METHOD AND SYSTEM FOR DETECTING AND AUTHENTICATING A CHEMICAL MARKER IN A BRAND BY ENHANCED SURFACE RAMAN SPECTROSCOPY

Abstract

The invention relates to a method and a corresponding system capable of verifying whether genuine SERS or SERRS chemical markers, which have a unique characteristic surface enhancement scattering feature, are present in a machine-readable mark applied to a valuable document by using a Raman spectrometer adapted to perform Raman spectroscopy analysis of the mark. The method according to the invention allows for rapid and reliable detection of the presence of SERS / SERRS chemical markers and is particularly suitable for verifying the authenticity of valuable documents, such as banknotes, by moving relative to the Raman spectrometer at a given speed, and possibly at a high speed, or by briefly exposing the Raman spectrometer.

Description

METHOD AND SYSTEM FOR DETECTING AND AUTHENTICATING A CHEMICAL MARKER IN A BRAND USING ENHANCED SURFACE RAMAN SPECTROSCOPY FIELD OF INVENTION The present invention relates to the technical field of detecting chemical markers (taggants) present on a mark on a substrate (e.g., a banknote) using surface-enhanced Raman spectroscopy (SERS) or surface-enhanced resonance Raman spectroscopy (SERRS). The chemical marker is of the SERS or SERRS type and, therefore, has a unique surface enhancement feature (i.e., respectively, a surface-enhanced Raman scattering feature or a surface-enhanced resonance Raman scattering feature) that allows the use of a standard Raman spectrometer for its detection. BACKGROUND OF THE INVENTION As experts in the field know, a SERS or SERRS chemical marker comprises an aggregate of nanoparticles exhibiting a plasmonic surface and Raman-active reporter molecules adsorbed onto the nanoparticle surface. The nanoparticles exhibiting a plasmonic surface are responsible for generating the electric field required for Raman amplification, while the Raman-active reporter molecules provide the unique vibrational fingerprint of the SERS chemical marker. A SERS or SERRS chemical marker may also include an outer coating layer that isolates the nanoparticle aggregate with adsorbed Raman-active molecules from the external environment.Thus, the outer coating layer a) isolates the SERS / SERRS chemical marker from the external medium, thereby preventing Raman-active reporter molecules from leaking from the SERS / SERRS chemical marker and protecting the SERS / SERRS chemical marker from external medium contamination that can lead to spurious peaks, b) increases the colloidal stability of the SERS / SERRS chemical marker, and c) provides a convenient surface for further chemical functionalization. Outer coating layers include silica and polymers, such as poly(ethyleneimine) (PEI), sodium salt of poly(styrene-alt-maleic acid) (PSMA), and poly(diethyldimethylammonium chloride) (PDADMAC). Raman spectroscopy is widely used for quantitative pharmaceutical analysis, but a common obstacle to its use is that sample fluorescence typically masks the scattered Raman signal. This is because the Raman signal has a much shorter lifetime than the fluorescence signal, as illustrated in Fig. 1. Here, a Raman intensity signal (10) (relative intensity values) due to illumination with a 600 ps laser pulse (a 1 ns gate is shown with dashed vertical lines), and various luminescence (fluorescence) intensities are shown as signals (11, 12, 13, and 14) (respectively, with lifetimes of 1 ns, 5 ns, 10 ns, and 50 ns). Time synchronization is known to provide an instrument-based method for rejecting most of the fluorescence signal by temporally resolving the spectral signal, thus enabling the acquisition of Raman spectra of fluorescent materials.An additional practical advantage is that spectral signal analysis is possible even under ambient lighting. Conventional partial least squares (PLS) regression enables quantification of the spectral signal, with active Raman time-domain selection (based on visual inspection) improving performance. Model performance is further enhanced by using kernel-based regularized least squares (RLS) regression with greedy feature selection (i.e., forward selection by choosing the best features one by one, or backward selection by removing the worst features one by one), where data usage in both the Raman shift and time dimensions is statistically optimized.Time-activated Raman spectroscopy, especially with optimized data analysis in the spectral and temporal dimensions, shows potential for sensitive and relatively routine quantitative analysis of photoluminescent materials (e.g., pharmaceuticals during drug development and manufacturing). Raman spectra are obtained by measuring the intensity distribution of Raman scattered photons received from a substrate containing a substance of interest and illuminated by a monochromatic light source, as a function of wavelength. Quantitative determination is based on the principle that the concentration of the substance of interest is proportional to the integrated intensity of its characteristic Raman bands. However, overlapping peaks from different compounds in a mixture present in the substrate, as well as experimental effects unrelated to the sample concentration, often complicate signal analysis. In such cases, multivariate analysis, which can incorporate a large amount of spectral data, is more reliable than methods that consider only one or a few spectral features. Several multivariate methods for interpreting Raman spectra have been established.The objectives of these methods are (i) to extract spectral information that quantifies the substance of interest, (ii) to estimate the uncertainties of the quantification, and (iii) to evaluate the performance of the constructed model. Partial least squares (PLS) regression is one of the most widely used chemometric methods for the quantitative analysis of spectra. PLS links the information in two data sets, X (e.g., spectral variation) and Y (e.g., sample composition), into a multivariate model that maximizes its covariance. Kernel-based regularized least squares regression (kernel-based RLS) is another approach that can learn features from nonlinear data characteristics. When combined with feature selection algorithms, such as greedy feature selection, it optimizes the use of the information provided by the data features. PLS and RLS are quite similar in that they aim to narrow the ordinary least squares solution toward the directions of the large sample variable space with less variability. Known sources of error in the quantitative analysis of powder mixtures using Raman spectroscopy include intraday and interday variation of the Raman instrument, changes in room temperature and humidity, fluorescence sample, mixing, packing and positioning, as well as the size and compactness of the sample particles. While most problems can be addressed with appropriate spectral processing and data analysis approaches, complete fluorescence subtraction without instrument-based methods is difficult, even with sophisticated algorithms. iviA / a / zu¿ o / uuu ru i Furthermore, the measured Raman spectrum is masked by a strong fluorescence background in many potential applications. This is because the probability of Raman scattering (cross-section) is much lower than that of fluorescence. In other words, Raman scattering and fluorescence emission are two competing phenomena, and the spectrum is dominated by the more probable phenomenon, which is typically fluorescence. This induces a continuous background in the residual spectrum and, in particular, increases photon shot noise, degrading the signal-to-noise ratio and resulting in uncertainty in both material identification and concentration measurements. However, fluorescence-scattered and Raman photons have different lifetimes. Raman photons are observed instantaneously during excitation (with laser light), while fluorescence photons can still be detected after nanoseconds or even milliseconds. Therefore, the fluorescence background can be suppressed if the scattered photons are collected only during the brief Raman scattering phase. This can be achieved by illuminating the sample with short, intense laser pulses (with a pulse width much shorter than the fluorescence lifetime) instead of traditional continuous-wave (CW) radiation and recording the sample response only during these short pulses. By synchronizing the measurement with the laser pulse period, the probability of detecting fluorescence photons can be reduced, as these are emitted primarily after the Raman-scattered photons.Furthermore, the accuracy of the Raman spectrum reference line is improved, leading to greater precision in both material identification and quantitative analysis. A timing (or gate) signal is a digital signal or pulse (sometimes called a trigger) that provides a time window for a particular event or signal to be selected from among many, while others are eliminated or discarded. Synchronization can be achieved using various detection systems, such as time-resolved photomultiplier tubes, high-speed optical shutters based on Kerr cells, enhanced charge-coupled devices, quantum dot resonant tunneling diodes, and complementary metal-oxide semiconductor single-photon avalanche diodes (CMOS SPADs). One of the key advantages of CMOS SPADs is their ability to reject both photoluminescence tails and photon noise. SPADs are implemented using standard CMOS technology and contain a pn junction that is reverse-biased above its breakdown voltage, meaning that the input of even a single photon can trigger an avalanche breakdown that can then be recorded. The width and position of the time gate must be carefully selected.Current CMOS single-photon avalanche diodes are compact and inexpensive, while also achieving adequate time resolutions (subnanoseconds). CMOS SPAD detectors have been used to evaluate fluorescence lifetime. More recently, the applicability of CMOS SPAD for fluorescence rejection in pharmaceutical Raman spectroscopy has also been demonstrated. Some previous studies have implemented this timing synchronization technique using a high-speed optical shutter based on a Kerr cell or a mode-locked laser with a spectrograph and an intensified charged-coupled device (ICCD). Additionally, some analyses have been conducted to determine the optimal ICCD and CCD gate position for achieving the best fluorescence rejection efficiency. However, these devices are highly sophisticated, physically large and expensive, or capable of measuring only one wavelength band of the spectrum at a time, thus requiring long measurement times and therefore unsuitable for in-situ applications and unsuitable for samples being transported to the Raman spectrometer. To overcome these problems, CCDs and ICCDs should be replaced with more suitable detectors. Problems arise when using a Raman spectrometer to authenticate a SERS or SERRS chemical marker present in a mark (e.g., a pattern printed with ink containing the SERS / SERRS chemical marker) applied to a valuable document, such as a banknote. More specifically, the spectrum measured by the Raman spectrometer includes the chemical marker's fingerprint (i.e., unique spectral identifying characteristics of the chemical marker), as well as additional interference or background information. The SERS or SERRS chemical marker fingerprint (spectral) comprises vibrational bands represented by multiple peaks with a Gaussian / Lorentzian distribution at different locations in the spectrum and with varying widths.The peak locations in the spectrum are not absolute and depend on the wavelength of the laser's excitation light (due to a change in the laser's wavelength). Raman and SERS / SERRS signals are physical effects distinct from fluorescence: the substrate of the negotiable instrument (e.g., the paper of a banknote) as well as the markings (e.g., the inks present on the banknote) have fluorescence spectra that can be measured using a Raman spectrometer. When different inks (e.g., multiple printings on a banknote), substrates (e.g., papers), and markings are present on the same spectrometer measurement track, the resulting spectral content is cumulative. Thus, a Raman spectrometer measurement typically comprises multiple spectral data resulting from cumulative effects.Some spectral information is known (known spectral data), such as that of the ink, paper, and chemical marker, and is stable over time (depending on the banknote design). However, some spectral information is unknown (unknown spectral data) and is influenced by external conditions (variables) during the measurement process, such as, for example, contaminating fumes (e.g., the presence of human sweat, beer, or food residue) or stains on the chemical marker substrate. This unknown spectral information is added during the banknote's circulation and cannot be anticipated.Furthermore, these problems are even more relevant if the measurement is performed on a valuable document that moves at high speed and requires very short integration times (e.g., 100-500 ps), such as, for example, in the case of a banknote transported at several m / s (e.g., 10-12 m / s or more) in a banknote sorting device, having a high spatial resolution (e.g., a few millimeters). Under such drastic conditions, existing prior art solutions involve, for example, as described in US Patent 10,417,856 B2, using a large number (i.e., 100 or more) of spectral channels to measure the entire Raman spectrum along with a small entrance slit (the higher the spectral resolution, the smaller the slit must be, and therefore less light reaches the CCD sensor), possibly along with light-absorbing walls (to partially absorb the Rayleigh-scattered excitation light) in the Raman spectrometer. The problem addressed in this patent is the situation in which composite banknotes must be authenticated by detecting a SERS spectrum of a chemical security marker. The described solution is to map the entire banknote using multiple small measurements along its transport path.This requires a few hundred microseconds of integration time, and one consequence is that readable signals are very low in this regime (hence the need for a compromise in spectral resolution). US 2007 / 0165209 A1 discloses improved discrimination between the Raman spectrum of the chemical marker and the spectrum due to other components of the banknote. However, there is still a need for faster detection of a Raman spectrum with a higher signal level to provide a more reliable diagnosis. BRIEF DESCRIPTION OF THE INVENTION The invention relates to a method and a corresponding system capable of verifying whether genuine SERS or SERRS chemical markers, which have a unique surface enhancement characteristic, are present in a machine-readable mark applied to a valuable document (e.g., a banknote or label, with a mark printed using ink containing chemical markers) by using a Raman spectrometer adapted to perform Raman spectroscopy (RS) analysis of the mark. The invention can be used to authenticate a valuable document or article marked with SERS or SERRS chemical markers according to various processes, for example: - One or more chemical markers may be present within a portion of a substrate of the document or valuable item, in a specific area: for example, in the case of a paper substrate (e.g., a banknote), the chemical marker may be fixed to the paper fibers in that area. In this case, the mark containing the one or more chemical markers is the portion of the substrate that is impregnated with said chemical markers. - One or more chemical markers can be mixed with an ink that is printed on a specific area of ​​a substrate of the document or valuable item. In this case, the mark containing the one or more chemical markers is the part of the substrate that is printed with the ink containing said one or more chemical markers. - One or more chemical markers can be mixed with a material, for example, a varnish, which is applied to a specific area of ​​a substrate of the document or valuable item (for example, as a coating). In this case, the mark containing one or more chemical markers is the part of the substrate to which the material is applied. - One or more chemical markers can be mixed with a specific material of a coating layer applied onto a plastic support. In all cases, the mark applied to the security document or item comprises a material (for example, the part of the substrate itself that contains chemically marked fibers, or the ink printed on the substrate, or the varnish layer applied over the substrate...) that includes one or more chemical markers of SERS or SERRS. The method according to the invention allows for a rapid and reliable detection of the presence of genuine chemical markers of SERS or SERRS, and is particularly suitable for verifying the authenticity of valuable documents marked with such chemical markers, for example, such as banknotes, which are moving relative to the Raman spectrometer at a certain speed, and possibly at a high speed (for example, 10 m / s or more), or are only briefly exposed to the Raman spectrometer (for example, as in sorting machines). To overcome the drawbacks of the prior art mentioned above, the invention relates to a method for authenticating a mark applied on a substrate and having a composition comprising a first material including a SERS chemical marker or a SERRS chemical marker, the method comprising the steps of: - define a complete model of a Raman spectrum of an authentic mark applied on an authentic substrate and have a composition comprising a first authentic material including an authentic SERS chemical marker, or an authentic SERRS chemical marker, as a first weighted sum of a reference Raman spectrum of the authentic chemical marker, a reference Raman spectrum of an authentic reference substrate, which is not marked with the authentic chemical marker, and a reference Raman spectrum of an authentic reference first material not including the authentic chemical marker, collected after the respective illumination of the authentic chemical marker, the authentic reference substrate and the authentic reference first material with excitation light; - define a reduced model of a Raman spectrum of a reduced mark, the reduced mark differing from the authentic mark only in its composition, which does not include the authentic chemical marker, as a second weighted sum of the reference Raman spectrum of the authentic reference substrate and the reference Raman spectrum of the first authentic reference material; - After illuminating the mark with the excitation light, measure a corresponding Raman light signal scattered by the mark using a Raman spectrometer to obtain a measured Raman spectrum of the mark; - fit the measured Raman spectrum to the full Raman spectrum model by calculating values ​​of the weights in the full model that minimize, under the non-negativity constraint of those weights, a difference between the full model and the measured Raman spectrum, and obtain a corresponding first residual; - fit the measured Raman spectrum with the reduced model of the Raman spectrum by calculating values ​​of the weights in the reduced model that minimize, under the constraint of non-negativity of said weights, a difference between the reduced model and the measured Raman spectrum, and obtain a corresponding second residual; - calculate an F-value corresponding to an F-test comparing the full model and the reduced model for the Raman spectrum measured from the first and second residuals obtained; and - decide whether the chemical marker is present or not in the mark based on the calculated F value. Thus, if the F-value is consistent with the presence of a genuine SERS or SERRS chemical marker on the tested mark, the mark is considered authentic. If the F-value is not consistent with the presence of a genuine SERS or SERRS marker on the tested mark, the mark may be considered counterfeit or at least suspect. The reference authentic substrate differs from the authentic substrate only in that it is not marked with the genuine chemical marker (SERS or SERRS). Similarly, the reference authentic first material differs from the authentic first material only in that it does not include the genuine chemical marker (SERS or SERRS). Of course, if the mark being tested is indeed authentic, its first material and chemical marker also correspond to the authentic first material, including the genuine chemical marker.The reference authentic substrate mentioned above denotes a corresponding authentic substrate without the mark (e.g., a paper substrate of a banknote before printing), and the first reference authentic material denotes a corresponding first authentic material without any inclusion of chemical marker. The method according to the invention is particularly adapted to a case in which, during the measurement operation of the Raman light signal scattered by the mark, the mark moves with respect to the Raman spectrometer. In the method described above, the marking composition may include a second material and the respective weighted sums of the full and reduced models. It may also include a reference spectrum of a corresponding second genuine material, collected after illumination of that second genuine material with the excitation light, with the corresponding weight. This second material (for example, an ink) is generally distinct from the first material, including the chemical marker, and does not include the chemical marker. In a preferred mode, the Raman spectrometer has a plurality of spectral channels and the operation of measuring the Raman light signal scattered by the mark comprises: - disperse the Raman light collected into a plurality of spectral channels and acquire a two-dimensional digital image of the dispersed spectral data with an imaging unit; - preprocess the acquired two-dimensional digital image by performing, using a processing unit equipped with memory, the following operations: - transform two-dimensional spectral data into one-dimensional spectral data by grouping lines and converting grouped data into wavelength data; - resample the one-dimensional spectral data to obtain a one-dimensional spectrum with data points equally distant in wavelength; - calibrate the one-dimensional spectrum with respect to a reference white light spectrum stored in memory to obtain a calibrated spectrum; - filter the calibrated spectrum with a low-pass filter to obtain a filtered spectrum; and - align the filtered spectrum in wavelength with the reference spectrum of the chemical marker stored in memory, thus obtaining a preprocessed spectrum; and - Perform the calculation operations of the first and second residues using the preprocessed spectrum as the measured Raman spectrum. The optics and grating of a Raman spectrometer cause a typical (two-dimensional) distortion of the Raman lines formed in the two-dimensional image (Raman lines are curved and compressed). Line grouping and calibration operations are performed to compensate for this distortion. The calibration operation is generally performed with an excitation (reference) light supplied by an argon lamp to calculate the two-dimensional distortion of the Raman lines compared to the observed image of the argon lines. According to the preferred mode above, the method may comprise: - define a spectrum measurement vector as a vector corresponding to the obtained preprocessed spectrum; - define a first spectrum vector as a product of a first weight vector and a complete design matrix and determine the respective non-negative components of the first weight vector that minimizes, by a least squares method, a first residual vector corresponding to a difference between said first spectrum vector and the measurement vector of the spectrum, the complete design matrix having columns that respectively represent the reference spectral data of the complete model; - define a second spectrum vector as a product of a second weight vector and a reduced design matrix and determine the respective non-negative components of the second weight vector that minimizes, by a least squares method, a second residual vector corresponding to a difference between said second spectrum vector and the measurement vector of the spectrum, the reduced design matrix having columns that respectively represent the reference spectral data of the reduced model; - calculate a first residual sum of squares RSS1 of errors corresponding to the first weight vector, the first weight vector having a number p1 of non-negative components; - calculate a second residual RSS2 sum of squares of errors corresponding to the second weight vector, the second weight vector having a number p2 of non-negative components; and - calculate the F value as a ratio of a difference between the second residual sum of squares RSS2 and the first residual sum of squares RSS1 divided by a difference between the numbers p2 and p1, and the first residual sum of squares RSS1 divided by a difference between a number N of components of the spectrum measurement vector and the number p1, F = ((RSS2-RSS1 ) / (p1p2)) / (RSS1 / (N-p1)). Furthermore, the operations of determining the respective non-negative components of the first weight vector and the second weight vector may include - represent the first weight vector that minimizes the first residual vector as a product of a pseudo-inverse matrix of the full design matrix and the spectrum measurement vector, and represent the second weight vector that minimizes the second residual vector as a product of a pseudo-inverse matrix of the reduced design matrix and the spectrum measurement vector; and - in case a component, respectively, of the first weight vector or the second weight vector has a negative value: - modify, respectively, the complete design matrix or the reduced design matrix by removing from said matrix a spectral vector corresponding to said negative component; - to zero out the negative value of said component; and - recalculate, respectively, a pseudo-inverse matrix of the modified full design matrix or the modified reduced design matrix, until the components obtained from the first weight vector and the second weight vector have only non-negative values. The invention further relates to an operable system for implementing the steps of the aforementioned method, the system for authenticating a mark applied on a substrate and having a composition comprising a first material including a SERS chemical marker, or a SERRS chemical marker, the system comprising a light source, a Raman spectrometer, an imaging unit and a control unit having a processing unit and a memory, the light source being controlled by the control unit through a current loop to deliver a calibrated excitation light, the system being configured to perform the operations of: - illuminate the mark with the excitation light delivered by the light source controlled by the control unit; and - collect a Raman light resulting from the mark and disperse the collected Raman light in the Raman spectrometer having a plurality of spectral channels and acquire a two-dimensional digital image of the corresponding spectral data with the imaging unit, and store in memory the acquired spectral data as a measured Raman spectrum of the mark; where - the memory stores a complete model of a Raman spectrum of an authentic mark applied on an authentic substrate and having a composition comprising an authentic first material including an authentic SERS chemical marker, or an authentic SERRS chemical marker, as a first weighted sum of a reference Raman spectrum of the authentic chemical marker, a reference Raman spectrum of an authentic reference substrate not marked with the authentic chemical marker, and a reference Raman spectrum of an authentic first reference material not including the authentic chemical marker collected after the respective illumination of the authentic chemical marker, the authentic reference substrate and the authentic first reference material with excitation light; - the memory stores a reduced model of a Raman spectrum of a reduced mark, the reduced mark differing from the authentic mark only in its composition, which does not include the authentic chemical marker, as a second weighted sum of the reference Raman spectrum of the authentic reference substrate and the reference Raman spectrum of the first authentic reference material; and the system being further configured to perform, through the processing unit, the operations of: - adjust the measured Raman spectrum stored in memory with the full model iviA / a / zuzo / uuu ru / stored of the Raman spectrum by calculating values ​​of the weights in the full model that minimize, under the constraint of non-negativity of said weights, a difference between the full model and the measured Raman spectrum and obtain and store in memory, a corresponding first residue; - adjust the measured Raman spectrum stored in memory with the stored reduced model of the Raman spectrum by calculating values ​​of the weights in the reduced model that minimize, under the constraint of non-negativity of said weights, a difference between the reduced model and the measured Raman spectrum and obtain and store in memory, a corresponding second residue; - calculate and store in memory, an F-value corresponding to an F-test comparing the full model and the reduced model for the measured Raman spectrum of the first and second stored residues; and - decide whether the chemical marker is present or not in the mark based on the stored F value, and deliver a signal indicating the result of the decision. In a preferred mode of the system, where, during the measurement operation of the Raman light signal scattered by the mark, the mark moves with respect to the Raman spectrometer, the control unit synchronizes the illumination of the mark with the light source and the acquisition of the Raman spectrum measured through the Raman spectrometer and the imaging unit with the movement of the mark. In the previous system, if the mark composition includes a second material, the respective weighted sums of the full model and the reduced model also include a reference spectrum of a corresponding second authentic material, collected after illuminating that second authentic material with the excitation light and stored in memory, with the corresponding weight. For example, in the case of a printed mark, that second authentic material might correspond to a set of inks used to print the mark, but excluding the SERS or SERRS chemical marker. In the previous system, the processing unit could be configured to perform preprocessing operations on the stored two-dimensional digital image. - transform two-dimensional spectral data into one-dimensional spectral data by grouping lines and converting grouped data into wavelength data; - resample the one-dimensional spectral data to obtain a one-dimensional spectrum with data points equally distant in wavelength; - calibrate the one-dimensional spectrum with respect to a reference white light spectrum stored in memory to obtain a calibrated spectrum; - filter the calibrated spectrum with a low-pass filter to obtain a filtered spectrum; - align the filtered spectrum in wavelength with the reference spectrum of the chemical marker stored in memory, thereby obtaining and storing a preprocessed spectrum in memory; and - Perform the calculation operations of the first and second residues using the preprocessed spectrum stored in memory as the measured Raman spectrum. In addition, the processing unit can also be configured to: IVIA / a / ZU4O / UUU fV f - define a spectrum measurement vector as a vector corresponding to the obtained preprocessed spectrum; - define a first spectrum vector as a product of a first weight vector and a complete design matrix and determine the respective non-negative components of the first weight vector that minimizes, by a least squares method, a first residual vector corresponding to a difference between said first spectrum vector and the measurement vector of the spectrum, the complete design matrix having columns that respectively represent the reference spectral data of the complete model; - define a second spectrum vector as a product of a second weight vector and a reduced design matrix and determine the respective non-negative components of the second weight vector that minimizes, by a least squares method, a second residual vector corresponding to a difference between said second spectrum vector and the measurement vector of the spectrum, the reduced design matrix having columns that respectively represent the reference spectral data of the reduced model; - calculate a first residual sum of RSS1 squares of errors corresponding to the first weight vector, the first weight vector having a number p1 of non-negative components, and storing in memory the first calculated residual sum of RSS1 squares and the number p1; - calculate a second residual RSS2 sum of squares of errors corresponding to the second weight vector, the second weight vector having a number p2 of non-negative components, and store in memory the second calculated residual RSS2 sum of squares and the number p2; and - calculate the F value as a ratio of a difference between the second stored RSS2 residual sum of squares and the first stored RSS1 residual sum of squares divided by a difference between the stored numbers p2 and p1, and the first stored RSS1 residual sum of squares divided by a difference between a number N of components of the spectrum measurement vector and the number p1, F = ((RSS2-RSS1) / (p1-p2)) / (RSS1 / (N-p1)). The processing unit can also be configured to determine the respective non-negative components of the first weight vector and the second weight vector when - represent the first weight vector that minimizes the first residual vector as a product of a pseudo-inverse matrix of the complete design matrix and the spectrum measurement vector; - represent the second weight vector that minimizes the second residual vector as a product of a pseudo-inverse matrix of the reduced design matrix and the spectrum measurement vector; and - in case a component, respectively, of the first weight vector or the second weight vector has a negative value: - modify, respectively, the complete design matrix or the reduced design matrix by removing from said matrix a spectral vector corresponding to said negative component; - to zero out the negative value of said component; and - recalculate, respectively, a pseudo-inverse matrix of the modified full design matrix or the modified reduced design matrix, until the components obtained from the first weight vector and the second weight vector have only non-negative values ​​and store the obtained components in memory. The present invention will be described more fully below with reference to the accompanying figures, which illustrate prominent aspects and features of the invention. BRIEF DESCRIPTION OF THE FIGURES Figure 1 illustrates the relative lifetime (not to scale) of photoluminescence and naman signals (including fluorescence). Figure 2 illustrates a nAA spectrum of a chemical marker of SEñS to show the effect of enhancing the intensity of the scattered light nAA due to the structure of the SEñS particle. Figure 3 illustrates a ñaman spectrum of a chemical marker of SEññS. Figure 4 is a flowchart illustrating one embodiment of the method according to the invention. Figure 5 is a flowchart illustrating the non-negativity constraint method according to the invention. Figure 6 is a schematic view of a system including a ñaman spectrometer according to one embodiment of the invention. DETAILED DESCRIPTION OF THE INVENTION To overcome the drawbacks of the prior art mentioned above and to detect the presence of a chemical marker of SEñS or a chemical marker of SEññS in a mark applied to a substrate for authentication, and also to reliably quantify the amount of signal coming from the fingerprints of the chemical marker of SEñS / SEññS (i.e., very specific peaks in their ñaman spectra) within the raw spectral data of the mark measured by a ñaman spectrometer, the method according to the invention compares the measured spectral data of the tested mark with reference ñaman spectral models of the various separate materials that make up a corresponding authentic mark, and a reference ñaman spectrum of a reference authentic substrate, and uses a robust quality model capable of reliably determining whether the chemical marker of SEñS / SEññS has been identified within the mark.If the chemical marker is identified as authentic on a mark, the mark itself is considered authentic and, in general, a valuable document that includes this mark (applied on the substrate of this valuable document) is considered authentic. The additional / undesirable spectral information in the raw spectral data acquired by the ñaman spectrometer is divided into two spectral subcategories that correspond respectively to the known and unknown spectral data mentioned above. This is done to improve the signal-to-noise ratio (SNn) and provide fast and reliable verification of the presence of the SEñS / SEññS chemical marker on a mark applied to valuable documents compatible with high-speed sorting devices. The known spectral data is used to model the measured spectral information, while the unknown spectral data, which is expected to be low-frequency data, is modeled using simple polynomials (e.g., Legendre polynomials, Jacobi polynomials, Gegenbauer polynomials, Zernike polynomials, Chebyshev polynomials, and Romanov polynomials). The spectral enhancement effect due to the structure of an example SERS chemical marker is illustrated in Figure 2, with a Raman spectrum and a SERS spectrum (scattering intensities are plotted against Raman shift in cm1), and the spectral enhancement effect due to the structure of an example SERRS chemical marker is illustrated in Figure 3 (where the Raman spectrum is scaled by a factor of 8 to better overlap with the SERRS spectrum). In both figures, the characteristic enhanced Raman scattering intensity peaks are clearly visible and are so specific to the structure of the nanoparticles that make up the chemical marker that they constitute identifying features (i.e., they are the fingerprint of the chemical marker). According to an illustrative embodiment of the invention, a mark (a pattern) to be authenticated is printed on the paper substrate of a banknote using various inks. If the mark (and therefore the banknote) is authentic, each (authentic) ink composition is known, and an authentic SERS chemical marker, whose reference Raman spectrum is known, has been added to one of these inks for printing on the banknote. The ink containing the SERS chemical marker corresponds to the first material mentioned above, and the second material mentioned above corresponds to the other inks. In this particular embodiment, there are four distinct inks (each with its own specific composition) present in the mark, and each ink, if authentic and without the inclusion of the chemical marker, has a known reference Raman spectrum.The reference Raman spectra of a genuine SERS chemical marker, a reference genuine paper substrate (from a corresponding genuine banknote), and each of the four reference genuine inks can be measured with a Raman spectrometer by illuminating the genuine SERS chemical marker, the reference genuine paper substrate, and each of the four reference genuine inks, respectively, with an excitation light (here, a laser). These reference Raman spectra are then used to derive a complete Raman spectrum model of a generic genuine mark as a linear combination of the different reference spectra. Each reference spectrum corresponds to the acquisition, via a Raman spectrometer, of a certain number of light intensity values ​​scattered at different wavelengths.Thus, an interpolated reference spectral curve giving the measured scattering intensity I as a function of wavelength λ, i.e., I(λ), can be obtained for each of the aforementioned genuine SERS chemical markers, original reference paper substrate, and four original reference inks. For simplicity, we assume that the same number n (e.g., n = 1024) of reference intensity values ​​(corresponding to different wavelength values) are extracted from each reference spectral curve. In the complete Raman spectrum model of a generic authentic brand (with the four authentic inks) applied to an authentic substrate, a (discrete) representation of the spectral curve comprises n Raman intensity values ​​h, i = 1, n, (taken along the spectral curve), and each intensity value h is modeled as a linear combination of (p1 -1) reference Raman intensity values ​​X¡2, ..., X¡Pi, (as X¡1 ξ 1, for i = 1, n), with p1 = 7 in the particular modality iviA / a / zuz o / uuu ru i (p1 is the number of independent variables in the model). Thus, we have: h = βι X¡1 + β2 X¡2 +...+ β? X¡7, where βι, ..., β7 are weights and - X¡2, i = 1, .... n, there are n intensity values ​​at representative points selected along the reference (normalized) Raman spectrum of the authentic SERS chemical marker. The selected points are in a wavelength band approximately 150 nm wide in the NIR (near-infrared, 750-1400 nm) range. The normalization of the spectral curve is obtained by removing the offset value (data are generally not centered at 0 on the ordinate axis) by taking the difference between the measured value and the minimum of the measured values ​​and setting the highest peak value to, say, 1000. - X.3, ¡ = 1, ..., n, are n intensity values ​​at representative points selected along the (normalized) reference Raman spectrum of the original reference paper; and - X¡4, ..., X¡7, i = 1, ..., n, are n respective intensity values ​​at representative points selected along the (normalized) reference spectra of the respective four authentic reference inks used to print an authentic mark (each of the four authentic reference inks is considered alone, i.e., without including the SERS chemical marker). In vector notation, a vector I can be associated with the n scalar components h, i = 1, ..., n; a vector β can be associated with the p1 (here, p1 = 7) scalar weights βι, β2, ..., βρι, and a matrix (η X p1) X can be associated with the complete model, of which the first column comprises the n values ​​X¡1 = 1 (i = 1, , n), and the second to the p1-th column are respectively formed by the components X¡2 (i = 1,..., n), ..., X¡pi(¡ = 1, ..., n). Thus, the representation of a Raman spectrum in the complete model is: I = X β. According to the invention, a reduced mark is a mark applied to the (genuine) paper substrate that differs from a genuine mark only in that it does not include a (genuine) SERS chemical marker. In a reduced model of a Raman spectrum of such a reduced mark, we therefore have n Raman intensity values ​​Ji, i = 1, ..., n, taken from the spectral curve that are modeled as a linear combination of (p2-1) reference Raman intensity values ​​(such as Z¡1 ξ 1, for i = 1, ..., n) Z¡2, ..., Z¡P2: here with p2 = 6. Thus, we have: J¡ = μι Z¡1 + pa Z¡2 +... + με Z¡6, where μι, ..., με are weights and - Z¡2, i = 1, ..., n, are n intensity values ​​at representative points selected along the (normalized) reference Raman spectrum of the original reference paper; and - Z¡3, ..., Z¡6, i = 1, .... n, are n respective intensity values ​​at representative points selected along the four (normalized) reference spectra of the four respective inks used to print a reduced mark (of course, not including the SERS chemical marker). In reality, by definition of the reduced model, here we have (for i = 1, ..., n): Zn = X¡1 = 1, and Z¡k = X¡(k+D, for k = 2, ..., p2. In vector notation, a vector J can be associated with the n scalar components Ji, i = 1, ..., n; a vector μ can be associated with the p2 (here, p2 = 6) scalar weights μι, μ2, ..., μP2, and a matrix (η X p2) Z can be associated with the reduced model, of which the first column comprises the n values ​​Z¡1 iviA / a / zuzo / uuu ru / = 1 (i = 1, n), and the second to the p2-th column are respectively formed by the components Z¡2 (i = 1, n), Z¡P2(i = 1, ..., n). Thus, the representation of a Raman spectrum in the reduced model is: J = Z μ. The mark on the banknote to be authenticated is illuminated with laser excitation light, and the corresponding Raman light signal scattered by the mark is measured with a Raman spectrometer to obtain a measured Raman spectrum of the mark. Preferably, a Raman spectrometer equipped with a multimode laser (MML) source is used. In fact, even though it is common practice to use a single-mode laser (SML) source to obtain the best possible resolution, experience shows that using an MML source actually improves the detection speed. For example, the laser power can be increased by a factor of ten (without any compromise) compared to an SML source, while the measurement integration time is reduced by a factor of ten (e.g., instead of 2 ms, we can achieve 0.2 ms).This is due to two main differences between SML and MML sources: the laser power (e.g., SML is about 100 mW at 760 nm, while MML is much higher, say about 1 W), and the line width (SML is about 0.02 nm while MML is 0.08 nm). This measured Raman spectrum gives a measured scattered light intensity Y (Raman) as a function of the scattered light wavelength λ, i.e., Y(λ). The Raman spectrometer has a plurality of spectral channels, and the Raman light signal scattered by the marker and collected by the spectrometer is first scattered into these spectral channels (through a grating). An imaging unit (a CCD) then acquires a two-dimensional digital image of the corresponding scattered spectral data as a two-dimensional array of intensity values ​​versus wavelengths, i.e., two-dimensional spectral data.Since the two-dimensional spectral data acquired from the Raman spectrometer is raw, it is pre-processed primarily to reduce the amount of data to be analyzed later in a processing unit (to reduce processing time and be compatible with banknote detection in high-speed sorters), improving the signal-to-noise ratio (SNR), and accurately locating the Raman band of the chemical marker fingerprint. The preprocessing stage of the two-dimensional digital image acquired by the image acquisition unit is performed by the processing unit, equipped with memory, and comprises the following operations: 1) Transform the acquired two-dimensional spectral data into one-dimensional spectral data by grouping lines and converting the grouped data into wavelength data. This transformation greatly reduces the amount of data to be processed and improves the SNR (noise is generally reduced by a factor of the square root of the number of pixels in a column of the two-dimensional digital image). 2) Resample the one-dimensional spectral data obtained to form a one-dimensional spectrum with data points equally spaced in wavelength. This operation is performed by spline or polynomial interpolation of the spectral data. This resampling has the advantage of reducing spectral compression along the x-axis and y-axis. IVIA / a / ZU4O / UUU fV f also provides linear spectrum resolution which allows the use of known signal processing tools (FFT convolution low-pass filtering, FIR convolution, etc.). 3) Calibrate the one-dimensional spectrum of the new sample against a reference white light spectrum (e.g., from a quartz tungsten halogen lamp, to balance the sensitivity of the Raman spectrometer), which is stored in memory, to obtain a calibrated (one-dimensional) spectrum. This operation allows balancing the intensity of the light delivered by the Raman spectrometer (since, in general, the spectrometer emits different values ​​for the same light intensity at different wavelengths). 4) Filter the calibrated spectrum with a low-pass filter to obtain a filtered spectrum. The unwanted high-frequency noise in the spectral data is primarily due to the imaging unit (i.e., its image sensor and circuitry) and is known to be a measurement artifact. This filtering can be performed using various methods, such as a moving average filter, an FFT (Fast Fourier Transform) filter, or a Savitzky-Golay filter. FFT filtering is preferred (as this method can also be used for spectrum alignment). 5) Align the filtered spectrum in wavelength with the reference spectrum of the authentic chemical marker stored in memory. In fact, the stored reference Raman spectrum of the authentic chemical marker is generally not aligned with the Raman spectrum measured from the marker due to many possible causes, such as spectrometer expansion, temperature variations affecting the wavelength of the light source and / or grating, mechanical disturbances due to vibrations, etc. Therefore, to obtain the best possible validation of the chemical marker fingerprint, the measured Raman spectrum obtained from the marker is aligned in wavelength with the reference spectrum. This alignment can be performed using different methods, such as: - running the algorithm at different displacement increments and selecting the best position on the wavelength axis; - running the algorithm at different displacement increments and interpolating to find the best position on the wavelength axis; - preferably, by means of the modality, in the frequency domain, of a convolution with the fingerprint of the chemical marker; - monitoring the position of the light source during measurement from the mark. As a result of the above operations, a preprocessed Raman spectrum is obtained from two-dimensional spectral data acquired by the imaging unit. A (discrete) representation of the spectral curve Y(λ) of the preprocessed Raman spectrum comprises n (preprocessed) Raman intensity values ​​Yi, i = 1, ..., n, (taken along the spectral curve) and an (n-dimensional) vector Y can be associated with the n scalar components Yi, i = 1, ..., n. To fit the (preprocessed) Raman spectrum to the full model, the (measured) spectrum vector Y is decomposed as Y = I + ε (linear regression analysis), with the first spectrum vector I = Xβ, where X is the ηXp1 (design) matrix of the full model, β is the first corresponding weight vector, and ε is an error vector, or residual vector, with components ει, i = 1, ..., n. The values ​​of the βκ components (k = 1, ..., p1; here pi = 7) of the first weight vector β that minimize the error vector ε can be determined using various well-known optimization methods. For example, it is possible to calculate (iteratively) the residual vectors for a plurality of selected values ​​of the β vector components and choose the β corresponding to the residual vector that has the lowest norm. Another method is to use a well-known optimization algorithm, such as Dantzig's simplex algorithm.Preferably, we use the Least Squares Residual (LSR) method which has the advantage of being less CPU computation intensive and is therefore more suitable for authenticating marks on banknotes in high-speed sorting machines. Similarly, to fit the (preprocessed) Raman spectrum with the reduced model, the vector Y is decomposed as Y = J + ε with the second spectrum vector J = Z μ, where Z is the η X p2 (design) matrix of the reduced model, μ is the corresponding second weight vector, and ε' is an error vector, or residual vector, with components εΊ, i = 1, ..., n. The values ​​of the components pm(m = 1, ..., p2; here p2 = (p1 -1) = 6) of the second weight vector μ that minimize the error vector ε' can be determined using the Least Squares Residuals (LSR) method. According to the LSR method, the least squares parameter estimates of β for the full model (resp. of μ, for the reduced model) in view of the Y measures are obtained from the normal equations p1 (resp. p2): 8¡ = Y¡ — βι X¡1 + β2 X¡2 +... + βρί Xipi (i = 1, , n), that is, ε = Y - X β y Σ^Σ^χ^Ρ* = = ι,·,ρΐ; or, respectively, ε' = Y¡ - μι Zn + μ2 Z¡2 +...+ μΡ2 Z¡P2 (i = 1,..., n): that is, ε' = Y - Z μ, and Σ^Σ^Ζί^ = j = 1,...,p2. The LSR method provides a solution that minimizes the squared residual, namely β = min ||ε||² for the full model, and μ = min ||ε'||² for the reduced model. If we assume that the L μ columns of the full model design matrix X are linearly independent, we can use the (left) pseudoinverse X+ of this full model design matrix X with X+ = (XτX)'1XT, where XT is the transpose of X, and write β = X+Y (and we have X+X = Id). If the rows of the full model design matrix X are linearly independent, we can use the (right) pseudoinverse X+ of this matrix X with X+ = Xτ(X XT)'1, and still write β = X+Y (and we have X* = Id). In practice, we use the singular value decomposition (SVD) method to calculate the pseudo-inverse of the design matrix to achieve a stable and fast calculation. Similarly, we calculate the pseudo-inverse Z+ of the reduced model design matrix Z and write μ=Z+Y.These pseudo-inverse matrices are preferably pre-calculated (once the corresponding design matrices are known) and stored in the processing unit's memory. Once the first weight vector β and the second weight vector μ are determined, the statistical significance of these estimated weights of the two models (with a view to the same measurement vector Y), i.e., the quality of the full model versus the reduced model, can be checked by performing a classic F-test. However, a problem with the LSR method mentioned above is that it doesn't consider whether the resulting solution is feasible. In fact, if the solution involves a negative value for a weight component β (j ε {2, ..., 7}) of the vector β, or a weight component μΓ (r ε {2, ..., 6}) of the vector μ, then the intensity of the related spectral component would be negative, which is not physically possible (this would constitute an unfeasible solution). It has been observed that the authentication method is much more robust when specific minimization methods are used to satisfy the non-negativity constraint (NNC) on the weight values. Several methods that incorporate this non-negativity constraint are known: for example, the Active-Set method (detailed in Charles L. Lawson and Richard J. Hanson's book, Solving Least Square Problems, SIAM 1995), or Landweber's gradient descent method.According to the invention, the LSR method is combined with the following method, illustrated in Fig. 5, to comply with the non-negativity constraint. This will be explained in the case of the full model with p1 = 7 weights, and can be directly transposed, mutatis mutandis, to the case of the reduced model (with p2 = 6 weights). The method for calculating the values ​​of the components ρ1 βι, ..., β? of the weight vector β begins (S1) by calculating them from the pseudo-inverse matrix X+Y and the measurement vector of the spectrum Y stored in the memory of the processing unit, i.e., with β = X+Y. Then, a check (S2) is performed to determine if there are any negative weight values ​​in the initially calculated weight vector β. In the example shown in Fig.5, two weights βζ and βε have negative values ​​(corresponding respectively to the chemical marker of SERS and the third ink), then the value of weight β2 is set to zero (S3) and the corresponding column of the design matrix X, i.e. the column corresponding to the Raman spectrum of the (genuine) chemical marker of SERS (with components X12, ..., Xn2), is removed (S4) from the (initial) design matrix X, and a new design matrix η X (p1-1) X' is thus obtained. A new corresponding pseudoinverse matrix X'+ is then calculated (S5) and used to calculate (S6) a new weight vector β', with β' = X+Y: this new weight vector has only (p1 -1) components β'1, β'3, β'4, β'δ, β'ε and β > (since we have set β2 to zero). A check (S7) is then performed to determine whether there is any negative weight value (yes, Y) in the calculated weight vector β' or not (no N). In the example shown in Fig.5, a weight β'ε has a negative value (corresponding to the third ink), then the value of weight β'6 is set to zero (S8), and the corresponding column of the design matrix X', i.e., the column corresponding to the Raman spectrum of the third (original reference) ink (with components Xw, ..., Xne), is removed (S9) from the design matrix X', and a new design matrix η X (p1 -2) X is thus obtained. A corresponding new pseudo-inverse matrix X* is then calculated (S10) and used to calculate (S11) a new weight vector β, with β = X+Y: this new weight vector has only (p1 -2) components βι, β3, β4, β5 and β? (since we have set β2 and β'ε to zero). A check (S12) is then performed to determine whether there are any negative weight values ​​(Y) in the calculated weight vector β or not (N). In the example shown in Fig. 5, the remaining weight component values ​​β'j, β3, β4, β'ε and β? are all positive.As a result (S13), the final p1 values ​​of the weight components obtained by the LSR method under non-negativity constraint, i.e., the LSR-NNC method, are βι, 0, β3, β4, β5, 0, and β?, and the calculation stops (S14). If there is a negative value in step S12 (i.e., Y), then steps (S8) to (S12) are carried out accordingly. The LSR-NNC method is also applied to the calculation of the (non-negative) values ​​of the components of the second weight vector, μ = Z+Y. Having obtained reliable values ​​(i.e., non-negative values ​​corresponding to physically possible ones) using the LSR method together with the non-negativity restriction (LSR-NNC), for the components of the first weight vector β and the second weight vector μ, a reliable F-test can now be performed to compare the quality of the full model with that of the reduced model. To achieve this, an F-value is calculated as a ratio of a difference between the second residual sum of squares RSS2 = Σ=1(ε'i)2 of the reduced model and the first residual sum of squares RSS1 = Σ[1i(ε()2) of the full model divided by a difference (p2-p1) between the numbers p2 and p1, and the first residual sum of squares RSS1 divided by a difference between a number n (here, n = 1024) of components of the spectrum measurement vector Y and the number p1, F = ((RSS2-RSS1) / (p1p2)) / (RSS1 / (n-p1)). Thus, F = [(RSS2-RSS1) / RSS1] x K, with a factor K = (n-p1) / (p1-p2).In the example considered, we have the same number of data points, n, for both models. The full model (model 1) has one more parameter than the reduced model (model 2). As always, the model with more parameters will always fit the data at least as well as the model with fewer parameters, and the F-test will determine whether the full model provides a significantly better fit to the data than the reduced model (without the chemical marker). From the classic formula above, we obtain a K-factor value given by (np1) / (p1 - p2) = (n - 7) / 1 = 1017. The F-value is a number that represents the probability of having a genuine SERS chemical marker in the mark. In general, the value of F depends on the SNR as follows: - With a low SNR and the presence of the SERS chemical marker in the signal: the F-value is low. This is normal since random noise has the same impact as the fingerprint of the SERS chemical marker discrimination. - with a low SNR and an absence of a genuine SERS chemical marker in the mark: the F value is low. - with a high SNR and a presence of the (authentic) SERS chemical marker in the mark: the F value is high. - with a high SNR and an absence of the (authentic) SERS chemical marker in the mark: the F value is low. The trend between SNR and F-value is linear; it is not suitable for determining the authenticity of a brand when the F-value is between 8,000 and 1,000,000. An additional compression stage can be applied to modify the F-value to create a plateau in a curve that represents a dependence of the F-value on the SNR. In this method, a modified (compressed) F' value is obtained by the transformation F' = constant x Log(F), for example, with the constant factor value of 5. Based on a series of experiments, it can be reliably concluded that: - An F' value below a low threshold value (LTV) of approximately 20 (say, between 1 and 20) corresponds to an absence of SERS (genuine) chemical marker in the marking, and a negative D- decision is delivered indicating that the corresponding banknote is not genuine. - An F' value above a high threshold value (HTV) of approximately 50 (say, between 50 and 80) indicates the presence of the SERS chemical marker on the mark, and a positive D+ decision is delivered indicating that the corresponding banknote is genuine. - whereas intermediate F' values ​​(say, between the low threshold LTV value and the high threshold HTV value) do not allow for a conclusion (the result depends heavily on the SNR level). In the latter case, since it cannot be determined whether the SERS chemical marker is present in the mark and therefore whether the banknote is genuine, the banknote is retained (R) for further (e.g., forensic) analysis. The steps of the preferred embodiment of the method for authenticating a mark applied to a substrate and having a composition that includes an ink and a SERS chemical marker (or a SERRS chemical marker) are summarized in Fig. 4. The method is initiated (M0), and the values ​​of the number of reference Raman spectra in the full and reduced models, p1 (with p1 > 4) and p2 = (p1 - 1), are specified and stored in the processing unit's memory (M1), along with the number n of points taken in the Raman spectrum measurement. The respective Raman spectra X12, X1pi (i = 1, n) of the full model and Z12, ..., Z1P2 of the reduced model are specified, and the corresponding full design matrix X and reduced design matrix Z are stored in step (M2). The corresponding pseudo-inverse X+ of the full design matrix and pseudo-inverse Z+ of the reduced design matrix are calculated and stored in step (M3).Next, a Raman spectrum measured from the mark is acquired via a two-dimensional image obtained by the Raman spectrometer's imaging unit (by illuminating the mark with the excitation laser light). This is pre-processed to obtain a one-dimensional spectrum and form a corresponding spectrum measurement vector Y with n components in step (M4). The LSR method together with the NNC method (i.e., LSR-NNC) is performed in step (M5) to calculate the first weight vector β = X+Y corresponding to the full model and the second weight vector μ = Z+Y corresponding to the reduced model. These minimize, respectively, the square of the first residual vector ε (i.e., YX β) for the full model and the square of the second residual vector ε' (i.e., Y - Z μ) for the reduced model.Then, the first residual sum of squares RSS1 = ZíLiUD2 and the second residual sum of squares RSS2 = Σ^χN,·)2 are calculated, and the corresponding F value is obtained in step (M6), with F = K (RSS2-RSS1) / RSS1 (and K = (n-p1) / (p1-p2)). In step (M7), a compressed value F' is calculated (e.g., with the transformation F = 5 Log (F)). Finally, a decision is made in view of the compressed value F and the stored HTV (high threshold value) and LTV (low threshold value) values ​​that are convenient for the mark. - In step (M8), the value F is compared to the HTV value: if F is greater than HTV (condition c1), a positive decision D+ is delivered in step (M9), i.e., the banknote bearing the mark is authentic (and the calculation stops (M9j)); if F is less than or equal to HTV (condition c2) then, ivi A / a / zu¿ o / uuu ru i - In stage (M10), the value of F' is compared to the LTV value: if F' is less than LTV (condition c3), a negative decision D- is delivered in stage (M11), i.e., the banknote bearing the mark is not genuine (and the calculation stops at (M11j); if F' is greater than or equal to LTV (condition c4), then the banknote is held (R) in stage (M12) for further analysis (and the calculation stops at (M12j). If a mark comprises multiple SERS chemical markers, or SERRS chemical markers, a decision on authenticity based solely on a single F-value may not be sufficiently reliable. According to the invention, it is possible to use multiple different reduced models and calculate different F-values ​​to compare the complete model of an authentic mark (i.e., comprising the plurality of reference spectra of the various chemical markers) with each of the reduced models. For example, the different reduced models may correspond to a mark that differs from an authentic mark only by the absence of one of the various chemical markers of the authentic mark.These F-values ​​are obtained from a (preprocessed) spectrum vector Y derived from a measured Raman spectrum of the mark to be authenticated. This is achieved by applying the previously mentioned LSR-NNC method to find the different weight vectors that minimize the squares of the corresponding residual vectors. A decision regarding the authenticity of a mark must involve different threshold rules for each of the calculated F-values, resulting in a certain degree of complexity. In this case, a decision on authenticity can preferably be based on a decision tree that incorporates these threshold rules. The invention also relates to a system (60), a particular embodiment of which is illustrated in Fig. 6, comprising a light source (61), a Raman spectrometer (62), an imaging unit (63), a processing unit (64), a memory unit (65), and a control unit (66). The control unit (66) controls the light source (61) (hereinafter, a laser) via a current loop to deliver a calibrated excitation light and illuminate a mark (67) on a banknote (68) to be authenticated, when the (moving) mark reaches the level of the imaging unit (65). The laser excitation light is directed through a dichroic mirror (69) to the mark (67). In response to the illumination, a Raman light is scattered from the mark, collected through the dichroic mirror (69) and scattered through a grid (70) towards a CCD sensor (71) of the imaging unit (63).A corresponding two-dimensional digital image of the collected Raman spectrum is formed by the imaging unit (63) and constitutes the 2D Raman spectrum measured and stored in the memory unit (65). The memory unit (65) stores the complete model of an authentic mark (applied to an authentic substrate of an authentic banknote), i.e., the number n of points from the selected reference spectra, the number p1 of weights forming a first weight vector β, and the number p2 of weights forming a second weight vector μ, as explained above. The reference spectra of the complete model are stored as components of a complete (design) array X, and the reference spectra of the reduced model are stored as components of a reduced (design) array Z.The memory unit (65) also stores the reduced model, the pre-calculated pseudo-inversions X+ and Z+, ivi A / a / zu¿ o / uuu ru i respectively, of the X matrix and the Z matrix. The stored two-dimensional measured Raman spectrum is pre-processed through the processing unit (64) as explained above to obtain a pre-processed (one-dimensional) spectrum in the form of a spectrum measurement vector Y having n components, which are stored in the memory unit (65). The processing unit (64) then calculates the first weight vector β = X+Y corresponding to the complete model, which minimizes the square of the first residual vector ε = Y - X β, and calculates the second weight vector μ = Z+Y, which minimizes the square of the second residual vector ε' = Y - Z μ, and stores the calculated residual vectors in the memory unit (65).The memory unit also stores the HTV and LTV parameter values, corresponding respectively to the high and low threshold values ​​to be considered with an F-test for the full and reduced models. The first residual sum of squares RSS1 = Z1' = i(£1)2 and the second residual sum of squares RSS2 = Z1UU'i)2, respectively associated with the full and second models, are calculated by the processing unit (64), and the corresponding F-value of an F-test is further calculated by the processing unit (64) as F = K (RSS2-RSS1) / RSS1, with K = (n-p1) / (p1-p2). The processing unit (64) calculates a compressed F' value as F' = 5 Log (F) and stores this value in the memory unit (65).The processing unit (64) finally delivers a decision (preferably displayed on a screen) based on the stored value F' and the stored values ​​of the parameters HTV and LTV, after comparing the value of F' with HTV and LTV (as explained above). If the mark is deemed inauthentic (corresponding to a negative decision Dj), the banknote is retained as counterfeit. If F > LTV, the banknote is considered suspect and retained for further (forensic) analysis. The subject matter disclosed above is to be considered for illustrative and non-restrictive purposes, and serves to provide a better understanding of the invention defined in the independent claims.

Claims

1. A method for authenticating a mark applied on a substrate and having a composition comprising a first material including a SERS chemical marker or a SERRS chemical marker, characterized by comprising the following steps carried out by means of a system comprising a light source, a Raman spectrometer, an imaging unit, and a control unit having a processing unit and a memory, the light source being controlled by the control unit through a current loop to deliver calibrated excitation light: storing in memory a complete model of a Raman spectrum of an authentic mark applied on an authentic substrate and having a composition comprising a first authentic material including a genuine SERS chemical marker, or a genuine SERRS chemical marker, as a first weighted sum of a reference Raman spectrum of the authentic chemical marker,a reference Raman spectrum of an authentic reference substrate, which is not marked with the authentic chemical marker, and a reference Raman spectrum of a first authentic reference material that does not include the authentic chemical marker, collected after the respective illumination of the authentic chemical marker, the authentic reference substrate, and the first authentic reference material with excitation light; storing in memory a reduced model of a Raman spectrum of a reduced mark, the reduced mark differing from the authentic mark only in its composition, which does not include the authentic chemical marker, as a second weighted sum of the reference Raman spectrum of the authentic reference substrate and the reference Raman spectrum of the first authentic reference material; after illumination of the mark with excitation light,Measure a corresponding Raman light signal scattered by the mark using a Raman spectrometer to obtain a measured Raman spectrum of the mark; using the processing unit: fit the measured Raman spectrum to the full Raman spectrum model by calculating weight values ​​in the full model that minimize, under the non-negativity constraint of said weights, a difference between the full model and the measured Raman spectrum, and obtain a corresponding first residual; fit the measured Raman spectrum to the reduced Raman spectrum model by calculating weight values ​​in the reduced model that minimize, under the non-negativity constraint of said weights, a difference between the reduced model and the measured Raman spectrum,and obtain a corresponding second residue; calculate an F-value corresponding to an F-test comparing the full model and the reduced model for the Raman spectrum measured from the first and second residues obtained; and decide whether the chemical marker is present or not in the label based on the calculated F-value.

2. The method according to claim 1, further characterized in that, during the measurement operation of the light signal dispersed by the mark, the mark is moved with respect to the spectrometer.

3. The method according to any one of claims 1 and 2, further characterized in that the composition of the mark includes a second material and the respective weighted sums of the full model and the reduced model also include a reference spectrum of a corresponding second authentic material, collected after illumination of said second authentic material with the excitation light, with the corresponding weight.

4. The method according to any one of claims 1 to 3, further characterized in that the ñaman spectrometer has a plurality of spectral channels and the operation of measuring the ñaman light signal scattered by the mark comprises: scattering the collected ñaman light into the plurality of spectral channels and acquiring a two-dimensional digital image of the scattered spectral data with an imaging unit; preprocessing the acquired two-dimensional digital image by performing, using the processing unit, the operations of: transforming the two-dimensional spectral data into one-dimensional spectral data by grouping lines and converting the grouped data into wavelength data; resampling the one-dimensional spectral data to obtain a one-dimensional spectrum with data points equally distant in wavelength;calibrate the one-dimensional spectrum with respect to a reference white light spectrum stored in memory to obtain a calibrated spectrum; filter the calibrated spectrum with a low-pass filter to obtain a filtered spectrum; and align the filtered spectrum in wavelength with the reference spectrum of the chemical marker stored in memory, thereby obtaining a preprocessed spectrum; and perform the calculation operations of the first residue and the second residue using the preprocessed spectrum as the measured spectrum.

5. The method according to claim 4, further characterized in that it comprises: defining a spectrum measurement vector as a vector corresponding to the obtained preprocessed spectrum; defining a first spectrum vector as a product of a first weight vector and a complete design matrix; and determining the respective non-negative components of the first weight vector that minimize, by means of a least squares method, a first residual vector corresponding to a difference between said first spectrum vector and the spectrum measurement vector, the complete design matrix having columns respectively representing the reference spectral data of the complete model;define a second spectrum vector as a product of a second weight vector and a reduced design matrix and determine the respective non-negative components of the second weight vector that minimizes, by a least squares method, a second residual vector ivi A / a / zu¿ o / uuu ru i corresponding to a difference between said second spectrum vector and the measurement vector of the spectrum, the reduced design matrix having columns that respectively represent the reference spectral data of the reduced model; calculate a first residual sum of squares RSS1 of errors corresponding to the first weight vector, the first weight vector having a number p1 of non-negative components; calculate a second residual sum of squares RSS2 of errors corresponding to the second weight vector, the second weight vector having a number p2 of non-negative components;and calculate the F value as a ratio of a difference between the second residual sum of squares RSS2 and the first residual sum of squares RSS1 divided by a difference between the numbers p2 and p1, and the first residual sum of squares RSS1 divided by a difference between a number N of components of the spectrum measurement vector and the number p1, F = ((RSS2-RSS1) / (p1p2)) / (RSS1 / (N-p1)).; 6. The method according to claim 5, further characterized in that the determination of the respective non-negative components of the first weight vector and the second weight vector comprises representing the first weight vector that minimizes the first residual vector as a product of a pseudo-inverse matrix of the full design matrix and the spectrum measurement vector, and representing the second weight vector that minimizes the second residual vector as a product of a pseudo-inverse matrix of the reduced design matrix and the spectrum measurement vector; and in the event that a component, respectively, of the first weight vector or the second weight vector has a negative value: modifying, respectively, the full design matrix or the reduced design matrix by removing from said matrix a spectral vector corresponding to said negative component; setting said negative component to zero;and recalculate, respectively, a pseudo-inverse matrix of the modified full design matrix or the modified reduced design matrix, until the components obtained from the first weight vector and the second weight vector have only non-negative values.

7. A system for authenticating a mark applied on a substrate and having a composition comprising a first material including a SERS chemical marker, or a SERRS chemical marker, the system comprising a light source, a Raman spectrometer, an imaging unit and a control unit having a processing unit and a memory, the light source being controlled by the control unit through a current loop to deliver a calibrated excitation light, the system being configured to perform the operations of: illuminating the mark with the excitation light delivered by the light source controlled by the control unit;and collect a Raman light resulting from the mark and disperse the collected Raman light in the Raman spectrometer having a plurality of spectral channels and acquire a two-dimensional digital image of the corresponding spectral data with the imaging unit, and store in memory the acquired spectral data as a measured Raman spectrum of the mark;the system being characterized in that: the memory stores a complete model of a Raman spectrum of an authentic mark applied on an authentic substrate and having a composition comprising a first authentic material including an authentic SERS chemical marker, or an authentic SERRS chemical marker, as a first weighted sum of a reference Raman spectrum of the authentic chemical marker, a reference Raman spectrum of an authentic reference substrate that is not marked with the authentic chemical marker, and a reference Raman spectrum of an authentic first reference material that does not include the authentic chemical marker collected after the respective illumination of the authentic chemical marker, the authentic reference substrate and the authentic first reference material with excitation light;the memory stores a reduced model of a Raman spectrum of a reduced mark, the reduced mark differing from the authentic mark only in its composition, which does not include the authentic chemical marker, as a second weighted sum of the reference Raman spectrum of the authentic reference substrate and the reference Raman spectrum of the first authentic reference material; and the system being further configured to perform, through the processing unit, the operations of: fitting the measured Raman spectrum stored in memory with the full stored model of the Raman spectrum by calculating values ​​of the weights in the full model that minimize, under the non-negativity constraint of said weights, a difference between the full model and the measured Raman spectrum and obtaining and storing in memory, a corresponding first residue;adjust the measured Raman spectrum stored in memory with the stored reduced model of the Raman spectrum by calculating weight values ​​in the reduced model that minimize, under the non-negativity constraint of said weights, a difference between the reduced model and the measured Raman spectrum and obtain and store in memory, a corresponding second residue; calculate and store in memory, an F value corresponding to an F test comparing the full model and the reduced model for the measured Raman spectrum of the first and second stored residues; and decide whether the chemical marker is present or not in the mark based on the stored F value, and deliver a signal indicating the result of the decision.

8. The system according to claim 7, further characterized in that, during the measurement operation of the Raman light signal scattered by the mark, the mark moves with respect to the Raman spectrometer, and the control unit synchronizes the illumination of the mark with the light source and the acquisition of the Raman spectrum measured through the Raman spectrometer and the imaging unit with the movement of the mark.

9. The system in conformity with any one of claims 7 and 8, further characterized in that the composition of the mark includes a second material, the respective weighted sums of the full model and the reduced model also include a reference spectrum of a corresponding second authentic material, collected after illumination of said second authentic material with the excitation light and stored in memory, with the corresponding weight.

10. The system according to any one of claims 7 to 9, further characterized in that the processing unit is configured to perform the preprocessing operations of the stored two-dimensional digital image by transforming the two-dimensional spectral data into one-dimensional spectral data by line grouping and converting the grouped data into wavelength data; resampling the one-dimensional spectral data to obtain a one-dimensional spectrum with data points equally distant in wavelength; calibrating the one-dimensional spectrum against a reference white light spectrum stored in memory to obtain a calibrated spectrum; and filtering the calibrated spectrum with a low-pass filter to obtain a filtered spectrum.Align the filtered spectrum in wavelength with the reference spectrum of the chemical marker stored in memory, thereby obtaining and storing a preprocessed spectrum in memory; and perform the calculation operations of the first and second residues using the preprocessed spectrum stored in memory as the measured Raman spectrum.

11. The system according to claim 10, further characterized in that the processing unit is configured to: define a spectrum measurement vector as a vector corresponding to the obtained preprocessed spectrum; define a first spectrum vector as a product of a first weight vector and a complete design matrix and determine the respective non-negative components of the first weight vector that minimizes, by a least squares method, a first residual vector corresponding to a difference between said first spectrum vector and the spectrum measurement vector, the complete design matrix having columns that respectively represent the reference spectral data of the complete model;define a second spectrum vector as a product of a second weight vector and a reduced design matrix and determine the respective non-negative components of the second weight vector that minimizes, by a least squares method, a second residual vector corresponding to a difference between said second spectrum vector and the measurement vector of the spectrum, the reduced design matrix having columns that respectively represent the reference spectral data of the reduced model; calculate a first residual sum of squares RSS1 of errors corresponding to the first weight vector, the first weight vector having a number p1 of non-negative components, and storing in memory the first calculated residual sum of squares RSS1 and the number p1;calculate a second RSS2 residual sum of squares of errors corresponding to the second weight vector, the second weight vector having a number p2 of non-negative components, and store in memory the second calculated RSS2 residual sum of squares and the number p2; and calculate the value F as a ratio of a difference between the second stored RSS2 residual sum of squares and the first stored RSS1 residual sum of squares divided by a difference between the stored numbers p2 and p1, and the first stored RSS1 residual sum of squares divided by a difference between a number N of components of the spectrum measurement vector and the number p1, F = ((RSS2-RSS1) / (p1-p2)) / (RSS1 / (N-p1)).; 12. The system according to claim 11, further characterized in that the processing unit is configured to determine the respective non-negative components of the first weight vector and the second weight vector by representing the first weight vector that minimizes the first residual vector as a product of a pseudo-inverse matrix of the full design matrix and the spectrum measurement vector; representing the second weight vector that minimizes the second residual vector as a product of a pseudo-inverse matrix of the reduced design matrix and the spectrum measurement vector; and in the event that a component, respectively, of the first weight vector or the second weight vector has a negative value: modifying, respectively, the full design matrix or the reduced design matrix by removing from said matrix a spectral vector corresponding to said negative component; setting said negative component to zero;and recalculate, respectively, a pseudo-inverse matrix of the modified full design matrix or the modified reduced design matrix, until the components obtained from the first weight vector and the second weight vector have only non-negative values ​​and store the obtained components in memory.

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