**1. Introduction**

Hyperspectral imaging (HSI) is a powerful technique of analysis where each pixel of the image is associated with the spectral content of the radiation coming from the scene in the spectral band of interest. Different solutions with different spectral resolutions have been

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

adopted to separate the spectral content of the radiation impinging on the pixel: starting from the three bands of the Bayer filter camera [1], to the tens of bands with fixed bandpass filters like in the OSIRIS camera on Rosetta spacecraft [2] or hundreds or even thousands of bands of imagers based on dispersive means with gratings or prism like on the VIRTIS camera on Rosetta spacecraft [3]. In this work, we are interested in hyperspectral imagers based on inter‐ ferometers: an interferometer is placed in the optical system in front of the camera, and while the optical path delay (OPD) of the interferometer is varied, the interferogram for each pixel is acquired by the camera and the spectrum is calculated with an algorithm based on the Fourier transform. The final attainable resolution in principle is only limited by the maximal optical path delay of the interferometer. HSI based on Michelson interferometers have been implemented with success in commercial instruments by Bruker [4] and Telops [5] ensuring more than 500 bands in the infrared region and reaching a resolution of less than 1 cm−1. At INRIM, we have realized a different concept of HSI based on Fabry‐Perot interferometer (FPI) and we have validated it in different regions of the spectrum: in the UV [6], in the visible [7] and in the near infrared [8] and in different applications [9].

In paragraph 2 of this chapter, we will describe the principle of the reflectance spectra calcu‐ lation based on the Fourier transform. In paragraph 3, we will show the application of this technique to the field of cultural heritage in collaboration with Centre for Conservation and Restoration *La Venaria Reale* (CCR). Reflectance spectra indeed contain information useful for identifying pigments and dyes and thus for discriminating original and possibly superim‐ posed materials (e.g. pictorial retouching) that is one of the main aims of a diagnostic campaign intended at preserving artworks and guiding the conservation treatment. Moreover, reflec‐ tance spectra can be used for rendering the artworks' colour appearance under different lights in order to choose the light source most suitable for enhancing some aesthetical aspects of the objects, for increasing the visitors' satisfaction, in the meantime taking into account the preven‐ tive conservation principles and the standard recommendations for lighting in museums. On the other hand, the possibility of studying the pigments' colour appearance can be of some help when choosing materials for the conservation treatment. Finally, spectra can be converted in colorimetric values for different light sources or standard illuminants useful for calculating chromatic differences for specific purposes. Results here presented concern some real artworks of different art periods (e.g. coffins from Ancient Egypt, Italian Renaissance polychrome art‐ works) and some mockups used as references made with known pigments and binders.
