volume was used for virtual visualization purposes (Figure 9) and/or computer calculations. Tis model made it possible, wit te elp of a rapid prototyping macine, to produce a small-scale manipulable replica (Figure 9).

7 (a) TEST.II (b) TEST.III.f Figure 7: Out of plane displacement (mm) of te panel versus TEST.I (a) Out of plane displacement (mm), (b) Corresponding curvature (mm -1 ) Figure 8: (TEST.III.f) versus ( TEST.II) Figure 9: Mapping of te tickness (mm): reverse side view (orizontal and vertical scale reduced to=14% and true relief scale) Conclusion SMT used for tis study was cosen because it is more accurate but specially less sensitive to te dark tints, canges of contrast and colour of te picture, or its lustre. Furtermore SMT made it possible to image te picture s relief as contour lines. Since it avoids pysical contact, it is a tecnique tat neiter damages te picture nor disturbs te

8 quantities tat are to be measured. It terefore allows measurements to be taken from te panel s painted side. Tests were undertaken in te actual room in te museum in wic te picture is displayed witout particular precautions regarding ligting. Just a few seconds were all it took to obtain te images, wic made it possible to perform multiple measurements and to witness cange, even fast cange, over time. Relief is obtained wit an average precision of 5/100 of a millimetre over a surface of 518 x 770 mm, and a resolution of te order of 600 x 900 points. Te quality of performance of SMT is directly linked to te line grating placed in front of te object. Tis grating, produced by ourselves, ad several defects, wic detracted from te metod s quality of performance on tis occasion. A more uniform grating will improve accuracy and above all render it more omogeneous. During te day of tests, te data collected on te relief of te panel made it possible to produce a digital 3-D model and to observe te mecanical beaviour of te panel. Bot are essential to effect realistic numerical simulations of te interaction between te frame and te panel and its reaction to exterior conditions. A contraction of te order of 3/10 of a millimetre was detected early on in te centre rigt part of te panel. It appeared during te earliest ours of andling (during te unscrewing and screwing back of te crossbars) and remained even after refitting. Tis distortion may originate in canges in te wood s beaviour in response to atmosperic conditions of umidity and temperature, wic are not necessarily te same in te room as in te glass case. Te greatest distortion was observed on removal from te frame (±1 mm), wen te panel assumed a bulging sape. Te distortion and curvatures are at teir greatest at te level of te split and also in te lower part of te panel. Tis is an indication tat tese two zones are more strongly affected by forces of flexion and are critical areas calling for careful monitoring. It is conceivable tat, by adapting te system wereby te line grating is fixed, it migt be possible to test te picture troug te glass of its case. If so, it would be possible to establis a procedure to ceck te panel frequently witout andling it or even opening te case. Suc an arrangement would allow long-term continuous assessment to monitor te panel s canges and anticipate any deterioration in te paint layer. Acknowledgments We tank Jean-Pierre Moen, Micel Menu and Bruno Mottin (C2RMF, UMR 171), Cécille Scallierez and Vincent Pomarède, Curators in te Louvre Museum for supporting te researc work. 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