The HSI device we used is based on a Fabry-Perot (F-P) interferometer and it measures the spectral content of each pixel of the image at the same time. This is obtained by acquiring the sequence of interference images while the optical path between the F-P mirrors is scanned by means of piezo actuators. The spectral information is finally stored in a dataset called ‘hyperspectral cube’: a 3D matrix formed by a 2D image and along the third dimension the spectral composition of each pixel is recorded. The technique does not need any mechanical scanning system, it is implemented in a compact set-up and it requires shorter exposure times when compared to classical methods, that could reach fractions of the second for scenes with high luminosity and with low resolution spectra [17].
This F-P interferometer could be inserted in an existing optical set-up, like a telescope or a microscope, allowing therefore the generation of a hyperspectral image of any scene of interest that could be acquired by an imaging system. From the recorded video, acquired during the mirror scanning, it is possible to extract an interferogram for each pixel and from this the spectrum, using an algorithm based on the Fourier transform. The CCD pixel dimensions limit the final spatial resolution. The final spectral resolution is related to the maximal distance between the mirrors L. In frequency, the spectral resolution 'Qis
where c is the speed of light.
In our prototype the spectral resolution could reach 5 THz for a scanning length of 30 μm and the spatial resolution is about 100 μm corresponding to about 250 ppi. The use of apodization functions applied to the acquired interferogram gives a compromise between the spectral resolution and the smoothing of artefacts present in the spectra, like sidelobes [18]. The calculated spectra have to be corrected for the spectral responsivity of the CCD, for the transmittance of the optical components and the most accurate way to obtain an accurate spectrum is to add a reference white to the scene. In this application, the system can measure spectra in two bands, from 400 nm to 720 nm, and from 600 nm to 1000 nm. The spectra can then be composed in a single band from 400 nm to 1000 nm.
The hyperspectral investigation concerned three different details of the painting and we acquired videos including a white reference (Spectralon © 99%) within the scene: detail 1 is the main central scene, displaying Mosè dividing the waters of the Red Sea (figure 2), details 2 and 3 are two lateral scenes crowded of people, one portrayed in the background (figure 3) and so characterized by very small brushes, and one in the foreground (figure 4). The dimensions of the acquired areas are about 10 cm x 10 cm, corresponding to an image size of about 1000 pixels x 1000 pixels, due to the aperture of our F-P interferometer (for acquiring scenes with different spatial resolution we could adapt the optical system). The choice of different scenes stayed on the aim of working with areas of paint or with brushes of different sizes, therefore trying to analyse also very small paintbrushes.
All videos took 180 seconds, with a 10 THz resolution: the painting was 120 cm distant from the camera and one halogen lamp lighted the scene at 45° angle on the right to the painting, in order to reproduce one of the illuminating/viewing geometry (45°x/0°) recommended by CIE [19] and the same geometry and illumination used for FORS analyses.
Fig. 2 – Area of the painting (DETAIL n.1) of 10 cm x 10 cm acquired by the hyperspectral imager; numbers on picture refer to the FORS analyses’ measurement points.
Fig. 3– Area of the painting (DETAIL n.2) of 10 cm x 10 cm acquired by the hyperspectral imager; numbers on picture refer to the FORS analyses’ measurement points.
Fig. 4– Area of the painting (DETAIL n.3) of 10 cm x 10 cm acquired by by the hyperspectral imager; numbers on picture refer to the FORS analyses’ measurement points.
Once we collected the three videos, we used hyperspectral data to extract reflectance spectra in correspondence of many figures and various interesting regions,
attempting to select as most as possible homogenous coloured areas. Here we report just some significant points of the artwork that is blue, green, yellow, orange, red and purple areas of paint or paintbrushes (see table 1): areas (called p1, p2, etc.) are from 20 to 279 pixel. The minimum area corresponds to a paintbrush that is about 0.4 mm wide and 0.5 mm high, as discussed above. The operator can choose the area from which to extract spectra: pixels are numbered by the software that extracts the interferograms and calculates the spectra.
On the same selected areas (p1, p2, etc.), we performed FORS analyses by using an Ocean Optics HR2000+ES spectrophotometer and an Ocean Optics HL2000 halogen lamp, bounded by optical fibres of 400 μm in diameter. By using also a probe, we worked in a 45°x/0° geometry following the CIE standard illuminating/viewing geometry [19] and measuring area of fixed dimensions (approximately 3 mm in diameter). For the analyses we used the same Spectralon © 99% white reference used for the HSI videos. Collected spectra are along a 350 nm to 1000 nm wavelength range with a 0.5 step resolution.
In order to testing the use of Fabry-Perot hyperspectral device as diagnostic tool, we then compared spectra collected by FORS to the ones extracted and calculated from the HSI videos.
Table 1. Description of the areas of paint selected in the details of figures 2, 3 and 4.