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Nonlinear optical microscopy for artworks physics

Abstract

Nonlinear optical microscopies (NLOMs) are innovative techniques recently introduced 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 materials, 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 conditions and instrumental requirements for the safe and in situ application of NLOMs on real cases.

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 reference 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, hampering the legibility of the painted surface. Such information becomes crucial especially in the context of restoring operations, like the cleaning, a delicate and irreversible procedure consisting in the selective removal or thinning of aged varnishes not fulfilling their protective/aesthetic function anymore, and/or over-paintings covering the historical 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 [2,3,4,5], and fluorescence microscopy [6]), and micro-analytical techniques [7,8,9,10] 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.

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 selective on a specific layer (reflectography in the visible range) or is integrated over the whole thickness of the artwork (Infrared Reflectography—IRR; single-energy standard 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 internal 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 optical 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 [15,16,17], 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 [17,18,19,20]. 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 [22,23,24,25,26,27,28]. 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 1–10 μm. 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 measure 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 interference is observed whenever the signal superimposes with the reference beam within the coherence length of the used light source. In this case, the n-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 aforementioned 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 provide 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 highlighting 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 provides 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 spectral 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 compression 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 resonance (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 effectiveness 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 provided axial profiles of paintings, by spanning several millimetres across depth ranges of up to 25 mm with a resolution better than 10 μm [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 50 μm) [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 (fs = 10–15 s) 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 photoacoustic (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 painting 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 operations 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, spherically/cylindrically focused) has already yielded promising results in the analysis of painted mock-ups [55]. To overcome the limitations of PA in resolving the superimposed 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 biomedical field, mainly for in vivo imaging and mapping of molecular structures [65,66,67,68,69,70,71,72]. 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, 79,80,81,82,83,84,85]. 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 several 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 nonlinear 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, parchments, 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 absorption 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 artefacts (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, ranging 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.

Nonlinear optics

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 nonlinearly 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 coherent light sources generating beams of high intensity (> 1012 W/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 \(\tilde{P}\left( t \right)\) tensor (dipole moment per unit volume) of a system upon the strength \(\tilde{E}\left( t \right)\) of the applied electric field. In linear optics, the induced polarization depends linearly on the electric field strength, as described by the relation

$$ \tilde{P}\left( t \right) = \chi ^{{\left( 1 \right)}} \tilde{E}\left( t \right), $$
(1)

where \(\chi ^{{\left( 1 \right)}}\) represents the linear susceptibility (for simplicity, from now on \(\tilde{E}\left( t \right)\) and \(\tilde{P}\left( t \right)\) will be considered as scalar quantities).

In nonlinear optics, the response is described by expressing \(P\left( t \right)\) as a power series in \(E\left( t \right)\), as

$$ \begin{aligned} P\left( t \right) & = \chi ^{{\left( 1 \right)}} ~E\left( t \right) + \chi ^{{\left( 2 \right)}} E^{2} \left( t \right) + \chi ^{{\left( 3 \right)}} E^{3} \left( t \right) + \ldots ~ \\ ~ & \equiv P^{{\left( 1 \right)}} \left( t \right) + P^{{\left( 2 \right)}} \left( t \right) + P^{{\left( 3 \right)}} \left( t \right) + \ldots \\ \end{aligned} $$
(2)

where \(\chi ^{{\left( 2 \right)}}\) and \(\chi ^{{\left( 3 \right)}}\) are the second- and third-order nonlinear optical susceptibilities, and \(P^{{\left( 2 \right)}} \left( t \right) = \chi ^{{\left( 2 \right)}} E^{2} \left( t \right)\) and \(P^{{\left( 3 \right)}} \left( t \right) = \chi ^{{\left( 3 \right)}} E^{3} \left( t \right)\) express second- and third-order nonlinear polarizations, respectively. Hence, the nonlinear optical signals are the consequence 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 (\(E_{{at}} = 5.14 \times 10^{{11}} ~\)  V/m),Footnote 1 the use of a perturbative approach, as that expressed in (2), for the theoretical description of the nonlinear phenomena is justified.

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.

Second-harmonic generation

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

Fig. 1
figure1

Second Harmonic Generation. a Sketch of the process. b Energy-level diagram, describing the SHG frequency \(\omega\) doubling process, from the ground state S0 (solid line) to the virtual levels (dashed lines), with the emission of a \(2\omega\) photon

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 strength \(E\left( t \right)\) at frequency ω, is represented by

$$ E\left( t \right) = E\cos \left( {\omega t} \right), $$
(3)

or using Euler's formula,

$$ E\left( t \right) = Ee^{{ - i\omega t}} + c.c., $$
(4)

where c.c. stands for complex conjugate and i is the imaginary unit [90].

According to Eq. (2), if the incident beam interacts with a material having nonzero second-order susceptibility \(\chi ^{{\left( 2 \right)}}\), the nonlinear polarization generated inside the material is \(P^{{\left( 2 \right)}} \left( t \right) = \chi ^{{\left( 2 \right)}} E^{2} \left( t \right)\) or

$$ P^{{\left( 2 \right)}} \left( t \right) = 2\chi ^{{\left( 2 \right)}} E^{2} + \left( {\chi ^{{\left( 2 \right)}} E^{2} e^{{ - 2i\omega t}} + c.c.} \right). $$
(5)

The second-order polarization is given by two contributions, the first at zero frequency (first term) and the second at \(2\omega\) frequency (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 \(\chi ^{{(2)}}\) is related to the polarizability of the molecule \(~\left\langle \beta \right\rangle = \chi ^{{\left( 2 \right)}} /N_{s}\), with \(N_{s}\) being the density of atoms or molecules, and the brackets denote an averaged orientation. Thus, \(\left\langle \beta \right\rangle\) is 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 species the nonlinear susceptibility \(^{{\left( 2 \right)}}\) 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 field \(E\left( t \right)\) changes, the induced second-order polarization \(P^{{\left( 2 \right)}} \left( t \right) = \chi ^{{\left( 2 \right)}} E^{2} \left( t \right)\) also changes. Hence, \(P\left( t \right)\) is replaced by

$$ - P^{{\left( 2 \right)}} \left( t \right) = \chi ^{{\left( 2 \right)}} \left[ { - E\left( t \right)} \right]^{2} = \chi ^{{\left( 2 \right)}} E^{2} \left( t \right). $$
(6)

Being \(P^{{\left( 2 \right)}} \left( t \right) = \chi ^{{\left( 2 \right)}} E^{2} \left( t \right)\), \(P^{{\left( 2 \right)}} \left( t \right)\) must be equal to \(- P^{{\left( 2 \right)}} \left( t \right)\), which occurs only if \(P^{{\left( 2 \right)}} \left( t \right)\) vanishes identically, meaning that

$$ \chi ^{{\left( 2 \right)}} = 0 $$
(7)

This result is described in Fig. 2. The waveform of the incident monochromatic electromagnetic wave of frequency \(\omega\) (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 distortion, with only odd harmonics of the fundamental frequency. Finally, for the case of a nonlinear, non-centrosymmetric medium (Fig. 2d), both even and odd harmonics 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.

Fig. 2
figure2

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]

Waveforms associated with the atomic response, see text.

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 fundamental and SH wave and is maximum when the photon momentum p is conserved. As p = kh/2π, k being the wave vector, momentum conservation means that

$$ k\left( \omega \right) + ~k\left( \omega \right) = ~k\left( {2\omega } \right). $$
(8)

The equivalent condition

$$ ~2n\left( \omega \right)\frac{\omega }{c} = ~n\left( {2\omega } \right)\frac{{2\omega }}{c}, $$
(9)

where n is the refractive index, implies that

$$ n\left( {2\omega } \right) = n\left( \omega \right). $$
(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 (subscript e) and the ordinary (subscript o) polarization for ω and 2ω, respectively, and by rotating the birefringent crystal, phase matching is possible, i.e.

$$ n_{o} \left( {2\omega } \right) = n_{e} \left( \omega \right), $$
(11)

as the refractive index ne depends 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].

Third-harmonic generation

Third-order polarization, \(P^{{\left( 3 \right)}} \left( t \right) = \chi ^{{\left( 3 \right)}} E^{3} \left( t \right)\), 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 \(\cos ^{3} \omega t = \frac{1}{4}\cos 3\omega t + \frac{3}{4}\cos \omega t\), the nonlinear polarization can be expressed by

$$ P^{{\left( 3 \right)}} \left( t \right) = \frac{1}{4}\chi ^{{\left( 3 \right)}} E^{3} \cos 3\omega t + \frac{3}{4}\chi ^{{\left( 3 \right)}} E^{3} \cos \omega t. $$
(12)

The first term describes a response at frequency \(3\omega\), due to an applied field at frequency \(\omega\). 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 frequency \(\omega\) are simultaneously converted in one photon of frequency \(3\omega\).

Fig. 3
figure3

Third Harmonic Generation. a Sketch of the process. b Energy-level diagram, describing the THG frequency \(\omega \) tripling process. The solid line and the dashed lines represent the ground state S0 and the virtual levels, respectively

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 condition ∆k = 0, equivalent to Eq. (8) for SHG, has to be fulfilled. For THG the corresponding condition reads as

$$ \Delta k = k\left( {3\omega } \right) - 3k\left( \omega \right) = 0. $$
(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 volume 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 efficiency 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 detection 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 number N of photons (2 or 3, for SHG and THG, respectively) of energy \(h\omega\) to emit one photon of energy \(Nh\omega\). The \(N\) th harmonic intensity scales with the intensity of the fundamental incident radiation \(I\) as \(I^{N}\).

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 (S2 and 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 (10−18 s) and team up to excite the molecule [94]. In principle, any combination of photons reaching the energy difference between S0 and S2 may 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 ∼10−8–10−9 s, 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.

Fig. 4
figure4

Jablonski diagrams of a single-photon excitation and b multi-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. c Stokes shift effect between normalized absorption and fluorescence emission spectra of a fluorophore

On the one hand, the capacity of a molecule for light absorption is determined by its molar extinction coefficient ε (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 yield Qf (dimensionless) and the emission spectrum (Fig. 4c). Hence, the brightness of a fluorophore is determined by the product εQf. The time that elapses between the absorption and the emission is called fluorescence lifetime (\(\tau )\), 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 ∼10−4 s 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

$$ Q_{f} = k_{r} /(k_{r} + k_{{nr}} ), $$
(14)

where \(k_{r}\) is the rate of relaxation to the ground state by fluorescence and \(k_{{nr}}\) is the rate of relaxation to the ground state by non-radiative processes [101].

Similarly, the lifetime of an excited state is defined by

$$ \tau = 1/(k_{r} + k_{{nr}} ). $$
(15)

As a general principle, the main difference between one and two photon absorptions relies on the diverse dependence on the applied field intensity \(I\) or, in other terms, on the field amplitude E. In fact, the transition rate of one photon, as well as the fluorescence intensity, is linearly dependent on the intensity \(I\) of the optical field

$$ Abs_{{1ph}} \propto ~E^{2} \propto I, $$
(16)

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

$$ Abs_{{2ph}} \propto ~E^{4} \propto I^{2} . $$
(17)

More generally, the probability of n-photon absorption by a molecule is proportional to \(I^{n}\), 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 (10−15 L). 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.

Fig. 5
figure5

Permission to use granted by Newport Corporation. All rights reserved

Comparison 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.

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 nonlinear 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 fluorophores, instead of using the product of εQf as in the 1PEF case, a two-photon action cross-section is defined as σQf, where σ is the 2-photon absorption cross-section and Qf is the quantum efficiency, as before.Footnote 2 The value of one-, two-, and three-photon 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 10–20 cm2, 10–50 cm4 s and 10–76 cm6 s2, respectively.

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 microscope 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 motorized xy translation 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.

Fig. 6
figure6

Basic 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

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 modality, 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 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 characteristics, namely the absence of toxic spills, extended spectral bandwidth (from 690 nm to more than 1 μm), 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.

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 index \(n\) of a medium, as well as to the angular aperture \(\vartheta\) of a given objective, following the relation \(NA = n \cdot \sin \vartheta\). By using the maximum angular aperture (around 144º) of an oil-immersion objective (\(n_{{oil}} ~\) = 1.52), the maximum NA will be 1.45, whereas with a dry, i.e. non-immersion objective, the maximum NA will be 0.95 (\(n_{{air~}}\) = 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, \(r_{0}\) and \(z_{0}\), respectively:

$$ r_{0} = 1.22~\lambda /2 \cdot \sin \vartheta = 0.61~\lambda /NA, $$
(18)
$$ z_{0} = 2n~\lambda /\left( {NA} \right)^{2} . $$
(19)

According to Eqs. 13 and 14, 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

$$ I\left( x \right) = e^{{ - x^{2} /2\sigma ^{2} }} , $$
(20)

for which the full width at half maximum (FWHM) is

$$ {\text{FWHM}} = 2\sigma \sqrt {2\ln \left( 2 \right)} . $$
(21)

For an Nth order process, the FWHM reduces to

$$ {\text{FWHM}}_{N} = \frac{1}{{\sqrt N }}2\sigma \sqrt {2\ln \left( 2 \right)} . $$
(22)

Hence, as a general rule, the interaction volume of a Nth order nonlinear process decreases by a factor of \(\sqrt N\), 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 nonlinearity of the process as

$$ \lambda ^{{\left( n \right)}} = N\lambda ^{{\left( 1 \right)}} , $$
(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 a N-photon absorption process increases by a factor of \(\sqrt N\), relative to its single-photon absorption counterpart [104].

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, 79,80,81,82,83,84] 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).

Fig. 7
figure7

Logarithmic 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, R2 = 9.97), shows the third order nonlinear dependence of the MPEF process to the applied pulse energy

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 magnification (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 0.4–0.7 μm and 1.5–3 μm, 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 translation xyz stages [111], enabling the acquisition of two-dimensional images of approximately 150 × 150 μm2 and 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].

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 cultural 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 compositional 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 characterized by different binding media and pigments, exploiting the relative transparency of most pictorial materials in the near-infrared region. The final aim of such applications 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.

Varnishes, oils and glues

Mechanical properties and aesthetic appearance of painted artworks may be significantly 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 application 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 identification 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 layers 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 maximum 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 fluorescence was detected. Concerning the acquisition of THG in transmission mode in a multi-layered sample, the refractive index mismatch between the media allowed distinguishing different interfaces (air/Vinavil, Vinavil/mastic, mastic/glass, glass/air). 3PEF signals arising only from the mastic layer provided complementary information on a single measurement, enabling the evaluation of the material thickness. Two overlaying layers of natural varnishes, colophony, and mastic resulted not distinguishable 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).

Fig. 8
figure8

COPYRIGHT: Adapted with permission from G. Filippidis et al., Opt. Lett. 33, 240–242 (2008) © The Optical Society [113]

Sections a by THG signal and b by 3PEF analysis of a multi-layered sample with mastic and colophony showing the interfaces, and the different nonlinear fluorescence, respectively.

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 mode, with an excitation wavelength of 1028 nm. The paint layers were prepared with different pigments and binders, including ready-made acrylics (lemon yellow, ochre yellow), oil-tempera (ochre yellow with linseed oil), and egg-tempera (titanium white and barium chromate). All paints were covered with colophony resin. MPEF and THG signal of colophony were preliminarily measured on a single-layer sample. In some cases, the presence of the paint underneath the varnish allows detecting the TH signal in reflection mode, although most of the signal is generally transmitted in the forward direction due to the coherent nature of the THG process. It was observed that the absorption behaviour of the different pigments to the excitation wavelength strongly influences the generation and detection of nonlinear signals from the varnish. All painting materials showed absorption at the fundamental laser wavelength (1028 nm) and different interactions at the wavelengths of the second (514) and third harmonic (343 nm). By contrast, the minimal absorption of colophony in the visible and infrared spectral regions indicated that the main contribution to the nonlinear fluorescence process was due to three-photon excitation. Furthermore, it was observed that the damage threshold for paintings was at a laser power of around 20 mW (less than 0.4 nJ per pulse). In the presence of ochre yellow and barium chromate substrates, air/colophony and colophony/pigment interfaces were detectable through THG in the reflection mode (with a clear visualization in case of air/colophony interface). The higher refractive index mismatch between ochre yellow and colophony, with respect to barium chromate and colophony, increased the efficiency of the THG process. It is worth mentioning that only the visualization of the outer structures of the model paintings was feasible, due to the strong absorption of the pigments, thus precluding the detection of THG in the transmission mode.

Concerning MPEF, the signals showed different intensity values depending not only on the pigment but also on the binding medium. Strong fluorescence signals from linseed oil and egg were observed, but no signal was detected from the acrylic paints. This indicates that, in specific cases, MPEF may provide complementary information about the painting technique.

A further combined application of THG and 3PEF was performed by Nevin et al. [116] for the analysis of multi-layer samples composed of triterpenoid varnishes (dammar and mastic) over linseed oil, laid on a glass support. Results obtained through nonlinear measurements were integrated with confocal Raman microscopy for the chemical characterization of the samples as a function of depth. CRM spectra acquired in the fingerprint region (between 500 and 1900 cm−1) and in the C–H stretching region (2600 and 3200 cm−1) at different depths were integrated with multi-photon measurements. Using a fs-laser at 1028 nm, strong THG signals were observed at the air/varnish, oil/glass, glass/air interfaces, whereas weaker signals were detected at the interface between varnish and oil. This was ascribed to the smaller refractive index mismatch between the organic media and auto-absorption of THG signal by the sample itself (Fig. 9a). 3PEF analysis was useful for a distinction between materials but with significant limits of interpretation because the fluorescence emitted by mastic, dammar and linseed oil was not easily distinguishable (Fig. 9b).

Fig. 9
figure9

Reprinted by permission from Springer Nature Customer Service Centre GmbH: Springer, Appl. Phys. A, Multi-photon excitation fluorescence and third-harmonic generation microscopy measurements combined with confocal Raman microscopy for the analysis of layered samples of varnished oil films, A. Nevin et al., Copyright (2010) [116]

a THG and 3PEF signal in a multi-layered sample of mastic/linseed oil on glass; the thickness of the different materials is indicated in light grey for mastic, dark grey for linseed oil, and diagonal lines for the glass support. b Reconstructed image of the same sample showing the THG signal at the interfaces (green lines) and the 3PEF signal (greyscale). Mastic and oil are characterized by similar 3PEF intensities.

Another study involving layers of natural varnishes was carried out by Filippidis et al. in 2015, for the in-depth determination of the affected regions due to artificial ageing [78]. Single-photon Laser-Induced Fluorescence (LIF) and Raman spectroscopy measurements were combined for the integrated investigation of the degradation in dammar and mastic. The artificial ageing was obtained by exposing the varnishes to a mercury discharge lamp for 61 days (~ 29 lx × 106 h), equivalent to 50 years of exposure in museum conditions [117, 118]. Nonlinear analysis was performed using a fs-laser at 1028 nm, and MPEF and THG signals were collected simultaneously in backward and transmission modes, respectively. The sample was analysed before and after ageing. As regards the dammar varnish, three different layers were distinguished via THG indicating the interface between the different media (dammar/air, glass/dammar, air/glass). The stratigraphy was complemented by the MPEF signal, which was mainly attributed to three- and four-photon excitation, i.e., absorption at 343 and 257 nm, respectively. Furthermore, MPEF measurements provided in-depth information related to the affected region of the dammar due to artificial aging (Fig. 10a and b).

Fig. 10
figure10

G. Filippidis et al., Assessment of In-Depth Degradation of Artificially Aged Triterpenoid Paint Varnishes Using Nonlinear Microscopy Techniques, Microsc. Microanal. 21, 510–517, reproduced with permission [78]

Multimodal nonlinear imaging of a fresh and b aged dammar varnish sample. THG and MPEF signals are highlighted in yellow and red colours, respectively. c Plots of the pixel brightness distribution of the cross-sectional images a) and b) across a vertical line (green and dark red line, respectively). The grey region denotes the affected area as a function of depth from the surface of the aged dammar sample.

Plots of the pixel brightness distribution across a central vertical line for the two images were performed, showing a significant increase in the MPEF signal from the surface up to a depth of 31 μm in the aged dammar sample (Fig. 10c). For mastic, the extension of the affected region due to artificial ageing was found to be around one-third of that of the dammar sample. Such difference was attributed to the higher absorption coefficient of mastic at 360 nm, which coincides with the emission peak of the mercury lamp, and to the exponential decrease of the incident light intensity as a function of the sample thickness.

In another study [119], THG and SHG in transmission and reflection mode were applied conjunctly to the analysis of lining glues, enabling the determination of layers’ thickness and the discrimination between different materials. Different types of natural and synthetic lining glues (rabbit skin glue, starch glue, Beva 371®, Lascaux 498 HV®, Mowilith®, Vinavil®) were cast on thin coverslips for the analysis. In all cases, the excitation wavelength was 1028 nm and average laser power on the specimen of 30 mW (0.6 nJ per pulse) was applied to prevent the samples from damage. The THG signals were collected in transmission mode using a 340 nm coloured glass filter, while SHG signals were detected in the backward direction using an interference filter centred at 514 nm. The THG signal was proved effective for the evaluation of layer thicknesses through the visualization of the interfaces, whereas SHG measurements provided complementary information related to the composition of the glues, specifically about the presence or absence of collagen and starch granules. As expected, the only materials producing SHG signals were rabbit skin glue and starch glue, all containing compounds with non-zero second-order nonlinear susceptibility. In the case of Vinavil, a small portion of the material was mechanically removed and the THG measurements before and after the treatment were compared to quantify the entity of the removal (Fig. 11).

Fig. 11
figure11

Reprinted by permission from Springer Nature Customer Service Centre GmbH: Springer, Anal. Bioanal. Chem., Second and third harmonic generation measurements of glues used for lining textile supports of painted artworks, G. Filippidis et al., Copyright (2009) [119]

Vinavil sample nonlinear spot measurements showing the THG signal arising from the interfaces air/glue and glue/glass, before a and after b the mechanical removal of glue. The thickness reduction of the layer was quantified, resulting in around 20 μm.

Seven years later, the same flour- and starch-based paste samples were analysed through polarized-resolved SHG imaging and THG for quantitatively discriminate fresh glues from naturally aged ones [87]. As indicated in Sect. 3.2.1, the SH signal is sensitive to the incoming excitation polarization and the architecture of the SHG active structures. By rotating the axis of the linear polarization impinging on the sample and by recording the SH signal, it is possible to gain structural information unachievable by common SHG imaging, basing only on signal intensity detection. Data analysis was performed with an FFT-based PSHG method enabling to significantly reduce the image processing time for the acquisition of three-dimensional (3D) stacks, showing pixel-by-pixel the orientation of the SHG angle (θ). A filtering method was also introduced to clean up the data by discarding erroneous pixels. This allowed obtaining information on both the organization of SHG molecules and the molecular helical pitch angle, thus proving the effectiveness of PSHG in discriminating between aged and fresh glues. Specifically, it was observed that the SHG effective orientation of starch granules (θ) shows significantly higher values in aged glues compared to the fresh ones, due to the different degree of hydration.

Paints

Only recently nonlinear optical microscopy analyses on painting layers have been carried out. In 2015, Filippidis et al. [75] performed THG measurements on two painted samples on a glass support, made with an ultramarine blue acrylic tempera, the first, and a titanium white (TiO2) egg tempera covered by colophony varnish, the second. The ultramarine acrylic layer was measured with a fs-laser emitting at 1560 nm. The detection of THG signals in imaging mode enabled both the determination of the thickness (58 µm) and the evaluation of the particle distribution in the acrylic medium. Since the refractive index mismatch between the pigment and the acrylic binder is minimal, the main contribution to the effective generation of THG was attributed to the abrupt change of the third-order susceptibility value. Moreover, a small portion of the pigment fluorescence, at 520 nm, allowed for the enhanced contrast among ultramarine particles/aggregates and the surrounding acrylic environment (Fig. 12a).

Fig. 12
figure12

Reprinted by permission from Springer Nature Customer Service Centre GmbH: Springer, Appl. Phys. A, Nonlinear imaging techniques as non-destructive, high-resolution diagnostic tools for cultural heritage studies, G. Filippidis et al., [Copyright] (2008) [113]

a THG cross-sectional imaging of a layer composed of ultramarine blue pigment in acrylic binder, on glass support. b Section of a multilayer model-painting sample: blue and green areas represent THG and MPEF signals, respectively. The scanning lateral dimension of the recorded image is 10 μm).

A multimodal image combining THG and MPEF signals was acquired on the multi-layer painted sample (Fig. 12b). Both signals were recorded in the reflection mode, using a 1028 nm excitation wavelength. The THG measurements revealed the thickness of the varnish layer (around 35 µm), whereas the nonlinear fluorescence signal, arising more strongly from the painting layer than from colophony, enabled the discrimination of the composition between the two different materials.

An example of a multi-analytical approach for the cross-sectional analysis of thin paint layers is the application of MPEF in combination with micro-Raman spectroscopy, Fibre Optics Reflectance Spectroscopy (FORS) and LIF to examine the thickness, the optical behaviour, and the chemical composition of blue and green copper–phthalocyanine (Cu–Pc) acrylic paints [84]. Information obtained by the synergic application of different complementary techniques served to select the adequate excitation and signal collection conditions for thickness measurement by MPEF. Axial signal profiles were normalized and fitted with a Lorentzian function, and the FWHM was taken as an estimation of the paint layer apparent thickness. To obtain the real thickness, FWHM values were subsequently corrected by applying the apparent depth correction factor (F) [120], which takes into account the refractive index of the sample and the effective NA of the focusing objective lens. The so-obtained thickness values were compared with those retrieved through OCT, showing significant consistency and paving the way for further nonlinear stratigraphic investigations on painting materials. This study also demonstrated the advantages of applying MPEF in the reflection mode, making it suitable for the measurement coatings of painting materials laying on an opaque substrate (board, wood, canvas, etc.) for in situ studies.

A comparable multi-modal approach was adopted for the 3D analysis of samples, purposely designed to simulate real egg-tempera painting on wooden support [80]. Red lead, cadmium yellow and Egyptian blue were finely ground in form of powder and mixed with the protein binder, thus creating paint layers characterized by different micrometric morphology. The use of different techniques yielded key information for the characterization of the constituting materials and for the interpretation of the nonlinear results. Furthermore, the comparison among three different nonlinear optical microscopes for MPEF cross-sectional analysis allowed evaluating the response of the analysed paints to different excitation wavelengths, scanning modality, and photon doses. Specifically, the underestimation of thickness or the lack of signal observed with two of the three NLOM setups was explained as a consequence of the applied photon dose affecting the chemical stability of the pigments, which proved useful for the definition of the most suitable measurement conditions. The crucial role of the photon dose in proving reliable thickness values, prepared the ground to further investigation for the definition of the safe threshold of laser power, which will be discussed in the next chapter. Noteworthy, 3D cross-sectional images and axial profiles provided by MPEF (Fig. 13) succeeded in revealing the micrometric morphology and thickness of the paint layers, where OCT did not, due to the strong scattering produced by the three pigments.

Fig. 13
figure13

Modified from Dal Fovo et al., 2020 [80]

MPEF imaging results: a–c z-scans of the MPEF signals of red, yellow and blue temperas (in black), fits by Lorentzian functions (in red), and FWHM values after refractive index correction, corresponding to the paint thickness (indicated in blue); d–f fluorescence intensity xy images (200 × 200 μm, 256 × 256 pixels) extracted from the MPEF stacks at a depth corresponding to the maximum signal intensity; g–i 3D fluorescence reconstructions showing the thickness of each paint layer.

Recently, the potential of NLOM in discriminating different material layers was also demonstrated by Mari et al. [73, 114], revealing the capability of MPEF to distinguish the pigment from the varnish layer due to the different fluorescent emission levels. The fresh varnish showed high transparency in the visible and infrared regions of the spectrum, while strongly absorbing in the near UV region, thus demonstrating a predominant three-photon excitation mechanism for the employed excitation wavelength (1030 nm), whereas the underlying paint layer exhibited two- and one-photon strong absorption properties. A low-intensity MPEF arose from the layer of dammar, while the painting layer emitted a higher intensity fluorescence signal, as shown in Fig. 14. The thickness of the dammar varnish and red led paint layer was estimated to be 82 μm and 98 μm, respectively.

Fig. 14
figure14

Modified from Mari et al., 2020 [73]

a MPEF signal deconvolution in a z-scan plot profile of a model multi-layer sample composed of a layer of red lead (red/green) and a layer of dammar (blue). The fitted model was used to decouple the nonlinear response (green points) into the signal components arising from dammar (blue line) and red lead (red line). Inset: White light optical longitudinal image (xy) of the irradiated region. Scale bar 20 μm. b MPEF cross-sectional imaging: the red lead (red/green) and the dammar (blue) are clearly distinguishable.

A research line, which goes in parallel with those previously described, concerns pump-probe microscopy analysis [63, 64] for the non-destructive 3D imaging of paintings with molecular and structural contrast [81]. Briefly, pump-probe microscopy uses a sequence of ultrafast pulses (typically 0.2 ps, in duration) to electronically excite molecules and then probe their response at a later time (up to about 100 ps) with a second laser. As the pump pulse moves a fraction of the ground state population into electronic excited states, a corresponding hole in the ground state spectral distribution is created. In response to the excitation, population distributions in both ground and excited states rearrange (excited state population tends to relax back to the ground state). The changes in population can be monitored by applying a second delayed pulse (probe). Each molecular process causes a specific pump-probe delay as a function of the pump intensity, making the detected signals molecular signatures [121]. With respect to biological tissues and skin imaging, the application of this technique on artworks is more challenging, due to the wide variety of organic dyes and inorganic minerals contained in artistic colorants, which hamper the achievement of the correct pump-probe contrast. However, by using an increased spectral range (from the NIR to the visible) of both the pump and the probe beams, with a variable time delay between the pump-probe pulses, it is possible to perform in situ 3D imaging of paintings with molecular specificity.

In the work of Villafana et al. [81], a Ti:Sapphire mode-locked laser emitting at a repetition rate of 80 MHz was used, tuning the excitation wavelength from 615 to 810 nm. An adjustable optical path length in the probe optical arm controlled the inter-pulse delay between the pump pulse train (intensity-modulated) and the probe pulse (unmodulated). Any nonlinear interaction of the pump laser with the sample transferred the modulation from the pump to the probe. A photodiode and a lock-in amplifier with a reference at the modulation frequency detected changes in the probe intensity. Tests were carried out on a set of mock-up paintings, including two different blue pigments, synthetic ultramarine and lapislazuli, covered or mixed with red pigment (quinacridone) to create a purple hue. Virtual cross-sections were obtained after the assessment of the pump-probe wavelength combination and interpulse delay characteristic of each colour. Such parameters served to separate the blue pigments from quinacridone red. Then, virtual cross-sections were obtained by combining the enface xy images (perpendicular to the beam axis) acquired at different depths (z direction).

Using the same approach, nonlinear pump-probe microscopy was applied to the analysis of a 14th-century painting and iron-oxide based earth pigments in ancient pottery [82], after chemical characterization of components. The main results are reported in Fig. 15. A pump-probe delay dataset was acquired using a combination of wavelengths (710 and 810 nm), and a false-coloured image was created. A pump-probe volume dataset was taken with a fixed 0.2 ps delay. Four different materials were detected, and false colours were assigned according to the signal delay: cyan for negative signal (corresponding to lapis lazuli), red and yellow for positive (iron oxide/mordant and gold, respectively).

Fig. 15
figure15

T. E. Villafana et al. 2014 [81]

Up-left: optical microscope cross-section of the painting layer in comparison with the false-coloured image created on the basis of the pump-probe delay showing lapislazuli (cyan), iron-oxide (red) and gold (yellow) components. Up-right: graph showing the cumulative pump-probe traces of all identified pigments. Middle: enface pump-probe xy images (185 × 185 μm2) acquired at different depth (surface; − 5 μm; − 12 μm). Bottom-left: xz slice taken from the volume data showing a positive component mixed within the lapis lazuli layer (most likely iron oxide) with another positive component underneath (most likely gold and possibly, underlying mordant). Bottom-right: maximum intensity projection of the entire volume cube highlighting the composition.

Over-paintings

Selimis et al. [122] in 2009 and Vounisiou et al. in 2010 [123] applied multi-photon excitation fluorescence on samples simulating real cases of over-paintings for the monitoring of the laser-removal of organic and inorganic acrylic paint layers. A thin layer of polymer imitating the original acrylic surface was covered with acrylic paint to simulate the real case of an over-layered modern painting. The polymer was poly-methyl methacrylate (PMMA) and Paraloid B72 (copolymer of ethyl-methacrylate), doped with aromatic compounds (1,4-Di[2-(5-phenyloxazolyl)] benzene, POPOP), whose strong fluorescent emission allows the use of LIF for the detection of modifications generated into the substrate upon the laser-assisted removal, performed with an excimer laser emitting at 248 nm (pulse duration 25 ns). Hence, the evaluation of the extent of the laser-induced photochemical modifications at the substrate was obtained by measuring the fluorescence emitted by the polymer. LIF was applied in combination with MPEF, using a femtosecond laser oscillator with emission at 1028 nm, for the in-depth monitoring of photochemical and structural alterations.

LIF allowed for the detection of changes in the POPOP fluorescence spectra after the irradiation of the overlaying acrylic paint with several pulses at specific fluences of the excimer laser, showing when the photochemical changes induced at the polymer substrate took place, once the over-painting was removed. Then, the irradiated layer was analysed by MPEF, enabling the analysis of the in-depth extent of fluorescence before and after laser irradiation. It was observed that the laser treatment affected the fluorescence properties within a depth of around 11 μm from the sample surface (Fig. 16).

Fig. 16
figure16

A. Selimis et al., 2009 [122]

MPEF measurement on POPOP before and after irradiation with excimer laser at 248 nm. The MPEF intensity profile (top graph) of the non-irradiated sample shows a FWHM of 58.8 μm, whereas the FWHM after laser irradiation (bottom graph) was reduced to 47.6 μm. The laser treatment affected the fluorescence properties on a thickness of nearly 11 μm from the sample surface.

A further study on polymeric coatings was performed by Filippidis et al. in 2015 [78], for the assessment of the affected region during laser cleaning. A thin film of Paraloid B72 was irradiated with a single-pulse at 248 nm (fluence 400 mJ/cm2) and the subsequent swelling of the polymer was analysed by THG imaging using a fs-laser at 1024 nm. It was observed that the swelling interfaces could not be precisely determined with a single measurement, since the laser light was intensely scattered from the rough surface. The propagation of the excitation beam was limited by scattering effects, thus obstructing the THG signal generation inside the material. To overcome this problem, the sample was reversed and THG signals were collected from each side of the sample: the visualization and the quantitative determination of the contour of the laser-induced swelling/bulk material interface was then feasible. A further application of THG on Paraloid B72 laid on a glass support is reported in [114]. Using a fs-laser at 1028 nm, the visualization of the sample’s stratigraphy was obtained through the detection of the TH signal generated at the interfaces between the different layers. Given the transparency of Paraloid B72 in the UV-NIR spectral region, no MPEF signal was collected after irradiation at 1028 nm.

In 2017, Oujja et al. [79] used the same photosensitive polymer for assessing structural and photochemical modifications upon laser removal of dammar varnish. Different wavelengths (266, 248 and 213 nm) and pulse durations in the ranges of nanosecond (10–9 s), picosecond (10–12 s) and femtosecond (10–15 s) were explored to find the right conditions for the partial or total removal of the varnish layer. Using a tightly focused femtosecond laser at 1028 nm as an excitation source, THG and MPEF responses were combined to characterize the extent of morphological and photochemical modifications in the varnish layer, as a function of depth. THG signals marked the thickness reduction under laser ablation, whereas changes in the intensity of MPEF signals were ascribed either to the dammar or to the photosensitive under-layer, and their dependence on the laser ablation parameters was defined. As an example, the results obtained through bimodal nonlinear imaging of a dammar/POPOP sample before and after laser ablation with 150 ps pulses at 266 nm are reported in Fig. 17. By using 115, 346 and 692 pulses of 150 ps, the varnish layer was gradually reduced until the complete removal and analysed after partial and total removal. The vertical displacement of the position of the air/dammar interface was detected through THG.

Fig. 17
figure17

Republished with permission of Royal Society of Chemistry from M. Oujja et al., Nonlinear imaging microscopy for assessing structural and photochemical modifications upon laser removal of dammar varnish on photosensitive substrates. Phys. Chem. Chem. Phys. 19, 22836–22843 (2017); permission conveyed through Copyright Clearance Center, Inc) [79]

Cross-sectional multimodal nonlinear imaging of a POPOP/PMMA sample coated with dammar upon irradiation at 266 nm, 150 ps (fluence of 310 mJ cm−2) with an increasing number of pulses, from 0 (a) to 115 (b), 346 (c) and 692 (d). Red and green areas correspond to MPEF and THG signals, respectively. The thicknesses of the initial and the remaining dammar layer are reported over the images. The horizontal dimension of the images is 100 μm. Next to the nonlinear images are displayed the corresponding plots of the pixel brightness distribution (e) and (f). The intensities of the MPEF and THG signals are normalized to the value obtained at the corresponding control region.

It was observed that the MPEF signal arising from the dammar layer increased in intensity with the number of pulses, due to oxidative degradation following the exposure to the UV laser light. It is worth mentioning that the affected region measured through MPEF resulted considerably larger than the mean penetration depth, estimated around 12 μm for 266 nm laser ablation [124], thus showing the capability of the NLOM to evaluate the real extent of the photochemical changes induced by laser. Furthermore, NLOM measurements showed that the absorption coefficient of the varnish at the ablation wavelength plays a more crucial role than that of the pulse duration: the increased UV light absorption due to ageing reduces the extent and the in-depth dimension of the photochemical modifications induced by laser ablation, thus highlighting the advantages of using ablation wavelengths that are strongly absorbed by the material.

Wood microstructures

In the last years, MPEF and SHG have been applied to the analysis of plant materials, providing key information on wood microstructures based on the acquisition of nonlinear optical signals generated by cellulose, starch, and lignin. Cellulose, one of the predominant components in most wood species, is a linear chain of polysaccharidic molecules with crystalline parts displaying a twofold ribbon conformation. These well-ordered molecular chains are organized in microfibrils [125, 126], whose hierarchical structure and parallel orientation make cellulose a good emitter of SH signal [127]. Another source of SH signal in wood is starch, which is stored as long-term carbon reserves in a wide variety of organs, such as seeds and tubers, and on a temporary basis in the photosynthetic tissues, specifically in the chloroplasts. Especially amylose is often highly crystalline and therefore likely to generate second-harmonic signals [127]. Lignin, a complex phenolic compound giving resistance and rigidity to wood macrostructure, is an emitter of single- and multi-photon excited fluorescence, which may be enhanced by resonance effects [127]. While lignin is the predominant fluorophore in cell walls, the polysaccharide components, such as cellulose and starch, are considered not fluorescent [128].

Mizutani et al. [129] imaged starch grains in living algal cells by SHG, using a pulsed neodymium laser at 1064 nm. Chu et al. [130] used a stage-scanning microscope with chromium forsterite laser at 1230 nm for generating 3D harmonic images of plant cells. Cox et al. [127] applied both SHG and 2PEF imaging using a Ti–Sapphire laser with a shorter wavelength—between 800 and 850 nm. They found that SHG signals from cellulose are not as strong as in starch, due to the reverse orientation of glucose residues in the polysaccharidic chains. Specifically, the imaging of cellulose requires rather high laser powers (above optimal values for live cell imaging), whereas starch can be easily imaged at laser fluences compatible with extended cell viability. Moreover, by applying PSHG microscopy, the SHG signal of the macromolecular structure of purified cellulose samples was found to be significantly similar to that of collagen from animal tissues, both in terms of morphology and polarization anisotropy [131]. It was also observed that the emission of the signal is strongly dependent on the orientation of the cellulose microfibrils, predominantly developing along the axis of longitudinal arrays of cells [132].

In 2012, the in situ application of nonlinear modalities (SHG and 2PEF) enabled both the imaging and the chemical characterization of wood microstructures inside a historical violin [76]. In the same study, the analysis of multi-layered model samples including varnish films, cochineal, sandarac, and plaster was performed. Pixel-wise images were recorded using a femtosecond Ti:Sapphire laser tuned to 860 nm and scanned within the sample.

Both 2PEF and SHG signals were detected in the backward direction: despite the higher efficiency of SHG detection in the forward direction, signals could be recorded also in epi-detection when enhanced by specific structures or backscattered by strong scattering media, as in the case of wood microstructures, i.e., cellulose. SHG and 2PEF measurements were performed on thin shavings (about 30 μm thick) of Acer wood, using a high-pass GG455 filter, revealing the well-known wood structure, specifically the wood fibres and groups of medullar rays (Fig. 18a and b). SHG signals were ascribed to crystalline cellulose, due to the hierarchical ultrastructure and the parallel orientation of the molecular chains, whereas 2PEF signals were attributed to lignin. The analysis was then applied on a locally damaged area of a historical violin, clearly revealing the cracks at 485 nm (Fig. 18c). The study showed that nonlinear optical imaging may turn useful to obtain quantitative information on wood composition for a comparison between different species and to study the effects of treatment or ageing on wood microstructure. Indeed, such microscopic properties are key parameters to characterize the macroscopic mechanical properties of wood.

Fig. 18.
figure18

COPYRIGHT: Adapted with permission from G. Latour et al., Opt. Express 20, 24623-24635 (2012) © The Optical Society [76]

2PEF measurement on a wood specimen. Merged 2PEF (red) and forward-SHG (green) image (a) and 3D reconstruction (b) of the same region. 2PEF signal (c1–3) filtered at 485 nm, acquired on a damaged area of a historical violin showing the micrometric cracks – scale bar 100 μm.

Skin-based artefacts

NLO microscopy has been applied for examining skin-based materials commonly found in cultural heritage, such as parchment, leather, and alum-tawed skins, showing different mechanism of degradation [133]. Due to its dense and non-centrosymmetric fibrillar structure, collagen in skin displays strong SHG signals and a slight 2PEF signal related to the molecular crosslinks (Fig. 19).

Fig. 19
figure19

Latour et al., 2016 [134]

Nonlinear optical microscopy imaging of parchment: A detail of parchment “1639” (©CRCC, Laurianne Robinet). B–E Preserved area of the parchment versus; C Grain side with hair follicles (arrows) and D, E flesh side are compared. SHG signals and 2PEF signals are displayed in green and red, respectively. In parchment, the distinction between grain and flesh side is possible by the presence of hair follicles (arrows in C) and large fibrillary stretched structures respectively, whereas these characteristics are not visible in conventional optical microscopy (B).

In 2016, NLO microscopy was applied to the study of ancient parchments and their degradation process [134], for the first time in combination with IR nanoscopy (nanoIR), a technique combining an Atomic Force Microscope (AFM) with an IR pulsed tunable laser [135]. The study required the use of complementary techniques to morphologically and chemically investigate the different stages of collagen denaturation to gelatine (i.e., gelatinization), at various structural levels. Information on the alteration stages may provide support to the identification of parchment at risk in museums or archive collections, to take suitable conservation measures before the process of degradation becomes irreversible.

The main results obtained by the synergic application of NLOM and nanoIR on a seventeenth century parchment are reported in Fig. 20, specifically on a tiny scrap originating from a gelatinized area. Nonlinear microscopy analysis enabled to associate parchment alteration with a decrease or loss of the SHG signal and an increase in the 2PEF signal. Imaging data also highlighted modifications in the structural organization of the collagen fibres, with a concurrent formation of an amorphous material emitting an intense fluorescence signal. The loss of SH signal was therefore attributed to the alteration or disruption of the hierarchical organization of the fibres, as confirmed by the AFM topography image and the changes in the IR spectra, evidencing the formation of a carbonyl vibrational band at 1724 cm−1, which was ascribed to mechanisms of acidification and hydrolysis of the collagen. The increase in 2PEF signal was also considered a sign of alteration in parchment, even though the correlation between 2PEF increase and gelatinization was not completely understood.

Fig. 20
figure20

Latour et al. 2016 [134]

Correlative imaging of the parchment’s scrap. Correlative A optical microscopy, B 2PEF microscopy, C SHG microscopy, D AFM topography, nanoIR mapping at E 1724 cm−1 and F 1660 cm−1. Arrows in the 2PEF microscopy image (B) show hot fluorescent areas in the cluster and are correlated with the nanoIR mapping at 1724 cm−1, corresponding to the gel-carbonyl band.

Corrosion products in metals

In 2013 [86], MPEF imaging was applied to the study of silver-based artefacts to evaluate the possibility of identifying corrosion layers, i.e., chlorargyrite, the mineral form of silver chloride (AgCl). The analysis was performed on reference silver-based alloys, purposely treated with an ageing procedure for accelerated degradation. MPEF signals were generated by irradiating the samples with a pulsed fs-laser at 1028 nm acquired in the backward direction. LIF measurements at an excitation wavelength of 257 nm allowed to spectrally characterize the fluorescence emission of chlorargyrite. On this basis, the MPEF signal was ascribed to a four-photon absorption process, and the subsequent 3D reconstruction enabled not only to evaluate the corrosion layer thickness but also to analyse the morphology and density of AgCl crystals (Fig. 21).

Fig. 21
figure21

Reprinted by permission from Springer Nature Customer Service Centre GmbH: Springer, Appl. Phys. A, Multi photon excitation fluorescence imaging microscopy for the precise characterization of corrosion layers in silver-based artifacts, Faraldi et al., [Copyright] (2013) [86]

a Maximum z-projection MPEF image of the chlorargyrite layer surface. b 3D reconstruction of 50 sequential optical planes, separated by a distance of 1 μm, of MPEF signal generated from the AgCl layer.

Safe limits for the application of nonlinear microscopies in cultural heritage

Liang et al. have recently discussed the advantages and limits of nonlinear optical techniques in the analysis of artworks [74], focusing on the degradation effects induced in painting materials by the high intensity radiation of fs-lasers sources. Different laser intensities were applied on painting materials showing absorption at the wavelength used for excitation, concluding that the possible induced damage is significantly influenced by the different absorption properties of the materials. Photodamage effects were found to be more common in paint layers, since most pigments absorb the excitation wavelength commonly used for nonlinear applications (typically up to 1200 nm), whereas high transparent media, like protective layers (varnishes and glues), underwent negligible alterations when examined through NLOM. The fluorescence emitted by painting materials was attributed to a combination of single and multi-photon absorption processes, in contrast to protective layers, where multi-photon absorption was found to be the predominant process. In the same work, it was assessed that the risk of photodamage is negligible in the case of coherent scattering nonlinear phenomena, such as harmonic generation processes, since they do not imply energy deposition in the medium, with subsequent minimal sample disturbance. As outlined above, the new photons are generated through a single step quantum process, the interacting material acting as an energy converter for the incident photons. However, the same high intensity beam causing harmonic generation may also be absorbed by the medium through MPEF and, thus, may cause photodamage in certain conditions.

It is worth underlining that, by setting the laser power under the damage threshold (which can be determined through experimental measurements), it is feasible to acquire NLOM signals with a sufficiently high signal-to-noise ratio, without inducing any alteration in the substrate. Moreover, depending on the objective lens and excitation wavelength, the size of the laser spot ranges from one to few microns, thus reducing the possible area of damage.

A new methodology was proposed in 2020 to determine safe limits for the application of NLOM in cultural heritage. A systematic study was carried out on a set of acrylic paints to define a procedure for damage evaluation during MPEF measurements with NIR femtosecond pulsed lasers, aiming at determining proper non-invasive conditions for the analysis [85]. Safe thresholds of laser power were identified, based on the observed variation of MPEF signal intensity upon repetitive irradiation, which was considered as the signature of possible photochemical alteration. Specifically, measurements were performed by irradiating the samples in different regions of interest, repeatedly, with a scanning depth of around 100 μm (z-steps of 1 μm) and, with increasing laser power. Fading or enhancement of fluorescence was observed in paints characterized by similar colour but different chemical composition. The monitoring was complemented with the concurrent acquisition of Raman spectra before and after each MPEF measurement session, and the presence of superficial alteration was verified with Optical Microscopy (OM). An example of the monitoring procedure is reported in Fig. 22.

Fig. 22
figure22

Reprinted from Microchem. J 154, A. Dal Fovo et al., [85] Safe limits for the application of nonlinear optical microscopies to cultural heritage: a new method for in-situ assessment, 9, Copyright (2021), with permission from Elsevier [OR Applicable socIety Copyright Owner]

Photodamage monitoring by MPEF, Raman spectroscopy and optical microscopy on Permanent Blue Light and Zinc White acrylic paints, irradiated with a fs-laser emitting at 800 nm, with a power of 8.5 mW and 41.5 mW, respectively. a, b MPEF z-profiles measured after each of the five z-scan; c, e fluorescence intensity images and d, f optical microscope images acquired after the five z-scans. The irradiated area (100 × 100 μm2) is highlighted by the dashed square. g, h Raman spectra measured in the purposely damaged area (black line), in a non-irradiated area (red line) and in the irradiated area after the five scans (blue line) for the PBL (g) and ZW (h) samples.

In the presented case, all the monitoring modalities, apart from OM imaging, allowed to detect the photo-induced alteration in the blue paint at the laser power of 8.5 mW. Differently, in the white paint, the damage produced at 41.5 mW was immediately evidenced by the changes in the MPEF intensity, while none of the other techniques showed sign of alteration. The study reports, for all the analysed paints, a generally higher sensitivity of MPEF to photo-effects, with respect to the sensitivity of the other monitoring methods, meaning that MPEF could be performed non-invasively by simply observing the variation in the signal intensity at a given laser power, which has to be chosen to ensure a good signal-to-noise ratio.

To highlight the possible dependence of the material response on the measurement settings, the analysis involved the use of two nonlinear setups with different illumination conditions for single-point and imaging acquisitions. Interestingly, it was observed that the safe range of laser power identified for the acrylic paints differed considerably (few tens of mW) according to the setup used. Such discrepancy was attributed to the diverse illumination conditions, namely to the number of laser pulses per irradiated point. Therefore, this latter parameter resulted crucial for defining the threshold of damage for a specific material, as well as the laser power and the exposure time. In conclusion, once defined the safe limits for the application of MPEF, cross-sectional measurements can be performed in safe conditions and good comparison with other more traditional non-invasive optical techniques.

Conclusions and future perspectives

Several studies reported in this review have proven the effectiveness of nonlinear optical microscopies (NLOMs) in Cultural Heritage (CH) science, specifically for the in-depth analysis of wood, protectives, adhesives, and paint layers. Apart from few exceptions, up to now measurements have been performed on ad-hoc prepared mock-ups simulating real cases. To envisage the application of NLOM on CH objects, few aspects related to the interaction between the laser radiation and the examined material should be better investigated, and some technical specifications of NLOM devices should be purposely customized for the specific application. Nevertheless, the potential of this technique is undeniable, especially when compared with other more established methods. For instance, OCT allows to measure larger areas and/or longer profiles than NLOM, which is limited to a few mm acquisitions, and makes use of portable devices working in backward configuration, but its application is confined to low scattering and semi-transparent materials, thus excluding strongly reflecting varnishes and turbid media. By contrast, NLOM has proven capable of probing opaque paints laid over different support materials and covered by protectives, enabling cross-sectional measurements with micrometric resolution. Another significant advantage of NLOM is that it provides complementary information (morphological, structural, and compositional) on the analysed material in one single measurement, by using a femtosecond laser for generating simultaneously SH, TH, and MPEF signals. As regards THG cross-sectional images, they can be considered directly comparable with OCT tomograms, both enabling the micrometric thickness measurement of transparent materials (protectives and glues) basing on the visualization of the interfaces. Nevertheless, being the detection of THG signals favoured in the forward configuration, further research must be carried out to explore the possibility of backward detection to perform THG measurements on paintings and other non-transparent materials. This limit can be already overcome with MPEF, which allows the epi-collection of the generated signals. Despite the severe drop of the nonlinear fluorescence intensity with increasing depth, the evaluation of painting stratigraphy with micrometric precision is feasible, provided a proper interpretation and deconvolution of the nonlinear fluorescence response. It has to be underlined that more extended calculations should be performed to define the proper correction factor for thickness measurements by NLOM, which are generally affected by distortions in the signal intensity profiles, related to the refractive index mismatch inside the material and the focusing/collection optics used.

Furthermore, the combination of MPEF and SHG turns successful for the discrimination of emitters in wood microstructures (i.e., lignin emitting nonlinear fluorescence, cellulose and starch generating second harmonic signal). One perspective is to perform polarization-resolved SHG imaging to determine the orientation of cellulose micro-fibrils and to improve their visibility in cell walls. MPEF/SHG could turn useful for analysis of wood deterioration, as well as for the recognition of different wood species based on the visualization of their micro-morphology. Moreover, the synergic use of these two non-linear modalities may provide in-depth information on highly scattering paint layers composed by pigments with crystalline molecular structures, capable of emitting nonlinear fluorescence or second harmonic signal—or both (e.g., Zinc white, lapislazuli, cinnabar, chalk, Egyptian blue) [136], which are sometimes extremely difficult to investigate using other optical techniques.

It was also demonstrated that through the combined application of well-established linear and the new NLOM techniques it is possible to obtain chemical and physical information on a variety of artistic materials, without endangering the integrity of the artworks. Each technique provides information that can be used both to address other investigations and to complement further results. The non-invasiveness of NLOM has been assessed in few studies, demonstrating that safe measurement conditions can be ensured by simply monitoring the variation in MPEF signal intensity, which is a forewarning of photochemical changes inside the focal volume of the laser beam. Phototoxic effects, which may precede changes of fluorescence, should be better studied on a wider selection of sensitive heritage substrates. Further analysis could be carried out to understand the mechanisms of damage, the relationship between the fluorescence behaviour and the chemical composition of the media, as well as the effect of laser illumination conditions on the threshold of damage. The latter can be assessed by comparing the optical properties of the analysed surface before and after the irradiation, i.e. changes in the reflectance behaviour (through FORS), fluorescence emission (LIF) and photoacoustic generation after light absorption (PA imaging), besides the monitoring of induced morphological and chemical variations through microscope analysis and micro-Raman spectroscopy.

Finally, the development of a transportable NLOM prototype would significantly enlarge the applicability of these techniques on a variety of artworks, enabling in situ measurements. To this purpose, technical requirements have been delineated by Mari et al. [73], as a base for the future construction of a transportable user-friendly non-linear device.

Notes

  1. 1.

    The characteristic atomic electric field strength is Eat = e/(4πε0α02) = 5.14 × 1011 V/m, where e is the charge of the electron and α0 is the Bohr radius of the hydrogen atom. (R. W. Boyd, 2003 [90]).

  2. 2.

    For example, rhodamine 6G has a σ2ωQf of 40 Göppert-Mayer units (GM; 1 GM = 10 − 50 cm4 s/photon) at 830 nm.

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

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

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Acknowledgements

This research has been funded by Regione Toscana (POR FSE 2014-2020, “Giovanisì”, Intervention Program “CNR4C”, CUP B15J19001040004), by the Spanish State Research Agency (AEI) through project PID2019-104124RB-I00/ AEI /1.0.13039/501100011033, by the TOP Heritage-CM (S2018/NMT-4372) program, by the H2020 European project IPERION HS (Integrated Platform for the European Research Infrastructure ON Heritage Science, GA 871034) and is supported by CSIC Interdisciplinary Platform “Open Heritage: Research and Society” (PTI-PAIS). Collaborations with Drs Mohamed Oujja and Mikel Sanz are gratefully acknowledged.

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Dal Fovo, A., Castillejo, M. & Fontana, R. Nonlinear optical microscopy for artworks physics. Riv. Nuovo Cim. 44, 453–498 (2021). https://doi.org/10.1007/s40766-021-00023-w

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Keywords

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