A method for calculating holograms for volumetric objects based on the representation of objects in the form of ensembles of virtual point sources distributed on a set of parallel planes has been proposed. The proposed method is the development of the well-known method in which objects are represented as ensemble of real point scatterers. The possibilities of the proposed method are demonstrated by calculating a hologram of a fragment of a sphere, on which 1000 points are randomly selected, at which radiation emanating from the center of the sphere is scattered. The choice of a fragment of a sphere as an object under study is due to the fact that when calculating its hologram, phase errors inherent in approximate calculations are most pronounced. The calculations were performed for the frequency range of 2...100 GHz, the sphere radius of 0.5 m, a two-dimensional hologram size of 0.65×0.65 m, and a pixel count of 512×512. It is shown that, in comparison with the known method, the proposed method makes it possible to calculate the amplitude of a hologram with satisfactory accuracy if virtual sources are placed on parallel planes in an amount of more than 64 pieces. In the case of objects that require representation in the form of an ensemble of point scatterers in the amount of more than 1000 pieces, the calculation of their holograms by the proposed method turns out to be much more efficient than the known method.
Recognizing volumetric objects in the presence of uncertainty
