Active Thermography for Non-invasive Inspection of Wall Painting: Novel Approach Based on Thermal Recovery Maps

The development of novel non-invasive diagnostic methods to support artwork conservation is an important aspect for preserving human culture. For many years the restoration work has been assisted by various technologies with digital imaging systems playing an important role. An important request is the use of non-invasive diagnostic tools that allow the detection of defects and a comparison between their state before and after consolidation treatments. Among these, infrared thermography is a well-known non-invasive and contact-less imaging method that can enable low-cost in situ analysis. This work investigates the feasibility of an innovative active thermography approach based on the calculation of thermal recovery maps to detect detachments in wall painting. Its capabilities are tested on a work of art datable in the XVIII century by making measurements in situ before and after a consolidation work. The results achieved show how this analysis can significantly support the restoration works in the detection of critical/defective areas and for a pre-post restoration comparison of the artwork.


Introduction
In planning a restoration on any work belonging to cultural heritage, the use of non-invasive techniques to analyze its pre-restoration condition is now a common practice [1][2][3].Among the cases of interest for cultural heritage, the restoration of wall paintings affected by structural degradation represents an important and complex problem that involves the knowledge of a variety of materials, environmental conditions, conservation status and possible causes [4][5][6][7].For the conservation of wall paintings, an important request is the use of adequate non-invasive diagnostic tools that allow the detection of defects and a comparison between their state before and after consolidation treatments.Among numerous diagnostics tools, imaging techniques have become widely applied in cultural heritage as they provide structural information of the artworks useful for conservators B M. Rippa m.rippa@isasi.cnr.it 1 Institute of Applied Sciences and Intelligent Systems "E.Caianiello" of CNR, Pozzuoli, Na, Italy 2 Department of Humanities, University Suor Orsola Benincasa, Naples, Italy to take a decision before and during restoration work, choosing the most appropriate intervention to apply [8][9][10][11][12].Active thermography (AT) is a well-known contact-less and noninvasive imaging technique and it represents a reliable means of providing a low-cost in situ analysis [13][14][15][16][17][18][19][20][21][22][23].According to this technique, the surface of the sample investigated is heated using an external source to produce a thermal response that can be recorded with an appropriate infrared camera.It represents an efficient approach of analysis applied in many fields, among which: materials, energy saving, biology, electronics, environment, medicine, agriculture, chemistry and increasingly to study samples of interest for cultural heritage [24][25][26][27][28][29][30][31][32].In these last cases, infrared thermography in the active configuration, is effective in detecting any type of anomaly that determines a change in thermo-physical properties of the sample under investigation.This analysis approach has been tested over the years by various research groups also for the analysis of wall painting.Poksinska et al. [33] used thermography to investigate gilding covered by paint layers.Their results allowed to localize gilded areas under the layers of whitewash and polychromy and to distinguish well preserved areas from those deteriorated.Daffara et al. [34] proposed an integrated diagnostic approach based on Mid-IR thermography and holography conoscopy to detect surfacesubsurface defect distribution, superimposing the results of the two techniques.Bodnar et al. [35,36] studied various examples of the use of the stimulated infrared thermography to support the restoration of wall paintings among which the association of random infrared thermography, singular value decomposition (SVD) and higher order statistics (HOS), showing as this method permits the detection of defect located in a real work of art.Mouhoubi et al. [37] tested the pulse phase thermography (PPT) to analyze a mural painting, showing, both theoretically and experimentally, as phase maps achieved can allow a good detection of defects.Agresti et al. [38] and Ricci et al. [39] studied the combined use of the hypecolorimetric multispectral imaging (HMI) and pulse-compression thermography (PuCT) on a 15th century wall painting demonstrating as relevant information about surface and sub-surface layers in terms of pigment composition, preparatory drawing/pentimenti and signatures of detachments can be achieved with this approach.
In this work, we report on in situ AT analysis based on the calculation of 2D thermal recovery maps (TRMs) performed in situ on a wall painting before and after a restoration work.The artwork investigated is preserved in the historical complex of Santa Caterina da Siena, seat of the Department of Humanities of the Suor Orsola Benincasa University of Naples (Italy) and it is datable in the XVIII century.The 2D TRMs allow to compare the state of health of the wall painting before and after restoration and to detect structural inhomogeneities that can be associated mainly with the presence of subsurface detachments.To the best of our knowledge, this is the first time that this approach based on TRMs has been used for a pre and post restoration analysis of a wall painting and for a work of art in general.Our results are supported by numerical simulations and they demonstrate as this approach of analysis allow a simple and quick view of the mainly defective areas and it can be used to effectively evaluate the results achieved from the restoration and consolidation works implemented.

Numerical Simulations
4-dimensional (3 spatial + 1 temporal) numerical simulations were performed to analyze the thermal response of a wall structure affected by the presence of sub-surface detachments.The numerical model is based on the heat equation in cylindrical coordinates with azimuthal symmetry (Eq.1).Using this scheme, it is only necessary to compute results on one pie slice of coordinates (r, z), because for the symmetry considered, the same values can be applied all around (0 < θ < 2π) (inset in Fig. 2a).In the model, the effects due to convection (Eq.2) and irradiation (Eq. 3) were also taken into consideration: (3) In the equations T ∞ is the air temperature, k is the thermal conductivity, ρ the density, c the specific heat, h the convection heat transfer coefficient, σ is the Stefan-Boltzmann constant, ε is the wall surface emissivity, L W and D W respectively the length and the thickness of the wall slice considered.We impose the following boundary condition.
An external heat source was considered to a induce a temperature increase from 0 to ΔT max 5 °C on the wall surface as transient perturbation in a time interval 0 − t heat 60 s using a linear relationship (Eq.4).Furthermore, in order to consider the even symmetry of the slice T (r) T (− r) the thermal exchange along the boundary (0, z) has been neglected (Eq.5).
Numerical simulation was performed through a discretization of the heat equation according to the finite volume method (FVM).For the calculation, a home-made MATLAB (R2019b, Math-Works) code was used.A regular spatial mesh of 128 × 128 pixels was considered and the spatial distributions of temperature were calculated for 180 s after heating with a Δt 0.2 s.In the calculations the elementary volumes through which thermal exchange occur respectively for z and r directions are ΔV z ΔzA z and ΔV r ΔrA r whit A z π [r 2 − (r − r) 2 ] and A r =2π rΔz.For the constants h, k, ρ and c of both the air and the wall, were taken into account the values reported in the literature [40].

AT Measurements
AT measurements were performed in order to identify the presence of detachments and anomalies within the wall painting investigated.The measurements were made in situ before (PRE) and after (POST) a restoration work carried out on the painting and conducted in reflection mode, with the camera and the thermal source placed on the same side of the painted wall.A hot air generator with tunable thermal power (Master BLP 33 M, Dantherm S.p.A.) placed about 1 m from the wall surface was used as heat source.During the heating, the temperature increase was monitored in order to obtain a T 5 °C as uniform as possible on the investigated area of the painting.The thermal response achieved during and after heating was recorded with a frame rate of 5 Hz using a LWIR camera AVIO TVS500 with a microbolometric detector (spectral range 8-14 μm, FPA 320 × 240 pixels and NETD ~50 mK at 25 °C) mounting a 11 mm focal lens with FOV 39 × 29°.During the image acquisition, the camera was positioned about 2 m from the wall surface.The commercial software IRT Analyzer (GRAYESS), with which the camera is supplied, was used for monitoring the temperature in real-time and for basic operations.The emissivity of some reference areas of the painting was evaluated both PRE and POST restoration using an opaque black reference disc with known emissivity calibrated with a black body in separate measurements and the estimated values were took into account in the analysis.
Spatial TRMs of wall painting areas were calculated using a home-made MATLAB code (R2019b, Math-Works) analyzing the temporal trend of the temperature from the frames acquired.The measurements were carried out under environmental conditions with a room temperature of about 24 °C and relative humidity of about 55% for both PRE and POST restoration analysis.Figure 1a, b respectively show a scheme of the experimental set-up used and an image of the wall painting analyzed.

Wall Painting Investigated and Restoration Work
The artwork analyzed was a quadrangular wall painting with an upper polycentric arch located in the historical complex of Santa Caterina da Siena, seat of the Department of Humanities of the Suor Orsola Benincasa University of Naples.
Monastery of Santa Caterina da Siena, seat of the humanities department of the University "Suor Orsola Benincasa" of Naples.The painting was 210 cm high, 140 cm wide and it was entirely painted with the dry technique (Fig. 1b).The restoration work essentially consisted in cleaning the surface by mechanical method, chemical-physical action and by using a laser source.Subsequently a consolidation treatment for the subsurface layers of the wall was carried out to improve the characteristics of cohesion and adhesion between the layers through a material connection.In particular, a hydraulic injection mortar diluted in water with a 5:1 ratio was used to consolidate the detachments in depth.

Results and Discussion
The purpose of this work is to develop an experimental strategy that allows, through the use of a non-invasive imaging technique such as infrared thermography, to detect the presence of areas in a wall painting mainly affected by damage and subsurface detachment and on which attention should therefore be focused during a restoration work.
For this purpose, before carrying out experimental measurements on the artwork taken into account, the response of a wall structure to external induced heating was numerically analyzed through the home-made calculation procedure described in the Sect.2.1.For these calculations, FVM was preferred.Compared to other approaches in the literature [41] based on finite element method (FEM), FVM takes into account the conservation of physical laws within each volume considered in the discretization, it is well formulated to work with inhomogeneous meshes and it allows for a much easier implementation of home-made procedures [42].
As an example of the calculations, Fig. 2 shows the numerical results achieved considering a portion of wall of length L W =30 mm and thickness D W =10 mm with inside a circular detachment with a thickness t h 1 mm, radius R 3 mm and placed at a depth D 1 mm under the surface (structure showed in Fig. 2a).
Figure 2b shows the temporal frame of the calculation representing the distribution of temperatures of the multilayer obtained 30 s after the thermal heating of the surface.Figure 2c shows the temporal trend of the temperatures (induced thermal gap T) calculated for the superficial points P A (above the detachment, black points) and P B (far from the detachment, red points) showed in Fig. 2a.As can be seen in this last graph, the thermal response of the two points is very different and in particular the presence of the detachment below the point P A slows down its thermal recovery.In fact, the supposed air present in the detachment acts as an insulator, influencing the thermal response of the surface area present above it.In order to introduce a quantitative parameter that allows to discriminate the two behaviors, we indicate with t A and t B the time that respectively the points P A and P B spent to recover a part of the induced thermal gap of ΔT 5 °C.As an example, in the graph in Fig. 2c (dashed blue lines) are represented the times t A and t B that the points spent to recover the 70% of T (3.5 °C). Figure 2d shows the recovery times ratio RTR t A /t B versus the percentage of the induced thermal gap recovered.As visible from this last graph, the maximum RTR is achieved when a recovery of about 70% of the induced thermal gap is considered.For this percentage, the numerical analysis shows a recovery time for the surface above the detachment greater than three times that estimated for the distant reference area.Repeating the calculation in the case of detachments with t h in the range 0.5-2 mm and D in the range 0.5-3 mm the maximum value of the ratio found ranging between 68 and 77% of the thermal recovery percentage.
After this numerical investigation, experimental measurements were carried out in situ on the painting under consideration as described below.
For experimental analysis, the surface of the wall painting was sectioned into four area A1-4 investigated separately.Each area was heated approximately 5 °C and their thermal response recorded as described in the Sect.2.2.The use of the hot air generator as heat source, already exploit in the past for thermographic analyzes of historical walls [43], has allowed a more uniform and homogeneous heating of the investigated surface compared to the optical source (halogen lamp) initially tested.To take into consideration the effects of cleaning on the thermal properties of the surface, the emissivity of some selected areas of the painting was evaluated both PRE and POST restoration.Average values for the emissivity of 0.89 in the PRE phase and 0.92 in the POST phase were estimated and taken into account in the analysis performed.
Figure 3 Active thermography analysis: pre and post visible images of the four sections of the painting investigated (first line), pre and post thermal images of the four sections achieved 10 s after heating (second line), pre and post TRMs calculated for the four sections analyzed (third line).
The thermal images shown are extrapolated from the recorded sequences and refer to 10 s after the end of the heating.The 10 s time point was selected because it is in the middle of the 5-16 s range (roughly estimated) where the differences between the PRE and POST thermal images appear By comparing the thermal images recorded before and after restoration shown in Fig. 3, more uniform temperature distributions can be observed in the POST-images respect to the homologous PRE-images as an effect of the consolidation and recovery work carried out on the wall painting.However, these data are strongly conditioned by the emissivity of the wall surface that change in correspondence with both the different color pigments and the different surface conditions of the painting.Furthermore, even if acquired with the same experimental protocol, by comparing single thermal images, it is practically impossible to distinguish the nature of the different types of defects that can affect the surface and subsurface of the painting.
TRMs of wall painting areas were calculated using a home-made MATLAB code (R2019b, Math-Works) analyzing the temporal trend of the temperature from the frames acquired.Each pixel of the maps represents the time that it spent to recovery the 70% of the induced thermal gap of 5 °C by the external heating.The 70% threshold represents the value that, according to the numerical analysis, allows to obtain a greater contrast between the areas affected by subsurface detachments and intact areas.In the TRMs, the gray pixels represent those that have a recovery time in the range 10-30 s, in yellow those in the range 30-45 s and in red those with this characteristic parameter higher than 45 s, about two/three times compared to the gray ones.
According the numerical analysis, the areas of the painting associated with higher recovery times represent the "suspicious" ones overlying the presence of detachments.In fact, the air present in the detachment acts as an insulator, slowing down the heat dissipation process and thus increasing the recovery times associated with these areas.
It should be noted here that the information obtained from the PRE-maps were a guide for the consolidation work relative to the re-proposing of the preparatory layers of the wall with coherent/similar materials to the original ones that was mainly focused on the suspicious areas of the wall highlighted.
As can be seen by comparing the PRE and POST-TRMs of the four areas investigated, in all of them a reduction in the size and recovery times associated with suspicious areas can be observed.Many red areas in the PRE-maps have become yellow in the POST-maps and many yellow areas in the PRE-maps have become gray in the POST-maps.This 'downgrading' of color can be associated with a reduction of the detachment present under the surface of the painting and therefore with a total or partial success of the consolidation work.Furthermore, the approach introduced allows an attempt to quantify the area subject to detachment that can be estimated from the 2D thermal maps.
It should be noted that the analysis approach proposed here based on the calculation of the TRMs, compared to other methods present in the literature which analyze the temporal thermal response [44], does not require any differential calculation, detection of the maximum values in the measured trends or, interestingly, the a priori and arbitrary choice of reference points.However, it should be emphasized that considering that the same analysis approach can hardly be successful for all types of the great variety of samples belonging to the cultural heritage field, the calculation of the TRM which has provided appreciable results for the analysis of the specific type of work examined here (wall painting) could be less effective for the investigation of other types of artworks where instead powerful and consolidated approaches present in the literature have given remarkable results.

Conclusions
In this work, AT was used to analyze the state of health of a wall painting before and after a restoration work.Preliminary, numerical analysis was made to study the thermal response of a wall to an external stimulus in presence of a subsurface defect.The results obtained from this analysis allowed to set up an experimental protocol based on the calculation of the TRMs to detect the presence of air detachments.Furthermore, the comparison of the maps obtained before and after the restoration made it possible to evaluate the effect of the consolidation work in the various areas of the painting.
The results achieved show how this experimental approach based on the use of TRMs allows to detect the areas most affected by structural defects and can be useful to support the restoration works also in order to evaluate the consolidation results achieved.

Fig. 1 Fig. 2
Fig. 1 AT measurements: a scheme of the experimental set-up used, b picture of the wall painting analyzed

Fig. 3
Fig.3Shows visible (first line), thermal (second line) and TRMs (third line) images obtained in the analysis performed before (PRE) and after (POST) the restoration work respectively most evident.They provide an overall representation of the structural homogeneity of the investigated area.In principle, the more homogeneous are the surface and sub-surface areas of the painting, the more the extrapolated thermal image shows a uniform distribution of temperature (color).By comparing the thermal images recorded before and after restoration shown in Fig.3, more uniform temperature distributions can be observed in the POST-images respect to the homologous PRE-images as an effect of the consolidation and recovery work carried out on the wall painting.However, these data are strongly conditioned by the emissivity of the wall surface that change in correspondence with both the different color pigments and the different surface conditions of the painting.Furthermore, even if acquired with the same experimental protocol, by comparing single thermal images, it is practically impossible to distinguish the nature of the different types of defects that can affect the surface and subsurface of the painting.TRMs of wall painting areas were calculated using a home-made MATLAB code (R2019b, Math-Works) analyzing the temporal trend of the temperature from the frames acquired.Each pixel of the maps represents the time that it spent to recovery the 70% of the induced thermal gap of 5 °C by the external heating.The 70% threshold represents the value that, according to the numerical analysis, allows to obtain a greater contrast between the areas affected by subsurface detachments and intact areas.In the TRMs, the gray pixels represent those that have a recovery time in the range 10-30 s, in yellow those in the range 30-45 s and in