Nonlinear optical microscopy for artworks physics

https://doi.org/10.1007/s40766-021-00023-w REVIEW PAPER

Nonlinear optical microscopy for artworks physics

Alice Dal Fovo¹·Marta Castillejo²·Raffaella Fontana¹

Received: 10 March 2021 / Accepted: 12 May 2021 / Published online: 5 July 2021

© Società Italiana di Fisica 2021

Abstract

Nonlinear optical microscopies (NLOMs) are innovative techniques recently intro- duced in the field of cultural heritage for the non-invasive in-depth analysis of artworks.

In this review, we report on the state-of-the-art of NLOMs on different artistic materi- als, i.e., varnish, glue, paint, wood, parchment, and metal, and we evaluate the potential and capabilities of NLOMs in comparison with other more established linear optical techniques. We also discuss the latest studies defining suitable measurement condi- tions and instrumental requirements for the safe and in situ application of NLOMs on real cases.

Keywords Nonlinear optical microscopies·Multi-photon excitation fluorescence· Second harmonic generation·Third harmonic generation·Artistic materials

Abbreviations

2PEF Two-photon excitation fluorescence 3PEF Three-photon excitation fluorescence AFM Atomic force microscope

CH Cultural Heritage

CLSM Confocal laser scanning microscopy CMC Carboxy-methyl cellulose

CRM Confocal Raman microscopy

FLIM Fluorescence lifetime imaging microscopy FORS Fibre optics reflectance spectroscopy IC Internal conversion

IRR Infrared reflectography

B

1 Consiglio Nazionale delle Ricerche-Istituto Nazionale di Ottica (CNR-INO), Largo E. Fermi 6, 50125 Florence, Italy

2 Instituto de Química Física Rocasolano - Spanish National Research Council (CSIC), C/ Serrano 119, 28006 Madrid, Spain

ISC Inter-system crossing LIF Laser induced fluorescence

MPEF Multi-photon excitation fluorescence NA Numerical aperture

nanoIR IR nanoscopy NIR Near infrared

NLOM Nonlinear optical microscopy NMR Nuclear magnetic resonance OCT Optical coherence tomography OM Optical microscopy

OPO Optical parametric oscillator

PA Photoacoustic

PAcSA Photoacoustic signal attenuation PIXE Particle-induced X-ray emission PMMA Poly-methyl methacrylate PMT Photomultiplier tubes

PSHG Polarization-resolved second harmonic generation

RF Radio frequency

SHG Second harmonic generation SORS Spatially offset Raman spectroscopy THG Third harmonic generation

THz-TDS Terahertz time-domain spectroscopy VR Vibrational relaxation

XRF X-ray fluorescence

1 Introduction

The importance of scientific analyses for the study and conservation of cultural heritage (CH) is nowadays well recognized, not only for the historical research on artworks, but also to assist in conservation treatments. As a matter of fact, the detailed knowledge of the chemical composition and the physical structure of the artwork is the starting point for art historians and conservators to reconstruct the history of the object, evaluate its authenticity, shed light on the author’s executive technique, and provide valuable support to restorers to plan and document conservative interventions.

Stratigraphic analysis is one of the most important procedures for looking inside those complex objects to get information about the layered structure, acting as ref- erence point for further chemical and physical examinations. Cross-sectional images turn relevant for the detection of pictorial detachments and internal discontinuities, the identification of over-paintings and multi-layered stratigraphy, and the recognition and quantification of foreign/altered materials, deposits of dirt/dust and pollutants, hamper- ing the legibility of the painted surface. Such information becomes crucial especially in the context of restoring operations, like the cleaning, a delicate and irreversible pro- cedure consisting in the selective removal or thinning of aged varnishes not fulfilling their protective/aesthetic function anymore, and/or over-paintings covering the histor- ical surface and, thus, infringing the ethical standards of art conservation. Restorers

may greatly benefit from the tracking of the whole cleaning process, by knowing with micrometric precision the in-depth extent of the unwanted materials, before, during and after their selective removal. Monitoring is particularly useful when carrying out cleaning tests following different procedures, before undertaking the final decision, and becomes essential in case of future conservation treatments for not compromising further historical interpretations.

The classic approach for stratigraphic analysis is based on either micro-sampling or direct observation of natural cross-sections visible at the edges of voids in the artwork’s structure. In all cases, these analyses are limited, in number and position, to very small areas, which are not always representative of the whole object. Cross- sections of micro-samples can be analysed by means of microscopic (stereomicroscopy [1], polarized light microscopy [2–5], and fluorescence microscopy [6]), and micro- analytical techniques [7–10] for achieving a more comprehensive information on the artwork’s stratigraphy.

However, scientific analysis based on micro-sampling is not always feasible: given the intrinsic cultural and historical value of artworks, it is essential to preserve their material integrity even during the scientific analyses, scilicet preventing sampling and contact measurements. Non-invasive methods fit this requirement, providing a variety of information without causing any damage to the analysed materials. It has to be underlined, though, that data obtained by means of such methodologies is not always exhaustive or completely unambiguous. Hence, a multi-analytical approach involving several complementary techniques is often considered the best choice [11]. In specific, there are cases in which non-invasive techniques do not yield the information requested, e.g. in the presence of highly scattering materials, which may significantly reduce the penetration of the radiation probe. For this reason, in the last decades, a significant effort has been made for testing novel non-invasive techniques in the field of CH science, as well as for developing cutting-edge technological solutions to meet the requirements of these specific applications.

2 State of the art of non-destructive cross-sectional analysis in cultural heritage

Many are the non-invasive and non-contact imaging techniques that have entered the diagnostics of artworks based on electromagnetic radiation, ranging from X-rays to Terahertz. However, all of these methods provide information, which is rather selec- tive on a specific layer (reflectography in the visible range) or is integrated over the whole thickness of the artwork (Infrared Reflectography—IRR; single-energy stan- dard Particle-Induced X-ray Emission—PIXE). Consequently, increasing attention is being given to alternative methods for non-invasively and contactless estimating the sequence and thickness of layers within inhomogeneous samples. For instance, optical sectioning performed by means of either confocal laser scanning microscopy (CLSM) or optical coherence tomography (OCT) enables the production of images of the inter- nal structure down to submicron and micron resolution, respectively, offering a unique possibility for the determination and visualization of the inner structure of objects. On the one hand, CLSM, traditionally carried out with either visible or ultraviolet light

[12,13] in laboratory environment, has been recently realized for in situ measurements of artworks, basing on a laser diode in the near infrared (NIR) at 1550 nm and an opti- cal fiber acting both as the illumination and the collecting pinhole of the microscope [14]. The limited depth of imaging and investigated field makes the survey of areas in the centimeter-scale very time consuming. On the other hand, OCT has recently become well established for the determination and visualization of the inner structure of semi-transparent objects, which weakly absorb and/or scatter light. Various setups have been developed, either in the time or frequency domain, basing on Michelson or Mirau interferometer. Since its first implementations in 2005 [15–17], over the past fifteen years, an increasing number of applications have flourished to investigate the structure of cultural heritage objects, ranging from paintings to ceramics, from metal to stone artworks [17–20]. Nevertheless, most OCT applications deal with the measure of paintings’ cross-sections [21], specifically to enable the in-depth probing of varnish layers, even though in some cases a complete stratigraphy is also achievable [22–28].

The technique has proved successful also for the identification of semi-transparent over-paintings [29], and for the discrimination between aged and new varnishes [16], with in-depth (axial) resolution in the range of 1–10μm. To overcome penetration limits related to highly reflecting varnishes, it was demonstrated that it is feasible to focalize the beam inside the sample rather than on the outer surface, by coupling confocal microscope optics with an OCT setup [30]. Despite the in-depth imaging of paint layers with OCT is at present restricted to specific cases, namely low scattering pictorial media with high degree of transparency to the radiation used, this method has revealed effective also for the 3D visualization of underdrawings materials, which resulted not detectable by means of reflectance imaging [31]. When it comes to mea- sure the thickness of semi-transparent or turbid media, unavoidable artefacts originated from spherical aberration and refraction of the laser light have to be taken into account.

As a matter of fact, the majority of the microscopy techniques, including OCT and Nonlinear Optical Microscopy (NLOM) (see below), may be affected by a decrease in the in-depth resolution and an alteration of the axial depth scale. In the case of OCT, the incident radiation is linearly back-scattered by the material in correspondence of interfaces between materials with different refractive index (n), and the optical inter- ference is observed whenever the signal superimposes with the reference beam within the coherence length of the used light source. In this case, then-mismatch among the overlaid layers causes a delay of the optical delay path of the reference beam and, therefore, the optical measured distances must be corrected to geometrical distances by dividing by the refractive index of the material.

X-ray emission techniques, such as X-ray fluorescence (XRF) and the aforemen- tioned PIXE, have played a pivotal role in compositional analysis for decades. The introduction of a confocal geometry, at first in a typical micro-XRF set-up [32] and later on the micro-PIXE probe [33], has allowed overcoming the limited capabilities of conventional X-ray based elemental techniques to resolve a stratigraphy or pro- vide axial profiles of elemental concentration, enabling in-depth analysis up to tens or even hundreds of micrometres [34]. To mention some representative applications of 3D micro-XRF on paintings, elemental depth profiles proved successful in highlight- ing the sequence of paint layers of different composition [32], and in evidencing the presence of over-paintings with the reconstruction of virtual cross-sections through

elemental scanning [35,36]. Nevertheless, most X-ray analyses on cultural heritage require the high elemental sensitivities of synchrotron radiation facilities, which are hardly accessible and not always applicable. Differential PIXE represents a solution to discriminate the depth sequence of elements within the analysed sample, but it pro- vides semi-quantitative information on the stratigraphy due to several factors affecting data interpretation [37]. XRF spectrometers equipped with X-ray tubes may contribute to a wider use of the method, but their sensitivity is considerably lower in comparison to the confocal set-ups available at particle accelerators [34].

The confocal geometry has been exploited also in confocal Raman microscopy (CRM) [38], to perform the optical sectioning of transparent specimens with improved in-depth discrimination. By moving the laser focus inside the material, intensity spec- tral profiles can be obtained, from which the thickness of the crossed layer may be estimated. To minimize the above-mentioned optical artefacts affecting cross-sectional microscopy analysis, oil-immersion objectives are an option to diminish the compres- sion effect on the axial scale. However, as this involves contact with the material surface, it should be avoided to safeguard the artwork’s integrity. There are cases of successful application of CRM with air-objectives, e.g. thickness measurement of transparent polymeric films after proper correction procedure to adjust the axial scale [39], but to expand its application to opaque materials different solutions must be defined.

In the last fifteen years, the introduction of spatially offset Raman spectroscopy (SORS) has represented a step forward in the in-depth analysis of opaque media, proving suitable for the determination of the chemical composition of inner materials that are covered by superficial, turbid layers [40]. Specifically, by using defocused micro-SORS [41] it is possible to access larger depths of scattering layers than those reached with confocal microscopy. This modality makes also feasible the non-invasive detection of distinct chemical components (i.e. pigments), either mixed in one layer or separated in two subsequent layers, underneath superficial opaque layers [42].

Notwithstanding these advantages, micro-SORS is still unable to provide information about the thickness of the examined layers or about the depth value from which the sublayer signal is originated [42].

Another method tested for the 3D imaging of paintings is nuclear magnetic reso- nance (NMR) [43], which employs low-energy frequencies between kHz and GHz to provide chemical information on molecular structure and slow molecular dynamics of protons and other magnetic nuclei resonating in magnetic fields. A breakthrough for its application in CH science has been the development of single-sided NMR sensors [44], which combine open magnets and surface radio frequency (RF) coils to generate a magnetic field inside the object under investigation. The evolving relaxation times measured by NMR through an object are indicative of changes in the rigidity of the constituting materials, and thus can be correlated with elasticity, crosslinking, and other phenomena linked to molecular reactions due to ageing [43]. Furthermore, by extracting the concentration gradient of different material components as a function of depth, it is possible, for instance, to reveal the presence of organic binders in paintings [45] or conservation agents below the surface in bones [46], to determine the effec- tiveness of conservation agents in stone artefacts by mapping their penetration depths [47], and to measure the solvent concentration in paint layers undergoing conservation

procedures [48]. In situ experiments performed with a single-sided NMR sensor pro- vided axial profiles of paintings, by spanning several millimetres across depth ranges of up to 25 mm with a resolution better than 10μm [43,49]. Despite the promising results obtained with NMR, cross-sectional imaging of paintings is still not feasible, mainly due to some limits related to signal detection and lack of homogeneity in the magnetic field generated by the magnets and coils. Moreover, the low mass sensitivity resulting from the low NMR frequencies reflects in long measurement times.

In the last decades, radiation falling in the THz spectral range has been profitably used for the non-invasive cross-sectional inspection of artworks, and specifically for the analysis of paintings. The high penetration capability (0.1–10 THz) through a wide variety of pictorial materials, usually opaque to both visible and infrared wavelengths [49], makes non-ionizing THz radiation an effective and harmless probe for bulk analysis, both in reflection and transmission modes. In specific, terahertz time-domain spectroscopy (THz-TDS) makes use of THz pulses to epi-detect the signal reflected by the crossed interfaces between materials characterized by different refractive index.

This allows reconstructing cross-sectional images of the object’s stratigraphy, a result that is comparable to tomographic 2D images provided by OCT, even though hampered by the low axial resolution. One of the first applications of THz-TDS for the in- depth inspection of paintings dates back to 2009 [50], demonstrating the visualization capability of the technique in revealing hidden paint layers in presence of highly opaque over-paintings, which is not always possible using other traditional methods, like X-ray radiography and infrared reflectography. Later, the potential of THz-TDS resulted also suitable for the cross-sectional analysis of ancient tempera panel paintings [51]. Despite the promising results, the typical paint layers of pre-nineteenth century easel paintings are optically too thin (less than 50μm) [52] for the time over which the THz pulse propagates within its duration, corresponding to the depth resolution of a typical THz-TDS system [53], and require complex data processing to extract the thickness information. However, it was demonstrated that by using a sparsity-based time-domain deconvolution algorithm, it is possible to resolve the THz overlapping echoes and, thus, to obtain a quantitative 3D mapping of the layers composing the structure of an easel painting [53]. Up to now, the need for complex and expensive instrumentations, often including femtosecond (fs10^–15s) pulsed lasers, lock-in amplifiers, and THz spectrometers, represents one of the main limits in the widespread use of THz set-ups.

New entries among the non-invasive in-depth analyses for CH are photoacous- tic (PA) methods, which are largely employed in the biomedical field for a variety of applications. Differently from pure optical techniques, PA takes advantage of the presence of opaque media inside the painting. The radiation coming from a pulsed or intensity-modulated source, irradiates the painted object from its backside (canvas support), with intensities that are safe for most materials. As the radiation penetrates through the object, ultrasonic acoustic waves are generated only in correspondence of the absorbing components and are collected from the other side (painted surface) of the object. This principle was successfully used for the visualization of underpaintings and underdrawings [54,55], also enabling the 3D survey of the superimposed paint- ing layers in the modality of photoacoustic signal attenuation (PAcSA) imaging [56, 57]. The thickness of thin layers was measured through the frequency analysis of the

transmitted photoacoustic waves, which undergo an exponential attenuation as they propagate through the material. It has to be underlined that, up to now, the collection of the PA signal requires the use of a coupling medium enhancing the transmission of the attenuated acoustic waves. The most suitable material is a water-based gel of carboxy-methyl cellulose (CMC) [57], which is commonly used in restoring opera- tions on painting, being inert and harmless for most of the hydrophobic materials, such as varnishes, oil-tempera, etc.). However, for guaranteeing the non-invasiveness of this method, new solutions for contactless analysis have been tested. For instance, the integration of highly sensitive air-coupled transducers (e.g., unfocused, spheri- cally/cylindrically focused) has already yielded promising results in the analysis of painted mock-ups [55]. To overcome the limitations of PA in resolving the superim- posed material layers, a combination of PA imaging and NLOM has been recently applied [58], allowing to complement the visualization of the stratigraphy of opaque materials with compositional in-depth information.

Recently, nonlinear optical microscopy has been tested for the non-invasive in- depth analysis of CH objects in the modalities of multi-photon excitation fluorescence (MPEF) [59], second and third harmonic generation (SHG [60] and THG [61], nonlinear fluorescence lifetime imaging microscopy (FLIM) [62], and pump-probe microscopy [63,64]. The application of NLOM was originally restricted to the biomed- ical field, mainly for in vivo imaging and mapping of molecular structures [65–72].

NLOMs are cutting-edge methodologies based on nonlinear optical processes, in which atoms and/or molecules simultaneously interact with two or more photons within the same quantum event. Such phenomena may be observed when a given material is excited by a tightly focused femtosecond-pulsed laser, propagating through a high numerical aperture (NA) microscope objective, enabling both good penetration capability and micrometric axial resolution. NLOM techniques [73,74] may provide compositional and structural information based on the detection of fluorophores (by MPEF) [75], crystalline or highly organized structures without inversion symmetry (by SHG) [76] or local differences in refractive index and dispersion, i.e., interfaces (by THG) [77]. In the last decades, NLOM has been applied in CH diagnosis for several aims, which will be illustrated in the following sections. To name a few, NLOM was used for the 3D imaging of protective layers, making feasible the in-depth monitoring of varnish degradation due to ageing [78] or to laser ablation [79]. Cross-sections of pictorial layers were obtained through the application of femtosecond pump-probe microscopy in the nonlinear modality and MPEF imaging [74,79–85]. Furthermore, wooden artefacts were analysed with SHG and MPEF, enabling both the imaging and the chemical characterization of wood microstructures [76]. Silver-based objects were also studied utilizing MPEF imaging to identify and quantify the presence of corrosion layers [86].

The research carried out so far has evidenced the advantages offered by NLOMs compared to other linear optical techniques. These can be summarized as follows: the use of a single femtosecond laser source enables the simultaneous generation of sev- eral nonlinear optical signals (SHG, THG, MPEF) in the focal volume of the examined object, entailing that different information, i.e. chemical, structural, morphological, optical, can be extracted from one single measurement. The nonlinear dependence of the generated signal intensity on the excitation light intensity implies that the efficient

nonlinear interaction is confined to the focal volume of the laser beam, thus providing intrinsic axial resolution. Out-of-focus damages (i.e., photobleaching phenomena) are drastically diminished, which is a priority for CH studies. In specific, the minimal disturbance to the analysed specimen is ensured by nonlinear scattering processes, such as SHG and THG, since no energy is deposited in the medium. As regards non- linear absorption processes (MPEF), safe measurement conditions can be achieved by keeping the laser power within specific limits that are related to the optical properties and chemical composition of each material [85]. The possibility to perform MPEF measurement in the reflection mode enlarges its applicability to a wide range of real cases, i.e. painting materials lying on opaque substrates (e.g. wood, canvas, parch- ments, etc.). A further application of NLOM involves the use of polarization-resolved SHG, enabling to discriminate between aged/deteriorated and fresh organic materials, such as starch-based glues [87,88] and collagen [89], commonly used for artworks conservation. In the next chapters, we describe the physical principles of NLOM (ch.

3.1), with a focus on nonlinear scattering phenomena (second and third harmonic generation, SHG and THG—ss. 3.2.1 and 3.2.2, respectively) and nonlinear absorp- tion with consequent emission of fluorescence (multi-photon excitation fluorescence, MPEF—s. 3.2.3). A brief description of the basic instrumentation used for nonlinear measurements follows in s. 3.3, with a hint to the most used laser sources (s. 3.3.1) and the optical resolution that can be achieved (s. 3.3.2). Then, we present an overview on the applications of nonlinear techniques in CH diagnosis in the last fifteen years (ch. 4), according to the analysed material, namely varnishes, oils and glues (s. 4.1), paints (s. 4.2), over-paintings (s. 4.3), wood microstructures (s. 4.4), skin-based arte- facts (s. 4.5), and corrosion products in metals (s 4.6). Chapter 5 is dedicated to the evaluation of the non-destructiveness of the NLOM modalities and to the monitoring of laser-induced effects for safe use on cultural heritage objects. Finally, prospects for enlarging the application of NLOM on artworks’ analysis are illustrated in ch. 6, rang- ing from the systematic assessment of the damage thresholds on painting materials and the full understanding of the interaction involved to the development of portable setups enabling in situ measurements.

3 Nonlinear optics 3.1 Physical principles

Nonlinear Optics (NLO) is the study of phenomena that occur as a consequence of the modification of the optical properties of a material, following its interaction with light [90]. The term nonlinear refers to the nature of the response of the medium to the applied optical field, i.e., the intensity of the generated signal tends to increase nonlin- early with the intensity of the incident light beam. In nonlinear optical processes, two or more incident photons may simultaneously interact with atoms or molecules of the material within the same quantum event. Such physical effects are strictly dependent on the intensity of light and may be observed with the use of monochromatic and coher- ent light sources generating beams of high intensity (> 10¹²W/cm²). Not surprisingly, the beginning of NLO studies is often considered to be right after the demonstration

of the first working laser (Maiman, 1960), with the discovery of the process of second harmonic generation by Franken et al.in 1961 [91]. Nonlinear effects were previously detected in the non-optical frequency domain (low-frequency electric and magnetic fields magnetization), but it was observed that the high electric field strength provided by lasers was necessary to produce such effects in the optical frequency range [92].

Specifically, the use of femtosecond pulsed lasers, tightly focused inside the specimen by high NA microscope objectives, enables the generation of nonlinear signals, while ensuring both good penetration capability and high axial resolution (in the range of micrometres).

The main difference between nonlinear and linear optics relies on the dependence of polarization P˜(t)tensor (dipole moment per unit volume) of a system upon the strength E˜(t)of the applied electric field. In linear optics, the induced polarization depends linearly on the electric field strength, as described by the relation

P(t˜ )χ⁽¹⁾E˜(t), (1)

whereχ⁽¹⁾represents the linear susceptibility (for simplicity, from now onE˜(t)and P˜(t)will be considered as scalar quantities).

In nonlinear optics, the response is described by expressingP(t)as a power series inE(t), as

P(t)χ⁽¹⁾E(t)+χ⁽²⁾E²(t)+χ⁽³⁾E³(t)+. . .

≡P⁽¹⁾(t)+P⁽²⁾(t)+P⁽³⁾(t)+. . . (2) whereχ⁽²⁾andχ⁽³⁾are the second- and third-order nonlinear optical susceptibilities, and P⁽²⁾(t) χ⁽²⁾E²(t)and P⁽³⁾(t) χ⁽³⁾E³(t)express second- and third-order nonlinear polarizations, respectively. Hence, the nonlinear optical signals are the con- sequence of the polarization induced by a specific order of interaction in Eq. (2).

Nonlinear susceptibilities are bulk properties depending on the energy levels involved.

In general, if the strength of the applied electric fields does not exceed the magnitude of the coulombic electric field inside the atoms or molecules (Eat 5.14×10¹¹ V/m),¹the use of a perturbative approach, as that expressed in (2), for the theoretical description of the nonlinear phenomena is justified.

3.2 Nonlinear optical processes

Depending on the optical and chemical properties of the material, the interaction with a focused laser beam may give rise to nonlinear scattering phenomena (harmonic generation) or nonlinear absorption with consequent emission of fluorescence (i.e., multi-photon excitation fluorescence). The order of the polarization determines the nature of the nonlinear interaction.

1 The characteristic atomic electric field strength isEate/(4πε0α02)5.14×10¹¹V/m, whereeis the charge of the electron andα0is the Bohr radius of the hydrogen atom. (R. W. Boyd, 2003 [90]).

Fig. 1Second Harmonic Generation.aSketch of the process.bEnergy-level diagram, describing the SHG frequencyω doubling process, from the ground state S₀(solid line) to the virtual levels (dashed lines), with the emission of a 2ωphoton

3.2.1 Second-harmonic generation

The second-order polarization process is schematically described in Fig.1, showing two photons of frequencyω, which are converted into one photon of frequency 2ωin a single quantum–mechanical process. An example of a second-order nonlinear process is SHG.

In terms of the polarization components, the second-order polarization can be explained as follows. Let us assume that the incident laser beam, with electric field strengthE(t)at frequencyω, is represented by

E(t)Ecos(ωt), (3)

or using Euler’s formula,

E(t)Ee^−iωt+c.c., (4)

wherec.c.stands for complex conjugate andiis the imaginary unit [90].

According to Eq. (2), if the incident beam interacts with a material having nonzero second-order susceptibilityχ⁽²⁾, the nonlinear polarization generated inside the mate- rial isP⁽²⁾(t)χ⁽²⁾E²(t)or

P⁽²⁾(t)2χ⁽²⁾E²+

χ⁽²⁾E²e^−2iωt+c.c.

. (5)

The second-order polarization is given by two contributions, the first at zero fre- quency (first term) and the second at 2ωfrequency (second term). While the former is responsible for the optical rectification effect that consists of the generation of a quasi-DC polarization [93], the latter can lead to the generation of the second-harmonic frequency.

The second-order polarization is proportional to the square of the electromagnetic field, where the nonlinear susceptibility χ⁽²⁾ is related to the polarizability of the molecule β χ⁽²⁾/Ns, with Ns being the density of atoms or molecules, and the brackets denote an averaged orientation. Thus,βis maximal for aligned dipoles and becomes zero for entities with antiparallel orientation, whose contributions interfere destructively due to their phase shift [94]. Similarly, SHG is possible only in presence of polarizable atoms or molecules with specific symmetry properties, namely without a centre of inversion, i.e., non-centrosymmetric. It is observed that for centrosymmetric

Fig. 2Waveforms associated with the atomic response, see text. Reprinted from R. W. Boyd, Nonlinear Optics, Second Edition, the Institute of Optics, University of Rochester, New York, USA, Academic Express (2003), Copyright (2021), with permission from Elsevier [or Applicablesociety Copyright Owner] [90]

species the nonlinear susceptibility⁽²⁾ vanishes. This principle can be theoretically verified by considering the second-order polarization produced in a molecule with inversion symmetry. In such a case, if the sign of the applied electric fieldE(t)changes, the induced second-order polarization P⁽²⁾(t)χ⁽²⁾E²(t)also changes. Hence, P (t)is replaced by

−P⁽²⁾(t)χ⁽²⁾[−E(t)]²χ⁽²⁾E²(t). (6)

BeingP⁽²⁾(t)χ⁽²⁾E²(t),P⁽²⁾(t)must be equal to−P⁽²⁾(t), which occurs only ifP⁽²⁾(t)vanishes identically, meaning that

χ⁽²⁾0 (7)

This result is described in Fig.2. The waveform of the incident monochromatic electromagnetic wave of frequencyω(Fig.2a) produces an identical waveform in a medium with a linear response (Fig.2b), whereas in the case of a nonlinear medium with a centre of symmetry (Fig.2c), the polarization leads to the waveform distor- tion, with only odd harmonics of the fundamental frequency. Finally, for the case of a nonlinear, non-centrosymmetric medium (Fig.2d), both even and odd harmon- ics are present in the waveform associated with the atomic or molecular response.

Furthermore, differently to the centrosymmetric medium, the time-averaged response is nonzero, because the medium reacts differently depending on the direction of the electric field.

Under proper experimental conditions, a significant part of the power of the incident laser beam is converted into radiation at the second-harmonic frequency. Particularly, the efficiency in SHG conversion depends on the phase matching between the funda- mental and SH wave and is maximum when the photon momentumpis conserved.

Aspkh/2π,kbeing the wave vector, momentum conservation means that

k(ω)+ k(ω) k(2ω). (8)

The equivalent condition

2n(ω)ω

c n(2ω)2ω

c , (9)

wherenis the refractive index, implies that

n(2ω)n(ω). (10)

Material dispersion (i.e., increase of refractive index with light frequency) prevents the phase-matching condition (8), thus limiting the frequency doubling efficiency.

However, birefringent crystals offer the possibility to circumvent this limitation, since they have different refractive indexes for ordinary and extraordinary polarization. By using the extraordinary (subscripte) and the ordinary (subscripto) polarization for ω and 2ω, respectively, and by rotating the birefringent crystal, phase matching is possible, i.e.

no(2ω)ne(ω), (11)

as the refractive indexnedepends on the propagation angle.

Taking advantage of this property of birefringent crystals, SHG serves to efficiently up-convert the output of a fixed-frequency laser to a different spectral region. For example, frequency doubling of the nanosecond Q-switched Nd:YAG laser operating in the NIR spectral region at a wavelength of 1064 nm provides green laser light at 532 nm.

The SHG signal is not only dependent on the intensity of the incoming fundamental frequency light, but it is also affected by its polarization. In polarization-resolved second harmonic generation (PSHG), measuring the dependence of this signal with the laser polarization offers additional information related to the arrangement, orientation, and structure of the molecular constituents of the sample. PSHG microscopy imaging has been used recently for the characterization of the molecular architecture of different types of active SHG scatterers, some of them of interest in cultural heritage, such as collagen or starch [87,88,95].

3.2.2 Third-harmonic generation

Third-order polarization, P⁽³⁾(t) χ⁽³⁾E³(t), is responsible for several nonlinear phenomena, such as THG and multi-photon absorption, which may lead to nonlinear excitation fluorescence.

For the description of third-order nonlinear interactions, only the case of a monochromatic field, given by Eq.3, is considered here.

By using the identity cos³ωt ¹₄cos 3ωt + ³₄cosωt, the nonlinear polarization can be expressed by

P⁽³⁾(t)1

4χ⁽³⁾E³cos 3ωt+ 3

4χ⁽³⁾E³cosωt. (12)

Fig. 3Third Harmonic Generation.aSketch of the process.bEnergy-level diagram, describing the THG frequencyω tripling process. The solid line and the dashed lines represent the ground state S0and the virtual levels, respectively

The first term describes a response at frequency 3ω, due to an applied field at frequencyω. This term leads to the process of Third-Harmonic Generation, which is illustrated in Fig.3. Similarly to SHG, in THG process three photons of frequencyω are simultaneously converted in one photon of frequency 3ω.

As discussed in the previous section, the efficiency of a nonlinear optical process is determined by the nonlinear susceptibility of the medium and the phase mismatch parameter. To achieve optimal energy conversion efficiency, the phase-matching con- dition Δk 0, equivalent to Eq. (8) for SHG, has to be fulfilled. For THG the corresponding condition reads as

kk(3ω)−3k(ω)0. (13)

In NLOM, a femtosecond Gaussian laser beam is used as an excitation source. The beam, passing through the objective lens, is tightly focused on the specimen under study. However, the crucial phase relationship between the frequency components involved in THG has to include the Gouy phase shift as the beam passes through the focus. Therefore, for an infinite nonlinear medium exhibiting normal dispersion (Δk

> 0) no harmonic radiation would be generated in the medium at the focal point and within the region covering many Rayleigh lengths (the Rayleigh length is the distance along the propagation direction of a beam from the waist to the position where the area of the Gaussian beam cross-section is doubled). However, if the thickness of the nonlinear medium along the propagation direction is shorter than the focal region, the cancellation of the contributions to the harmonic signal from the two sides of the focus is no longer complete. This is why THG is effective when the excitation beam is focused at the interface of two optically dissimilar materials [96].

Efficient THG under tight focusing conditions at an interface within the focal vol- ume of the excitation beam was firstly explored by Tsang [97]. The THG power can be calculated as a function of the interface uniformity, as done by Barad et al.[98], showing that, when there is either a change in refractive index or third-order nonlinear susceptibility, the third harmonic power does not vanish. Because of this interface effect, THG imaging is possible and specifically suitable for transparent specimens with low intrinsic contrast, being also sensitive to changes in the specimen’s nonlinear optical properties [99].

Both frequency doubling and tripling processes—i.e., SHG and THG—arise from coherent scattering, and the generated signal propagates mainly in the same direction as the incident laser beam. The exact ratio of forward (transmitted) and backward (epi)

signal depends on the sample characteristics, but generally, the backwards-propagating signal is much weaker than its forward counterpart. Moreover, the epi-collection effi- ciency critically depends on the microscope field-of-view even at shallow depths, due to the diffusive nature of the backscattered light. The efficiency of the backward detec- tion of THG can be improved through either the coherent excitation of a large number of scatterers or resonance effects, enabling to overcome the limitations of the weak third-order susceptibility in most media. Differently, the higher efficiency of Second Harmonic Generation in biological structures allows for the detection of SHG signals also in the backward configuration [100].

In these nonlinear optical scattering phenomena, no energy is deposited in the medium and the new photons are generated through a single-step quantum process [90]. The interacting material acts as an energy converter of the incident photons, combining a numberNof photons (2 or 3, for SHG and THG, respectively) of energy hωto emit one photon of energyN hω. TheN th harmonic intensity scales with the intensity of the fundamental incident radiationIas I^N.

3.2.3 Multi-photon excitation fluorescence

When a laser beam interacts with a material, specific molecules (fluorophores) can be excited by the near-simultaneous absorption of one or two (or more) low-energy photons, which approximately match the energy difference between the excited and the ground state (S2and S0, respectively). After few nanoseconds from the absorption, the excited molecule drops to the ground state, possibly generating the emission of fluorescence (Fig.4). Multi-photon excitation fluorescence refers to the excitation of a fluorophore when two or more photons arrive within a time window of an attosecond (10⁻¹⁸s) and team up to excite the molecule [94]. In principle, any combination of photons reaching the energy difference between S0and S2may generate nonlinear fluorescence. In Fig.4b, two photons of equal wavelength are used to describe the phenomenon. Once in the excited state, after the transition to the singlet state S2, the electron movements are the same as in single-photon excitation: the molecule undergoes a non-radiative decay with loss of energy by a sequence of iso-energetic Internal Conversion (IC) to reach S1, followed by Vibrational Relaxation (VR), in which energy is dissipated in form of heat within the vibrational structure of the S1

electronic state. Generally, most molecules return to the electronic ground state without emission of light, by transferring their energy to the surroundings through collisional quenching and internal photo-conversion. However, after a delay of∼10⁻⁸–10⁻⁹s, the relaxation to the ground state may also result in the emission of light (fluorescence), which is characterized by lower energy (i.e., longer wavelength) than the absorbed one, following a phenomenon known as Stokes shift. The emission is independent from the excitation wavelength, being the radiative decay generated at the lowest vibrational level of the excited state, and absorption/emission spectra are representative of each molecular species.

On the one hand, the capacity of a molecule for light absorption is determined by its molar extinction coefficientε(measured at peak absorption per mole and cm of optical path-length) and its absorption spectrum. On the other hand, the ability of a molecule to fluoresce is determined by the fluorescence quantum yieldQf (dimensionless) and

Fig. 4Jablonski diagrams ofasingle-photon excitation andbmulti-photon excitation, respectively. The electronic energy levels and their vibrational substructure are shown with horizontal lines, whereas the physical processes that cause transitions between these levels are depicted by vertical arrows. The singlet ground, first and second electronic states are labelled S₀, S₁ and S₂, respectively, and the first triplet state is labelled T₁. For each electronic state, the molecule can exist in a multitude of vibrational states indicated by the dashed lines. Internal conversion (IC) and inter-system crossing (ISC) are represented by the jagged arrows.cStokes shift effect between normalized absorption and fluorescence emission spectra of a fluorophore

the emission spectrum (Fig.4c). Hence, the brightness of a fluorophore is determined by the productεQf. The time that elapses between the absorption and the emission is called fluorescence lifetime (τ), which is typically exponentially distributed and is highly sensitive to the fluorophore environment.

From S1, another possible event is the emission of a phosphorescent photon. In this case, the excited electron undergoes a sequence of Inter-System Crossing (ISC) to attain the triplet state, before dropping to the ground state through a sequence of vibrational processes. In this case, the lifetime of the excited state is significantly longer than in the fluorescence process, ranging from∼10⁻⁴s to minutes, or even hours. The drop to the ground state is accompanied by the emission of a photon of lower energy than the exciting one.

For each of these processes, the relative importance of a given decay pathway can be defined by a quantum yield (Q). Specifically, the fluorescence quantum yield (Qf) is expressed by the ratio of the emitted and the absorbed photons – i.e., the fraction of excited states that relaxes via the emission of a fluorescence photon

Qf kr/(kr +knr), (14)

wherekr is the rate of relaxation to the ground state by fluorescence andknris the rate of relaxation to the ground state by non-radiative processes [101].

Similarly, the lifetime of an excited state is defined by

τ 1/(kr +knr). (15)

As a general principle, the main difference between one and two photon absorptions relies on the diverse dependence on the applied field intensityIor, in other terms, on the

field amplitudeE. In fact, the transition rate of one photon, as well as the fluorescence intensity, is linearly dependent on the intensityI of the optical field

Abs1ph ∝ E²∝ I, (16)

whereas the transition rate of two photons is proportional to the square of the intensity I

Abs2ph ∝ E⁴∝ I². (17)

More generally, the probability ofn-photon absorption by a molecule is proportional toIⁿ, thus increasing by concentrating the incident beam both spatially and temporally to obtain high photon flux (typically 10²⁰–10³⁰ photons/cm²s). This is commonly obtained by using a pulsed laser, instead of continuous-wave light sources, tightly focused by a high numerical aperture objective. Hence, under daylight or arc-lamp illumination, the probability of two-photon absorption is virtually zero. That is why the experimental demonstration of Maria Göppert—Mayer’s prediction of multi-photon excitation [102] had to await the advent of a mode-locked laser emitting photons intermittently in high-intensity bursts. As a result of the beam focusing, the intensity along the optical axis increases towards the focus and then decreases as the squared distance. Correspondingly, Two-Photon Excitation Fluorescence (2PEF) rises and then dwindles as the distance raised to the fourth power, confining 2PEF to the immediate vicinity of the focal spot (Fig. 5). The effective 2PEF volume, i.e., the volume in which the beam intensity is high enough to produce nonlinear absorption, is less than a femtolitre (10⁻¹⁵L). This three-dimensionally confined excitation greatly enhances the collecting efficiency in NLOM, while reducing the out-of-focus photodamage.

The latter is unavoidable in One-Photon Excitation Fluorescence (1PEF), where the excitation occurs also in out-of-focus regions. To obtain cross-sections, the beam focus is scanned across the sample, as in confocal laser-scanning microscopy, but without the need of using a confocal pinhole. Furthermore, the penetration depth is usually increased with respect to UV–vis CLSM, because the typically employed excitation wavelengths fall in the near-infrared spectral range, where scattering and absorption losses are low for several materials.

One- and two-photon excitation fluorescence emission spectra have the same trend and are both independent of the excitation wavelength. On the other hand, the 2PEF absorption spectra can substantially differ from their 1PEF counterparts. In the case of two-photon excitation, the momenta of the two excitation photons combine to give a higher degree of freedom than in single-photon excitation, meaning that nonlin- ear excitation allows electrons to access excited states like S2 and S4, higher than what is accessible with 1PEF, resulting in broader 2PEF absorption spectra for many fluorophores [94]. To compare and quantify 2PEF brightness among different fluo- rophores, instead of using the product ofεQf as in the 1PEF case, a two-photon action cross-section is defined asσ2ωQf, whereσ2ωis the 2-photon absorption cross-section andQf is the quantum efficiency, as before.²The value of one-, two-, and three-photon

2 For example, rhodamine 6G has aσ2ωQ_f of 40 Göppert-Mayer units (GM; 1 GM10−50 cm⁴ s/photon) at 830 nm.

Fig. 5Comparison of one-photon fluorescence (beam on the left) and 2PF (beam on the right) in a fluorescent dye cell (a), and schematic representation of the phenomenon (b). The linear absorption is produced by the interaction with a continuous-wave laser (upper objective lens on the right-hand side of the sample), generating the expected Gaussian beam pattern of excitation. The lower objective lens on the left focuses a pulsed infrared laser beam, leading to the nonlinear interaction. The excitation volume is confined in a spot in which the density of photons is sufficiently high to generate 2PEF. Permission to use granted by Newport Corporation. All rights reserved

excited fluorescence depends very much on both the molecular species involved and the fundamental frequency of the excitation laser [103], nevertheless, a rough estimate is 10^–20cm², 10^–50cm⁴s and 10^–76cm⁶s², respectively.

3.3 Basic instrumentation for nonlinear optical microscopy

Typically, the detection of the nonlinear optical response in the imaging mode requires a scanning system enabling the movement of either the laser or the specimen. The device includes a femtosecond pulsed laser, which is introduced into an adapted micro- scope and directed to the specimen through a high NA objective lens. The scheme of a basic nonlinear microscope setup is depicted in Fig.6. The raster scanning (xy) of the sample surface can be achieved with the use of galvanometric mirrors, or by placing the object in a motorizedxytranslation platform, whereas the movement of the focus through the sample in the axial (z) direction is generally controlled by a motorized stage. The signal is amplified and detected in the backward direction, passing through the same objective as the incident beam, or collected in the forward direction by a second objective.

3.3.1 Laser sources

The pioneering work of Denk in 1990 [71], introducing the use of a pulsed mode-locked dye laser for the nonlinear excitation of fluorescence in living cells in imaging modal- ity, paved the way for the development of fs-pulsed lasers for nonlinear microscopy applications. Before that, the use of dye lasers was anyway decreasing, due to their toxicity, fast ageing, low average power (with a maximum around 10 mW) and limited

Fig. 6Basic scheme of a nonlinear optical microscope:

the fs-laser beam (fs LS) is collimated by a lens (L) and partially reflected by a dichroic mirror (DM) to an objective (O1) oriented towards the sample (S), which is placed on a motorized stage (Z). The generated signal is collected both in backward and forward directions by the objectives (O1 and O2). After passing through the optical filters (F1 and F2), the output signals enter the photomultipliers (PMT) and is processed by the acquisition system

tuning range, with steps greater than ~ 30 nm requiring a complete dye change [104].

The capability of ultrashort pulsed lasers increased abruptly with the introduction of high-quality solid-state Titanium-Sapphire lasers, thanks to their advantageous charac- teristics, namely the absence of toxic spills, extended spectral bandwidth (from 690 nm to more than 1μm), very short pulse duration (in the order of 10 fs), good durability with excellent thermal conduction properties, and outstanding energy storage enabling significantly higher average power. Ti:Sapphire lasers, based on an active medium of crystal sapphire (Al2O3) doped with titanium ions, have the most efficient emission at around 800 nm and are typically pumped by other lasers emitting in the range from 514 to 532 nm, such as argon-ion and frequency-doubled (Nd:YAG, Nd:YLF, and Nd:YVO) lasers. The potential of Ti:Sapphire crystals in ultrashort pulse oscillators was shown by Spence et al.in 1991 [105], sparking a revolution in solid-state ultrafast oscillators. In a few years, the development of Kerr lens mode-locked lasers increased the average power to 1 W, while dramatically reducing the pulse duration. Although other sources, such as Yb:YAG, Cr:LiSAF, Nd:YLF, Nd:glass, Cr:fosterite, and fibre- based lasers, have proven useful for multi-photon imaging applications, Ti:Sapphire lasers have become the first choice for multi-photon microscopy, despite their cost, which is still high.

3.3.2 Microscopes and signal acquisition systems

The interaction volume in NLOMs is determined not only by the focusing properties of the microscope objective (its numerical aperture) and the radiation wavelength used, but also by the order of the nonlinear optical interaction. The NA is related to the refractive indexn of a medium, as well as to the angular apertureϑ of a given objective, following the relation N A n ·sinϑ. By using the maximum angular aperture (around 144º) of an oil-immersion objective (noil 1.52), the maximum NA will be 1.45, whereas with a dry, i.e. non-immersion objective, the maximum

NAwill be 0.95 (nair 1.0). The optical resolution is traditionally defined applying the Rayleigh criterion, which states that two components of equal intensity should be considered resolved when the main intensity maximum of one coincides with the first minimum of the other [106]. The diffraction-limited focusing properties of a high-NA microscope objective and, subsequently, its optical resolution, can be described by the minimum lateral and in-depth distance between resolvable points, i.e. the radial and axial coordinate,r0andz0, respectively:

r01.22λ/2·sinϑ0.61λ/N A, (18)

z02nλ/(N A)². (19)

According to Eqs.13and14, the resolution in radial and axial directions increases when using shorter wavelengths and higher NA.

In general, a signal with nonlinear dependence on the electric field intensity tends to reduce the interaction volume with respect to its linear counterpart, thus increasing the optical resolution. In fact, considering the focal field intensity as Gaussian distribution I(x)e^−x2/2σ2, (20) for which the full width at half maximum (FWHM) is

FWHM2σ

2 ln(2). (21)

For anNth order process, the FWHM reduces to

FWHMN 1

√N2σ

2 ln(2). (22)

Hence, as a general rule, the interaction volume of aNth order nonlinear process decreases by a factor of√

N, with respect to the linear interaction volume at the same optical wavelength.

However, in multi-photon absorption processes, the excitation of the one-photon transition of the fluorophore requires a longer wavelength, that scales with the non- linearity of the process as

λ⁽ⁿ⁾Nλ⁽¹⁾, (23)

where (n) denotes the order of the process.

Thus, in multiphoton absorption processes, the decrease in resolution from the increase in wavelength is compensated only in part by the decrease in the interaction volume, due to the nonlinearity of the interaction. Effectively, the interaction volume for aN-photon absorption process increases by a factor of√

N, relative to its single- photon absorption counterpart [104].

Fig. 7Logarithmic increase of MPEF signal intensity detected on an acrylic paint layer irradiated with increasing laser power (1–13 mW). The slope (2.69) of the nonlinear fit (red line, R²9.97), shows the third order nonlinear dependence of the MPEF process to the applied pulse energy

3.3.3 Nonlinear optical devices for artworks analysis

As regards the evolution of nonlinear optical microscopy devices, starting from the first two-photon laser scanning fluorescence microscope realized in 1990 by Denk et al.

[71], technical features and performances have been greatly improved in the last twenty years, concurrently with the impressive spread of NLOMs in biological sciences.

Indeed, thus far, the setups used for the analysis of artistic materials are originally developed for the biomedical branch. Most of the available devices enable to perform point- and/or area-wise measurements, by collecting the nonlinear optical signals both in the epi- and trans-detection modes. All kind of NLO analysis (MPEF, THG, SHG, and FLIM) can be carried out with a custom-built laser-scanning microscope equipped with the proper acquisition systems. The excitation sources commonly used for this kind of application are Ti–Sapphire [76, 79–84] and Yb:KGW [107] femtosecond lasers, as well as Optical Parametric Oscillators (OPO) pumped by Yb-based pulsed lasers [108] emitting in the NIR range. Typical excitation wavelengths for CH studies are 800 nm [80], 860 nm [77], 1028 nm [80], 1040 nm [85], which have proved suitable for the generation of nonlinear signals in different artistic materials, making it possible to observe the nonlinear dependence of the signal to the applied power. For instance, by irradiating a cadmium yellow paint layer with increasing laser pulse power (range 1–13 mW) at 800 nm, the third-order nonlinear dependence of the MPEF process is demonstrated by the logarithmic increase of the signal intensity (Fig.7).

In CH application, the irradiation pulses may range from 70 to 90 fs [77,85], with a repetition rate between 50 [78] and 80 MHz [85], determining different photon doses—i.e., number of laser pulses per irradiated point on the sample surface. This parameter has turned crucial for the definition of safe measurement conditions in paint analysis (thresholds of laser power—see ch. 4).

Objective lens characterized by different NA (typically, 0.4, 0.7, or 0.8), and mag- nification (10–40×) are used for the excitation and collection of the nonlinear signals.

Lateral and axial resolutions achievable near the sample surface are approximately in the range 0.4–0.7μm and 1.5–3μm, respectively [76,79,88,109].

Generally, the signal is amplified by Photomultiplier Tubes (PMT), with spectral sensitivity covering the visible range, whose extent depends on the filtering selected for the specific application. The setups designed for fluorescence lifetime microscopy consist of a photon-counting PMT equipped with a diffraction grating allowing for spectrally resolved measurements of the fluorescence light [110]. Imaging systems based on raster scan make use of galvanometric scanning mirrors and motorized translationxyzstages [111], enabling the acquisition of two-dimensional images of approximately 150×150μm²and 1000×1000 pixels, in about 1 –3 s measurement time [88,108].

Some devices are implemented with a motorized rotation stage to control the orientation of the excitation linear polarization at the sample plane, enabling polarization-resolved SHG (PSHG) imaging. A rotating polarizer is also inserted in front of the PMT to measure the anisotropy due to the polarization of the SHG signals [88].

4 Applications of nonlinear optical microscopy in cultural heritage In the last years, the use of NLOM has spread in several scientific fields, although originally it was restricted to biomedical applications, mainly for in vivo imaging and mapping of subcellular structures. Specifically, second harmonic generation has proven useful for the analysis of stacked membranes and arranged proteins with organized structures, such as collagen [69,110], as well as for probing membrane- potential-induced alignment of dipolar molecules [70]. Third harmonic generation, being generated from regions with optical discontinuities [99], has been used for detecting structural and anatomical changes of biological samples at cellular or sub- cellular level [111,112]. Since 1990 [71], MPEF has been playing a pivotal role in the study of biological matter, together with confocal microscopy, for a variety of applications, ranging from the tracking of individual molecules within living cells to the visualization of whole organisms [72].

More recently, nonlinear optical imaging has been introduced in the field of cul- tural heritage for the analysis of several types of artworks [113,114]. Its application ranges from the study of varnish layers, oils, synthetic glues and over-paintings, to the visualization and characterization of wood microstructures, from parchment to the identification of corrosion layers in metal-based objects. The potential to provide com- positional and structural information of different materials makes these non-destructive high-resolution modalities a promising tool for art diagnostics.

As regards paintings, some tests have been performed on painted mock-ups charac- terized by different binding media and pigments, exploiting the relative transparency of most pictorial materials in the near-infrared region. The final aim of such applica- tions is to obtain the micrometric surface mapping and the in-depth profiling of thin films of pictorial materials basing on refractive index changes, variation of optical

activity and presence of fluorophores. This information may turn definitely useful for the analysis of painted objects, as well as for the monitoring of restoring operations, like the cleaning process, which irreversibly modify the morphology and thickness of the superficial layers.

4.1 Varnishes, oils and glues

Mechanical properties and aesthetic appearance of painted artworks may be signifi- cantly compromised by structural discontinuities, detachments and chemical alteration of the superficial layers, due to ageing and environmental agents. The cohesion and adherence among the constituting materials are commonly restored through the appli- cation of an adhesive material, called consolidant (e.g., natural or synthetic glue), which is generally injected inside the damaged layers. Furthermore, to prevent the paint layer from deterioration, as well as to improve its aesthetic appearance [75] a thin film of a transparent material (called protective, typically consisting of a varnish which can be of several types) is often laid or vaporized over the surface. A variety of natural and synthetic polymeric materials have been used in the past and are still routinely employed for the consolidation and protection of paintings. The identifica- tion and in-depth quantification of such materials is especially useful in the case of restoring processes, including cleaning (see the Introduction).

In 2008, Filippidis et al.applied Three-Photon Excitation Fluorescence (3PEF) and THG imaging for the determination of thickness in natural and synthetic varnish lay- ers laid on glass coverslips [113]. A diode-pumped Yb-doped solid-state laser with a central wavelength of 1028 nm was used for exciting 3PEF and THG signals, which were collected simultaneously in backward and transmission modes by using two different objective lenses placed at both sides of the sample. Several natural (mastic and colophony) and synthetic (Vinavil®) varnishes were studied. Preliminary UV–vis absorption analysis attested the transparency of all the materials at 514 nm and max- imum absorption of UV wavelengths. The fluorescence emission excited at 343 nm was also investigated, showing a maximum at 428 nm and 408 nm for mastic and colophony, respectively, whereas, when exciting at 514 nm, no emission was detected.

These results confirmed that the nonlinear fluorescence observed by irradiating the two natural varnishes with the 1028 nm fs-laser was a three-photon excitation process.

The absorption of Vinavil was less than 3% at 343 nm and, consequently, no fluo- rescence was detected. Concerning the acquisition of THG in transmission mode in a multi-layered sample, the refractive index mismatch between the media allowed dis- tinguishing different interfaces (air/Vinavil, Vinavil/mastic, mastic/glass, glass/air).

3PEF signals arising only from the mastic layer provided complementary informa- tion on a single measurement, enabling the evaluation of the material thickness. Two overlaying layers of natural varnishes, colophony, and mastic resulted not distinguish- able by THG, due to the too low difference between the respective refractive indexes.

However, by exploiting the different absorptivity, two different levels of nonlinear fluorescence signal were observed (Fig.8).

In 2008, Gualda et al.[115] determined the thickness of varnish layers in painting samples, using a combination of THG and MPEF imaging modalities in the reflection