Samples
The letters ‘UCL’ were handwritten with a clean nib pen (i.e. without ink) on a contemporary print paper and on a historical parchment sheet from 1752, the latter obtained from the Institute for Sustainable Heritage Historic Reference Material Collection. The flexible nib had a central slit which would separate when the tip of the nib is pressed against the paper, with a larger handwriting pressure causing a wider opening of the slit. If dipping the nib into ink, this split of the nib allows for more ink to be deposited on the paper surface [7]. A rag paper sheet with sieve lines from the nineteenth century from the same collection was also used in this study. A sieve line is a topographic feature in the paper sheet formed during its manufacture that is left by the threads forming the sieve when covered with wet paper pulp and left to dry.
Profilometry
A portable optical contact-free profilometer (TRACEiT from Artec) capable of scanning a maximum area of 5 × 5 mm at a lateral and axial resolution of 2.5 μm was used to observe indentations left on the surface of the support by a clean nib pen as well as historical sieve lines. Depth profiles from indentations and sieve lines are displayed in Fig. 1a, b and c. A photograph of the entire sieve line on rag paper further analysed with terahertz time-domain imaging is also displayed in Fig. 1d: the letter ‘L’ can be distinguished.
Terahertz Time-Domain Imaging
Terahertz images were acquired in reflection mode using a commercial terahertz time-domain imaging system (TPS spectra 3000 from TeraView Ltd, Cambridge UK), equipped with a reflection imaging module fitted to a nitrogen-purged sample compartment. This module comprises an optical system that focuses the generated terahertz pulses at an angle of incidence of 30° onto the sample surface that is sat atop a motorised scanning stage. Samples were held taut flat by placing them between two ring-shaped magnets
Spatial resolution was determined by scanning a regularly spaced two-dimensional grid (i.e. a 1951 USAF resolution test target, Product ID R3L3S1P and R3L3S1N, Thorlabs Inc.). At the limit of resolution defined by Rayleigh, two features spaced by r = (1.22 * f * λ. )/D in the scanned area are considered not resolved and the composite intensity distribution of the electromagnetic fields reflected from those features exhibits a central depression with a decrease in intensity of 19% [8]. If this definition of resolution could be translated to the amplitude of the electromagnetic field, considering that the ratio of the focal length f and aperture diameter D of the imaging system used in this study is equal to 1, it would follow that the limit of resolution of our system is approximately 180 μm at 2 THz. When scanning the grid with a lateral step size of 100 μm and producing a two-dimensional image from the amplitude at 2 THz of the Fourier-transformed reflected time-domain waveform recorded at each location of the grid, such central depression in the field amplitude was observed for features spaced by 180 μm. This figure coincides with the resolution limit set by Rayleigh. Using the same threshold for the central depression, the limit of resolution for images of the grid produced using the maximum amplitude of the reflected time-domain waveforms was reached for features spaced by 280 μm. While this threshold of 19% was arbitrarily set by Lord Rayleigh based on the capacity of the eye to discern objects through telescopes or microscopes [9], the display performances of today’s monitors, together with the advance of image processing algorithms enhancing the image contrast from inscriptions and enabling character recognition, encourage the revision of this threshold. If setting the threshold of the central depression in the electromagnetic amplitude distribution to the standard deviation of the amplitudes collected from a blank area of the grid, a new resolution limit of 180–200 μm is reached, for images of the grid produced from the maximum amplitude of the pulse, with a lateral step size of 100 μm.
The lateral width of the indented lines left with the nib pen was measured with the profilometer and ranges between 85 and 420 μm for print paper and 85–235 μm for parchment. The lateral width of the sieve lines was measured from the photograph acquired with transmitted light and ranges between 350 and 800 μm. While the spatial resolution discussed above indicates that two indented lines spaced by less than 180 μm would not be discernible, a single indented line (farther than 180 μm from any other line) with a width smaller than the spatial resolution, or even smaller than the pixel size, may still be detected with our terahertz imaging device. Two parameters influence the detectability and contrast of any feature (i.e. single indented line in this study): the position of the feature with respect to the pixel grid (i.e. scan steps in our case) and the difference in amplitude between the electromagnetic field reflected from the feature and the electromagnetic field reflected from the surrounding background. The feature is more likely to be detected and show a good image contrast if it is fully inscribed within a single pixel, rather than overlapping two or more adjacent pixels. Plus, a large difference between the field amplitude reflected from the feature and from its surrounding background leads to an intense signal collected from the feature and a weaker signal collected from the background, resulting in a good signal-to-noise ratio and therefore to an improved detectability and contrast. When using a scanning step size (i.e. a pixel size) half the width of the indented line, there is always a pixel which is fully inscribed within the line and faithfully renders the signal from the line, so shows the maximum contrast, regardless of the position of the line with regards to the pixel grid. Using a scanning step size below half the width of the line does not improve the contrast of the inscriptions. However, selecting a smaller step size enables to render the width of the lines more accurately. To obtain an optimal contrast from the narrowest indented lines (85 μm) and ensure their detection, a step size of 40 μm should be used. This step size was not reachable with our set-up. Instead, a step size of 75 μm was used, which still enables to render an optimal contrast for lines wider than 150 μm (i.e. most of the scanned lines). For sieve line, a step size of 150 μm was sufficient to faithfully render the signal from the narrowest lines (350 μm).
A total of 4096 time points were sampled over 47.7 ps to reconstruct the waveform. Time points are therefore separated by ≈0.01 ps. However, for each sweep of the optical delay line, needed to record a single time-domain waveform, any jitter or drift in the waveform signal may introduce uncertainty into the measurement of the time at which the waveform maximum occurs. To determine this uncertainty, a flat gold-coated mirror was scanned with the reflection imaging module and the time at which the maximum amplitude of the waveform reflected from it occurs was measured. The standard deviation in the recorded time at which the amplitude maximum occurs is on the order of 0.05 ps, which corresponds to a distance of approximately 15 μm. It follows that only topographic features on the surface of a measured sample at a height (depth) 15 μm above (below) the nominal surface height can be reliably resolved and attributed to features associated with the document.
Signal Processing
For each measured sample, three-dimensional terahertz datasets were acquired in which the z-axis corresponds to the time domain of recorded terahertz waveforms. Corresponding two-dimensional images parallel to the plane of the scanned area (C-scans) and cross-sectional images (B-scans) were extracted. C-scans were produced by setting the colour axis of a two-dimensional image to one of a number of quantities extracted from individual waveforms recorded at each location in the scanned two-dimensional area: maximum waveform amplitude, time delay at which the waveform maximum occurs, waveform amplitude at a specific time delay, spectral power at a single terahertz frequency, as well as correlation, covariance and cross-correlation of terahertz waveforms.
A sheet of support constitutes two interfaces with a difference of refractive indices: the air–front surface of the sheet interface and the back surface of the sheet–air interface. As a result, the incident pulse is reflected on both interfaces, with the pulse reflected on the back surface of the sheet–air interface being collected at a later time than the pulse reflected on the first air–front surface of the sheet interface. If the thickness of the sheet is comparable to the width of the incident pulse multiplied by the speed of light in nitrogen-purged air, the two reflected pulses of interest may overlap. The signal resulting from this overlap would not accurately render the position and amplitude of each of the reflected pulses of interest. To circumvent this, the sample waveform which would have been detected if the incident pulse was an infinitely narrow pulse, free from any environmental or instrumental distortions, needs to be recovered. This is also called the impulse response function (IRF) and it is obtained by deconvolution [10, 11]. When acquiring data in reflection mode, Fourier deconvolution consists of the inverse Fourier transform of the reflectance ratio:
$$ IRF(t)=FF{T}^{-1}\left[\frac{FFT\left(s(t)\right)}{FFT\left(r(t)\right)}FFT\left(f(t)\right)\right] $$
The reference signal r is the signal reflected from a flat gold-coated mirror and can be assimilated to the signal from the incident pulse. Yet, due to division by the reference spectrum R = FFT(r) in the calculation of the reflectance ratio, any high-frequency noise in the sample waveform s passing on to the sample spectrum S = FFT(s) is amplified. To circumvent this, a filter f can be applied to the sample waveform. A double Gaussian filter was used here, as recommended by Zeitler and Shen [11]. It consists of two Gaussian filters, one high-pass (time width HF) and one low-pass filter (time width LF).
$$ f(t)={e}^{-\frac{t^2}{H{F}^2}}-{e}^{-\frac{t^2}{L{F}^2}} $$
Deconvolved signals were calculated for each scanning position (i.e. each pixel) using the built-in double-Gaussian deconvolution tool in the TVL Imaging Suite software (TeraView Ltd). The same high-frequency and low-frequency cut-offs were consistently used for all scanned samples.
One means of highlighting differences between reflected waveforms from different regions of a document that have varying topographical features, including indentations left by inscriptions, is to examine the degree of similarity between individual waveforms. Similarities between time-domain signals shifted in time were estimated by calculating the cross-correlation signal, as described by Smith [12], with the target signal being set to the waveform from the central pixel. When individual test time-domain waveforms are aligned with the target waveform, their resemblance is at a maximum, leading to a peak in the cross-correlation signal. The amplitude of this peak is maximal when the two signals have identical features, but decreases with the number of time-domain features that the two signals do not have in common. Similarly, only the cross-correlation of two identical and aligned signals would lead to a cross-correlation signal symmetrical on either side of its maximum peak, i.e. a cross-correlation signal with both the same number of points and the same features on either side of its maximum position. A time shift between two signals sharing identical features would only break the symmetry in the number of time points on either side of the maximum peak of the cross-correlation signal. However, if two signals do not have identical features, the cross-correlation signal does not have the same features on either side of its maximum position. Therefore, both the amplitude of the maximum of the cross-correlation signal and its degree of symmetry can be used as estimates of the similarity between individual time-domain signals. Since only the symmetry of the cross-correlation signal in terms of features is of interest here, as discussed below, the cross-correlation signal was modified to set an equal number of time points n on either side of its maximum peak. The degree of symmetry S of the cross-correlation function f was calculated as follows:
$$ \begin{array}{l}{f}_{+}(x)=\frac{f(x)+f\left(-x\right)}{2}\kern1em \\ {}{f}_{-}(x)=\frac{f(x)-f\left(-x\right)}{2}\kern1em \\ {}S=\frac{\parallel {f}_{+}\parallel }{\parallel {f}_{+}\parallel +\parallel {f}_{-}\parallel}\kern1em \end{array} $$
with the position of the maximum peak of the cross-correlation signal being set as the origin of the x-axis, where x refers to coordinates superior to the position of the maximum peak, and –x to coordinates inferior to this position, and ║f
+
║ and ║f
-║indicate the Euclidean norm of the vectors f
+
= [f
+
(x
1), …, f
+
(x
n
)] and f
- = [f
-(x
1), …, f
-(x
n
)].
When analysing the frequency-domain representation of the recorded terahertz waveforms, similarities between frequency-domain spectra were estimated by calculating the covariance and correlation between the spectral power at each pixel (or scanning step) in the scanned area and the spectral power contained in the pixel at the centre of the scanned area.
Additional pulses resulting from multiple internal reflections on the sheet surfaces were detected in the waveform transmitted through each sheet of support. Such phenomenon is often called a Fabry-Perot or ‘etalon’ effect [13]. These subsequent pulses overlapped with the main pulse transmitted through the sheet and therefore changed the time delay between the main peak of the raw waveform transmitted through the sample sheet and the main peak of the reference waveform. To avoid such errors in readings of the time delay, also inducing errors in the calculation of the constant refractive index, deconvolution [10, 11] was used to separate the main transmitted pulse from the pulses originating from the etalon effect.