## 2 Materials and Methods
### Rgb-Itr  
The RGB-ITR (Red Green Blue Imaging Topological Radar) scanner (Figure 3 left) is a prototype developed at the Diagnostic and Metrology Laboratory of the ENEA Research Centre in Frascati (Rome, Italy). The system uses three laser sources with wavelengths in the visible range corresponding to red, green, and blue (660 nm, 517 nm, and 440 nm, respectively). It is able to digitise in 3D and in RGB colour works of art even of large dimensions. It works remotely, up to 35 m distance from the target, with sub-millimetric spatial resolution and with a maximum image resolution of the order of Giga Pixels. The system enables the simultaneous recording of range and colour information by the phase shift between the back-reflected signal and the reference modulating wave, and the elaboration of back-reflected RGB triplets from the scanned object, respectively. More detailed information can be found in [27].  
The ITR system is based on a double amplitude modulation (AM) range-finding technique, where the laser beam is exploited as the carrier wave of a radiofrequency signal, which modulates the beam intensity [28; 29]. Structural digitalisation of the surfaces is elaborated from the distance measurements, determined indirectly from the phase delay of the collected back-reflected signal with respect to the reference modulating wave. The colour information is estimated by normalising the back-reflected signals with the intensities, acquired directly on-site, obtained by illuminating a calibrated white target at  
Figure 3: RGB-ITR system (**on the left**) and LIF scanning system (**on the right**) during the measurement campaign in House of Diana.  
Figure 2: Plan of the House of Diana during the different building phases, from the earliest phase, first half of the 2 nd century AD (**top**), to the intermediate phase, last quarter of the 2 nd century AD (**center**), to the latest phase, 2 nd half of the 3 rd century AD (**bottom**) (Studio 3R, PA-OANT Photo Archive inv. 11,560–11,562).  
several distances: this procedure creates a lookup table used for extracting the corrected intensity normalisation value and balancing the scene signals collected at the different distances, as expressed by the equation:  
\[I_{norm,i,j}(wl,\ d_{i,j})=\frac{I_{scene,i,j}(wl,d_{i,j})}{I_{white,i,j}(wl,d_{ i,j})}\]  
where:  
\(I_{norm},\ I_{scene},\ I_{white}\) are respectively the normalised, collected-on-the-scene, and the white-calibrated intensity values,  
\(wl\) is the corresponding wavelength (660, 517, or 440 nm),  
\(d_{i,j}\) the distances at each single pixel expressed by the coordinates (\(i\),\(j\)).  
A further colour correction is performed considering the back reflected intensity dispersion determined by the incident angle of the laser beam over the surface. This compensation is regulated by the equation:  
\[I_{angle,i,j}(\theta_{i,j})=\frac{I_{norm,i,j}}{\cos\left(\theta_{i,j}\right)}\]  
where:  
\(I_{angle}\ I_{norm}\) are respectively the angle-corrected and normalised (as described above) intensity values,  
\(\cos\theta_{i,j}\) is obtained by the scalar product between the laser incident and surface normal vectors.  
The final resulting colours are not complete in terms of spectral components due to the use of only three wavelengths. However, they are metrically correct, and the lock-in technique can reveal small intensity signals even in a light-noisy environment. This results in a final coloured texture of the investigated scene that is white-balanced at each distance and free of shadows, even at large distances (up to 35 m). Developed to operate in hostile environments, such as in the presence of ionising radiation, it has also been successfully used in other fields, such as the Cultural Heritage domain, helping to evaluate both the state of conservation from a structural point of view and colour alterations.