Doppler effect in the multiple-wavelength range-gated active imaging up to relativistic speeds.

Having laid down previously the foundations of the combined multiple-wavelength range-gated active imaging (WRAI) principle recording a moving object in a four-dimensional space represented by a single image, it was necessary to know if a Doppler effect could appear in the direction of the radial velocity of the object. This is due to the fact that this imaging principle requires the emission of laser pulses at a certain frequency in relation to this speed. To know the limits, the radial velocity of the object was supposed to go up to relativistic speeds. From a theoretical approach, some temporal behaviors leading to the Doppler effect were shown. To validate this effect experimentally, a setup based on the fictional positions (represented by mirrors) of an object moving at extreme speeds was performed. The results obtained with WRAI confirmed the presence of the Doppler effect, which must be taken into account when the radial velocity of the object is extreme. In this case, some conditions must be met as in the period and the time of the shutter aperture. Singular behaviors have also been shown in the case of relativistic speeds. So despite the Doppler effect, the distance of the fast-moving object and the different moments are well identified according to the different wavelengths in the combined WRAI principle.