Time- and frequency-domain descriptions of spatially averaged one-way diffraction for an unfocused piston transducer
Abstract
Time-domain and frequency-domain expressions describing spatially averaged effects of one-way diffraction in the case of an unfocused piston transmitter and finite receiver are of theoretical and practical interest. Here, a time-domain description based on the arccos diffraction formulation and a frequency-domain description based on the Lommel diffraction formulation are derived. Numerical results obtained from the two descriptions are then compared. It is shown that the two descriptions show satisfactory agreement for finite receivers of practical interest. Two mathematical lemmas are also provided.