## 2 FTIR Microspectroscopy  
FTIR spectroscopy is based on the spectral analysis of the IR radiation absorbed by a sample. The energy of radiation absorbed is equal to the energy to be provided for inducing a transition between two vibrational states of a specific functional group present in the sample. This means that the contributions from different biochemical bonds present in a sample originate the IR absorption spectrum, which comprises several peaks or bands, each referred to a particular mode of vibration characteristic of functional groups in the sample [1; 2]. FTIR is an advanced and powerful optical technique for obtaining absorption spectra in the infrared region from various kinds of samples and thus getting qualitative information on the structure of the analyzed substances. Quantitative data about the compounds can be obtained, too, also thanks to the use of modern computational algorithms. In FTIR spectroscopy, high-resolution spectra are collected simultaneously over a wide spectral range. This confers a significant advantage over traditional IR absorption spectroscopy, which enables the detection of spectral data over a narrow range of energies at a time. On the contrary, using FTIR spectroscopy, all the frequencies are simultaneously analyzed and registered by the detector. FTIR spectroscopy offers other practical advantages compared to traditional IR, such as a lower energy dispersion, high precision, and accuracy, in the discrimination of wavelengths with the possibility to superimpose the monochromatic radiation of a laser source as an internal standard and the possibility to obtain spectra from a very wide range of samples at any temperature (the source is sufficiently far from the sample and, therefore, there is no heating effect) and pressure with appropriate devices and accessories. The main component of an FTIR system is [PERSON]'s interferometer (Figure 1), which replaces the monochromator usually employed in traditional IR spectrometers. Thanks to the use of the interferometer, each wavelength of the light beam is periodically blocked and transmitted due to the fact of wave interference. The interferometer consists of three mirrors: A fixed mirror and a moving one forming an angle of 90\({}^{\circ}\) with the first mirror. The third mirror (called a \"beam splitter\" mirror) is placed at an angle of 45\({}^{\circ}\) with respect to the incident light. The beam coming from the source arrives on this splitter, which collimates and divides it into two perpendicular rays of equal intensity (see Figure 1). One of these two rays is reflected along a path directed to the fixed mirror, and the other goes through the splitter and is then transmitted to the moving mirror. The first ray is reflected by the fixed mirror and arrives again on the splitter. From the splitter, the light is partially sent back to the source and partially transmitted and focused on the detector. The third mirror moved forward parallel to itself along the other branch of the interferometer path and reflects the other ray on the splitter from different distances. This ray is then partially returned to the source and partly reflected towards the detector, where an intensity given by the algebraic sum of the intensities of the two rays is detected and represented as an interferogram. These data are treated by the instrument through the Fourier transform algorithm to obtain the traditional absorption spectrum. The sample to be investigated is placed between the two arms of the interferometer. The FTIR spectroscopy apparatus can be equipped with a microscope to allow the microscopic analysis of samples or parts of samples up to one micron in size. In Figure 2 of Reference [26], typical SR-\(\mu\)FTIR spectra of cells exposed to proton beams are reported. It was obtained for living prostate cancer PC-3 cells. The spectral features are reported in dependence of the wavenumber (defined as the number of wavelengths per unit distance) expressed in cm\({}^{-1}\).