Marble is a metamorphic rock formed when limestone (CaCO3) or dolomite (CaMg(CO3)2) is exposed to high temperatures and pressure, and its colour depends on the ‘impurities’ present in the parent limestone or dolomite. In general, marble has many different crystal sizes, most of which are in the millimetre to sub-millimetre range and can be seen with the naked eye. Thus, these crystal ‘grains’ interact strongly with THz radiation (1 THz is about 300 μm) through Mie scattering [28]. THz radiation can, therefore, sense any grain boundary, slippage or cracks on the surface or even inside marble structures. At the same time, being a rock, marble is inherently susceptible to water inclusion, especially through the grains and pores of the inner structure.

It must be noted that rocks are naturally occurring formations on the Earth and may comprise one or more minerals, with each mineral in a rock being of fixed chemical composition and structure. Table 2 provides all the rocks and corresponding minerals thereof that are discussed and/or probed in the present topical study.

In our study, to assess whether different rock materials, i.e. marble (mineral calcite) and alabaster (mineral gypsum), will elicit a unique optical response through various non-contact sensing tools we obtained two different varieties of visually similar coasters: one made of marble/calcite and the other made of alabaster/gypsum.

Figure 3 shows the visual image, microscopic image and SEM image of the marble coaster (top, hereafter labelled Coaster A) and alabaster coaster (bottom, Coaster B); additionally, the report of the EDAX study is also appended which confirms the presence of a significant sulphur content (16% by weight) in Coaster B. However, it must be noted that for both these measurements the samples had to be cut and broken into pieces, which is certainly not a suitable mode of investigation for heritage structures. To understand the applicability of various non-contact, non-destructive optical spectroscopic techniques in assessing the condition of both the surface and volume of the specific minerals under study (i.e. calcite and gypsum), as well as the extent of damage caused by the environment, erosion or any other sources, we conducted the various following measurements.

Figure 3. Microscopic and SEM image of two types of rock: marble (coaster A) and alabaster (or sulphated marble, referred to in the text as Coaster B). These images show that even under a powerful microscope the internal structures do not show any significant difference, while mechanically gypsum (the primary component of the rock alabaster) is flakier and lacks the natural hardness of calcite (rock marble) which contains no sulphur, as confirmed by the EDAX study.

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A custom-built micro-confocal Raman spectroscopy setup in a back-scattering geometry with multiple excitation laser sources (having central wavelengths of 532.1, 561.4 and 491.7 nm) was employed for the ultralow-frequency Raman spectroscopic analysis. The scattered signal was collected using a 500 mm focal length monchromator, followed by a back-illuminated charge-coupled device. A detailed description of the system can be found in our earlier research work [29]. It must be noted that though the Raman spectroscopy in this work was done using a laboratory-based set-up, field-ready systems are also becoming increasingly available [30].

In figure 4 (top panel) the red plot shows the Raman spectra with characteristic peaks of gypsum around 413 and 1006 cm−1 obtained from Coaster B from any spot devoid of ornate structure; thus confirming the presence of gypsum in Coaster B. The blue plot in the same panel obtained from Coaster A shows the characteristic peaks of calcite around 710 and 1086 cm−1 [31]. The spectrum in the middle panel from the green inlay work of Coaster A clearly indicates the presence of malachite in the probed area [32]. The spectrum corresponding to the violet inlay (bottom panel), however, could not be assigned to any known reported mineral but could be due to violet pigment (e.g. violacein [33]). Table 3 lists the characteristic peaks of each mineral and the reference(s) used for attribution.

Figure 4. Micro-Raman spectra of the surface of the gypsum (red) or Coaster B and calcite (blue) or Coaster A in the top panel. Raman sensing of the green inlay work (middle panel) shows the presence of malachite and violet inlay work (bottom panel), which could not be assigned to any known mineral and is possibly due to pigments. All spectra were recorded with a 532.1 nm laser. The white box indicates the Raman probing region.

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Table 3. Characteristic Raman peaks of each mineral related to this study and corresponding reference(s).

 ColourMineralCharacteristic peaks (cm−1)Reference1WhiteCalcite710, 1086[31]2WhiteGypsum413, 1006[31]3GreenMalachite1100, 1485[32]4VioletNo known mineral, possible pigment1200, 1400[33]

Since this technique has been shown to be highly sensitive to the surface condition of the coasters, we wanted to investigate whether Raman spectrocopy is sensitive to the presence of algal growth for an objective assessment of this persistent problem of the Taj. For this purpose, we exposed roughly half of the backside of the marble slab with green flowers to methane and phosphate-rich stagnant water for 2 weeks.

Raman spectroscopy with its working wavelength in the visible range can sense material signatures even in contours with curvatures. Hence, as shown in figure 5, even with algal growth on the marble surface the Raman response (in red) bearing the hallmark of the calcite line, matches with the yellow pigment from the flower sample stained over the ceramic slide (in blue) and a freshly plucked green leaf by itself (in green). Thus, Raman sensing can be very successful in objectively detecting the growth of algae causing the discoloration of the marble surface by detecting of the presence of chlorophyll.

Figure 5. Raman spectra corresponding to algal growth on the marble surface (in red), yellow pigment from a flower sample stained over a ceramic slide (in blue) and a freshly plucked green leaf by itself (in green). The inset in the lower panel shows a coaster with algal growth on the half that was submerged in water.

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While micro-Raman sensing can reveal the spectral features on the surface of the marble, a complementary study in the THz range, especially THz TDS and time domain imaging (TDI), can reveal the volumetric spectral and spatial features owing to greater penetration of THz range wavelengths. In this spectroscopic imaging technique an object is usually imaged with a broadband THz source and the transmitted or reflected signal off the object is recorded through a gated coherent detection scheme to obtain a rather high signal-to-noise (SNR) ratio. This is achieved by direct measurement of the THz electric field with both amplitude and phase information from the object under THz transmission or reflection [34]. The resulting composite multidimensional data in three-dimensions represent an image of the object, where each pixel corresponds to a physical location in the object under study while the third dimension carries THz spectral information about that location over a certain frequency band. In simple terms, a THz spectral image of an object is essentially a 2D THz spectral map that can be obtained by proper Fourier deconvolution from the experimentally obtained time domain image. In heritage conservation applications, where the object is often shrouded under composite barriers, such as a sarcophagus or fresco [34], or the object itself could have layers, such as an old manuscript or painting [35], THz TDI can be particularly useful. Apart from sub-surface information, most of the typical chemical substances such as ink, dye, glue, glaze and metal oxides found in these heritage objects have characteristic THz spectroscopic signatures [23]. Another important aspect of this technique is time domain signal acquisition with low-frequency components (less than 1.5 THz). This range of frequencies ensures greater penetrability through dielectric layers, while the time-of-flight (TOF) information for each sub-picosecond THz pulse essentially provides information about various layers under study with resolutions of tens to hundreds of micrometres. This strategy of using the lower-frequency band, however, suffers from compromised spatial resolution of features of interest in the lateral dimensions, and thus to gather a complete spatial profile of various features it is essential that an object be probed both through lower- and higher-frequency components.

In this report, for the THz TDS and TDI studies a commercial broadband THz fibre-coupled photoconductive antenna system was used (details of the system can be found in earlier works [34]). The system employed here has a 6 THz useable bandwidth under nitrogen purging and a peak dynamic range of 90 dB (at 1.0 THz) with a trace average of 2000. All experiments were performed in a controlled environment at a temperature of 21 ± 2 °C and relative humidity of 42% ± 5%, unless otherwise specified. The spectroscopic results of THz transmission measurement are given in figure 6, where the black solid line corresponds to the THz TDS reference through air and the solid lines in 10 different colours represent the time domain signal through 10 randomly selected points without any inlay motifs through the 3 mm thick calcite coaster. From the inset figure, we notice that the time delay of the reference pulse and the transmitted pulse through the marble is ∼42.5 ps, which signifies a broadband optical refractive index of 4.25 for the coaster. Additionally, we notice that the average transmitted THz amplitude through these 10 points is less than 18% of the reference THz amplitude. These high values for the real and imaginary parts of the complex refractive index of the marble could be attributed to the nature of the marble structure rather than the CaCO3 material. Both under visual and microscopic inspection we see the polycrystalline nature of the marble with grain boundaries varying from tens of micrometres to the order of millimetres, which would naturally result in very strong Mie scattering in the forward direction during transmission, giving rise to a substantially high value of the complex refractive index. This fact also suggests that higher-frequency components of the THz pulse will suffer even higher attenuation, and the transmitted THz field amplitude is the result of principally the low-frequency components having greater penetrability through the marble’s polycrystalline structure. The spectral amplitude in figure 6 clearly shows that while the THz system has a strong spectral response even beyond 4.5 THz, the transmitted signal through the marble is limited to ∼1.5 THz. In fact, frequency components above 300 GHz (wavelength of ∼1 cm) suffer exponentially increasing attenuation due to the scattering from the grain boundaries, as discussed above.

Figure 6. THz time domain transmission response of the calcite coaster showing less than 18% THz transmittance irrespective of the spatial position of the probing point accompanied by a large temporal shift of the pulse through the coaster with respect to the reference pulse through the air, indicating a very high value of k and a high value of n (4.25), respectively the imaginary and real parts of the complex refractive index of the marble. The corresponding Fourier deconvolution shows that the transmitted THz pulse through the calcite coaster contains only low-frequency components up to 1.5 THz.

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Due to the limited transmission of high-frequency components of THz radiation through marble, we employed the THz TDI technique in reflection configuration to further probe the coaster. In this modality, a plane metal surface was used as the reference for THz alignment and as the holder to place the coaster. From our transmission studies it became clear that for frequency components above 0.3 THz, THz radiation passing through the marble coaster—even where there are no motifs—will suffer significant absorption through the volume of the marble due to scattering and any reflection by the metal holder at the back of the coaster and will not be able to reach the receiver after double transmission through the thickness of the coaster.

The raw acquisition of THz time domain images in reflection provides an image matrix where each row corresponds to the entire THz reflection spectrum of the spatial position of the coaster under raster scanning with the number of columns corresponding to the frequency components. Hence, the pixels of the THz time domain image only show the highest peak-to-peak value of the reflected THz signal, corresponding to a specific spatial position, and do not represent the frequency-dependent properties of the coaster [24]. Fourier deconvolution is applied from the time domain to the frequency domain, corresponding to the raw time domain data of a scanned area of about 33 mm × 22 mm with 0.2 mm stage movement (corresponding to 165 pixels × 110 pixels) around the stem of the orange flower coaster shown in figure 2. The resulting reconstructed intensity images of the coaster with the orange flower are shown in figure 7 for 0.8 THz and 2.8 THz for easy comparison. The false colour representation shows a pixel assignment where red represents high reflectivity, blue represents low reflectivity and all other colours represent variable reflectivity across the scanned area. While the high-contrast intensity image at 0.8 THz in the top left corner of figure 7 shows the distinctive random network of polycrystalline grains of the marble by the scattering-driven interaction with the THz radiation, it suffers from low spatial resolution due to relatively long wavelength of interaction (∼375 µm). The blue outlines of the motif could still be captured due to strong material absorption of the THz radiation by the bonding glue used in these areas to bind the different coloued inlay stones on the coaster. The resultant image appears to be a defocused flower motif ‘floating’ on the strong reflective marble background, which also indicates that at 0.8 THz there is still sufficient penetration of THz radiation despite the scattering interaction. This pseudo tomographic intensity image is well complemented by the corresponding phase image at the bottom, where the abundance of red in the false colour image represents considerable phase accumulation. However, this phase is not regular over any spatial scale as the polycrystalline grain boundaries within the volume of the coaster destroy the phase front completely and the reflected image signal also suffers from multiple internal reflections from the edges of the motif. One significant feature observed in this phase image is a very strong phase accumulation at the spot corresponding to the green stalk. This suggests that this specific material (which could be malachite as per the Raman study shown in figure 4) is more dielectric in nature, having lower attenuation in the THz range yet with a significantly high real part of the refractive index due to which THz radiation accumulates such a high phase without much loss in signal.

Figure 7. The THz reconstructed images of the coaster with an orange flower motif in reflection configuration at 0.8 and 2.8 THz obtained through Fourier deconvolution from the experimentally obtained raw time domain image. The top images are the intensity images, while the bottom images correspond to the THz phase accumulation of the radiation through the coaster. Reproduced with permission from [24].

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In contrast, the top right-hand image corresponds to a higher-resolution 2.8 THz image but with compromised contrast as the source power of THz radiation, as described in figure 6, is only about one thousandth of the peak spectral power at about 1 THz. This image also supports that at such a high frequency there is barely any penetration of the THz wave and it essentially captures the motif at the surface with sharp edges. However, the corresponding phase image at the bottom suffers from a complete lack of definition due to very poor signal strength and hardly any penetration of the 2.8 THz radiation through the coaster. This ‘layered’ aspect of THz images in reflection—the deeper marble base at lower frequencies and the sharper surface image of the glue/mortar and the colourful stonework at higher frequencies—make THz TDI a very powerful technique for studying stone architecture, minerals etc [36, 37].

An intentional hairline crack ∼120 µm thick was introduced at one side of the coaster with the orange flower, as shown in figure 8(a), with the corresponding microscopic image in figure 8(b) with 1 mm spatial resolution. Figure 8(c) shows the THz time domain image of the crack in transmission. In this transmission image, red represents 100% transmission through air while blue represents very low transmission either because of high material absorption or acute scattering extinction. In the case of the crack, THz waves experience very high scattering at the irregular boundaries of the surface as well as the entire volume of the marble slab. Consequently, very limited transmission occurs at the site of the crack. It must also be kept in mind that the spatial resolution of the THz image is not only limited by the THz wavelength but also depends on movement of the imaging stage (which is set at 0.2 mm on both X and Y axes). However, as already discussed, since the transmitted THz pulse consists of only low-frequency components there is a severe penalty in the resolution of such an image. Figure 8(d) shows the THz TOF image of the crack in transmission. In this image every pixel corresponds to the difference in time taken by the THz radiation to reach the detector from the transmitter through air and through the sample. In this TOF image, blue represents zero difference or the place where there is no sample (or air) and red represents the highest time difference, which in the present case is almost constant through the marble slab. However, the presence of a crack offers a slightly smaller time difference for the THz waves to penetrate through the slab and reach the detector, and shows up as a slightly lighter red colour. In fact, some disjointed yellow spots in this image represent the places where the crack is wider than its average thickness of 120 µm, offering an even lower time of flight for the THz radiation. Upon frequency deconvolution of the time domain image, we reconstructed the THz image at 0.8 THz, where the contrast of the image is severely compromised as expected, as shown in figure 8(e). Our previous transmission studies have already proved that a transmitted THz signal is very limited beyond 0.5 THz, however; at this frequency, with a corresponding wavelength of 375 µm, the resolution of the 120 µm crack is not clearly discernible but the central portion of the crack, which is slightly wider, is clearly visible. This result shows the potential of this THz technique in detecting surface and sub-surface cracks in marble structures such as the Taj Mahal in a non-contact, non-invasive manner.

Figure 8. (a) Visual image of the hairline crack. (b) Microscopic image with 1 mm spatial resolution gives a thickness of ∼120 µm. (c) THz time domain image of the crack in transmission. (d) THz TOF image of the crack. (e) Frequency resolved THz image of the crack at 0.8 THz where the detection of the crack is evident. Reproduced with permission from [24].

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The next part of our study involved the same marble slab where algal growth was induced. Figure 9(a) shows the THz TDI of this sample in transmission configuration obtained immediately after algal formation while 9(b) shows the same area of the same coaster after 1 week of drying in the controlled environment of the laboratory. In these two images, the abundance of bluish green spotting represents the site of high material absorption due to which the THz transmission becomes low (blue represents zero transmission). These two images were acquired 1 week apart, and with careful observation one can notice that in figure 9(b) the prevalence of a red colour is slightly greater than in figure 9(a). This is representative of water inclusions in the marble slab as it was exposed to water for 2 weeks. During storage of the same coaster in the controlled, dry environment of the laboratory (temperature ∼22 °C and RH ∼40%) for 1 week, some evaporation of the water inclusions results in stronger THz transmission in figure 9(b). Other research groups have also reported that THz studies can indeed sense this kind of water porosity in natural rocks [38]. Thus, it can be ascertained that while the THz transmission study cannot sense the presence of algal growth on the surface of the marble, the THz TDI technique could effectively map water inclusion damage inside the volume of the marble coaster.

Figure 9. (a) THz time domain image of the calcite coaster with the green flower in transmission configuration immediately after algal formation, or rather exposure to liquid water. (b) The same coaster after 1 week of drying in the laboratory environment. Reproduced with permission from [24].

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The imaging studies described so far were all conducted with the pure marble coaster. Collectively, this set of studies helps us understand how different frequencies in the THz range interact with pure calcite polycrystalline structures as well as the ornamentations made from various types of minerals, or the presence of water inside the marble or even how a crack might appear in THz range images. As an extension of this, we wanted to investigate if we could observe significant contrast from single-point spectroscopic measurements in THz transmittivity or reflectivity for two types of coaster materials, i.e. calcite and gypsum. We hypothesized that while pure calcite has significant absorption due to the visually large grain boundaries of the polycrystalline calcite, gypsum, which has similar polycrystallinity but a different chemical composition altogether (i.e. calcium sulphate dihydrate, CaSO4 · 2H2O), may offer greater absorption due to the presence of low-energy van der Waals bonds of the hydroxyl group and is a well-known strong absorber in THz range [39].

The THz transmission spectrum through Coaster B (averaged over several clear white marble portions without any inlay work), i.e. primarily gypsum, was found to have significantly reduced bandwidth relative to that of Coaster A made of pure calcite, as shown in figure 6.

To highlight the large transmission contrast, the experimental peak-to-peak amplitude of the transmitted THz time domain pulses corresponding to this frequency spectra study is found to be 120 nA for Coaster A and only 1 nA (with a significant noise contribution) for Coaster B, as shown in figure 10(a). This is the reason why, even for the 0.5 THz frequency component which corresponds to a sufficiently large wavelength of 600 µm, the dynamic range of the pulse transmitted through Coaster B is barely 10 dB while the same through Coaster A is around 30 dB, as can be seen in figure 10(b). Through these spectroscopic and imaging studies, it is quite evident that THz time domain technique can distinguish calcite and gypsum coasters clearly, and that the extent of THz penetration in a specific type of material would determine the SNR of THz spectroscopy or the depth of contrast in THz imaging, making it a valuable tool in marble heritage conservation applications. However, the cost of the THz system, its footprint and weight are still not suitable its deployment in the field.

Figure 10. (a) THz time domain transmission response of the gypsum coaster (Coaster B) showing less than 10% THz transmittance relative to that of the calcite coaster (Coaster A), indicating a high value of n and high very value of k. (b) THz spectral response through Coaster A (calcite, blue line) compared with coaster B (gypsum, red line). Reproduced with permission from [26].

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Another promising approach for investigating defects in marble is to utilize LFI. This unique sensing scheme, which uses a THz QCL as both a source and detector of THz radiation [40], allows high-speed, high-resolution imaging in various application scenarios [41–43] with high power and in a dynamic range in excess of 120 dB [44]. The QCL employed in this study features a 12 μm thick GaAs/AlGaAs nine-well phonon-assisted active region for frequencies of 2.7–3.2 THz. A typical system setup is shown in figure 11 and the parameters of the system [45] are shown in table 4.

Figure 11. Schematic of the THz QCL LFI system. © [2024] IEEE. Reprinted, with permission, from [45].

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Table 4. THz-QCL-LFI system parameters.

System parametersFast THz QCL LFIFrequency2.8 THz with 600 MHz frequency sweepOutput power2 mW peakImage scan area50 (H) × 40 (W) mm2Image pixel area1000 (H) × 400 (W) (0.4 megapixels)Pixel size50 (H) × 100 (W) µmImage acquisition time2 min 40 s (mechanically limited)

The LFI system is an interferometric and coherent imaging technique which allows for the generation of amplitude and phase images containing the properties of reflectivity and absorption of the material being imaged [46]. Detecting changes in materials such as marble in high resolution (∼100 µm) is of great potential for cultural heritage tasks. Many external THz detectors struggle to suppress background radiation, but this self-detection scheme uses the source’s coherent properties to do so. LFI systems, which are both source and detector, are compact, self-aligned and sensitive enough for interferometric imaging because they provide target amplitude and phase information. The fringe amplitude is directly related to the target’s reflectivity, which can change due to material changes during THz radiation scans or with the angle of the optical axis of the interrogation beam. The phase is indicated by peaks in the time domain, and results from either a change in the lateral surface profile (a minor distance change corresponding to a complete phase cycle/fringe shift of half a wavelength of the THz radiation out of the source) or a material change affecting reflection phase shift. Scanning the beam and collecting interferograms at various target surface points creates target amplitude and phase maps/images. Fast Fourier transform can efficiently extract information from the interferogram by focusing on the frequency bin that corresponds to the interferometric fringes for both amplitude (real) and phase (imaginary) data.

The resulting images from the system can be seen in figure 12. Two marble coasters with pietra dura motifs were imaged one after the other. The top row of the figure corresponds to the calcite marble that could not be scratched with a fingernail while the other shows marble that has been exposed to sulphuric conditions, resulting in conversion of the marble surface into gypsum (a common problem with marble monuments exposed to acid rain) that could be easily damaged with a fingernail [47, 48]. Both the amplitude and phase images contain complementary information that is not necessarily apparent in the visual photographs, as shown in the left-hand images in figure 12.

Figure 12. THz QCL LFI images of two marble coasters, one with the surface converted to gypsum and the other natural marble. © [2024] IEEE. Reprinted, with permission, from [45].

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The information provided by the amplitude–phase pair can also be combined into a composite representation for easier visual interpretation.

Figure 13 explores this concept by using the phase value (−π to π) to encode the hue and amplitude (scaled between 0 and the maximum reflection of the system) and the saturation in a cylindrical hue, saturation, value (HSV) colour space. The intensity of the colour space was kept constant. The resulting pseudo-colour composite images (figure 13(b)) demonstrate the stark difference in surface properties between the two materials. In particular, the areas that have been damaged or placed under stress, where the marble has been carved out for fitting the semiprecious inlay, show a stark contrast to the area of bulk marble/gypsum. Additionally, the contrast from these effects is quite different depending on the base material, with the gypsum suppressing many interesting structural features observed in the pristine calcite marble surface. This disparity in contrast essentially indicates a difference in chemical composition, revealing the fascinating structural characteristics present in the calcite marble coaster.

Figure 13. (a) Combined pseudo-images obtained from HSV colour space mapping of THz QCL LFI amplitude and phase images. (b) Visual and pseudo-images of calcite marble and gypsum. © [2024] IEEE. Reprinted, with permission, from [45].

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