The invention relates to the remote measurement of the dielectric permittivity of dielectrics. A 3D microwave and a 3D optical range images of an interrogated scene are recorded at the same time moment. The images are digitized and overlapped. A space between the microwave and optical image is measured, and a dielectric permittivity of the space between these images is determined. If the dielectric permittivity is about 3, then hidden explosive materials or components of thereof are suspected. The invention makes it possible to remotely determine the dielectric permittivity of a moving, irregularly-shaped dielectric objects.