## 1 Introduction
Also, Raman spectroscopy enables very small samples (<1 \(\upmu\)m) to be analyzed with a high spatial (\(\leq\)1 \(\upmu\)m) and spectral (<1 cm\({}^{-1}\)) resolution [14]. In turn, low laser radiation power (\(\sim\)4 mW) is sufficient to obtain Raman spectra, bringing the risks of potential laser-induced degradation to a minimum [15]. Nevertheless, there is at least one shortcoming of this method: a fluorescence signal yielded by a sample, which interferes with the recording of high quality spectra. The fluorescence of some organic compounds may arise due to the exposure of the sample to laser irradiation. This phenomenon results in intrinsic wide band radiation that may be significantly more intense than Raman scattering. Fluorescence problems may be avoided if a longer wavelength of radiation is used [15]. However, it is necessary to remember that the intensity of Raman scattering is proportional to the fourth power of the excitation frequency intensity. As a result, excitation by long-wave irradiation yields a Raman signal, which is considerably less intense than one obtained using short-wave excitation [14]. The development of forensic methods requires the implementation of new approaches. The current study proposes a modified methodological approach for data analysis, which in many cases gives an opportunity to conduct experiments in the absence of a large database of an expert entity, increasing its efficiency, reducing labor consumption, and allowing us to focus on the study of the spectral properties of dyes free from the influence of, not only a dye, but also other components of writing inks. For that reason, a detailed investigation into the mutual influence of the volatile and dye components of writing inks was performed. In turn, for convenience and better understanding, in the proposed methodology, we have to appeal to some previously reported results [16]. The methodological distinction of this from similar studies [1; 2; 13; 17; 18] was in considering the fact that the peak intensity in Raman spectrum also depends on the concentration of the studied compound within the focal spot of the laser beam, which was impossible to control in our case. Thus, in order to eliminate the influence of the concentration factor, we used the ratio of intensities instead of absolute intensity values. Furthermore, in [16] we found that the time dependency of Raman peak ratios has a complicated nature: it consists of three fragments of monotonous change in spectral properties and two extrema, making it impossible to use this dependency for the estimation of the age of writing ink without further analysis of its nature [16]. The choice of peaks used in the corresponding dependencies was determined as follows: the first peak corresponds to vibrations of the peripheral bond, which is most susceptible to change over time. The second peak corresponds to vibrations of the most stable bond (e.g., vibrations of carbon in the chromophore). The peak ratios chosen for each type of writing ink are shown in Table 1. The establishment of the dates when writing inks were drawn on paper can be illustrated by the type B inks, for which triarylmethane dyes are used. There are two possible mechanisms of degradation of this type of writing ink. The first mechanism is \(N\)-demethylation, in which the methyl group of a dye is sequentially replaced by hydrogen when exposed to light [19]. In the second mechanism the degradation occurs due to attack of a dye molecule by singlet oxygen [20; 21]. In order to build the aforementioned dependencies, Raman peaks centered at 729 cm\({}^{-1}\) corresponding to C-N vibrations and at 1580 cm\({}^{-1}\) corresponding to complex C-C vibrations have been chosen. These vibrations are differently sensitive to degradation. The obtained curve can be divided into three monotonic intervals (Figure 1). These intervals display dynamics of the dominant processes. The first interval (Period 1) corresponds to the transformation of the dye matrix (volatile components evaporate, resin hardens).