Lineær og ikke-lineær propagering av akustiske felt. Lineær tilnærming til ikke-lineært felt.

Abstract

In this master thesis we study the linear and nonlinear acoustic field propagation. We also look into the possibility of estimating the non-linearly generated second harmonic by linear propagation of two times the fundamental frequency. The linear acoustic field propagation is calculated by the numerically implemented angular spectrum approach (ASA). The derivation of the ASA is based on the convolution theorem applied to Rayleigh-Sommerfeldts diffraction formula. In many cases the acoustic propagation is nonlinear which leads to a generation of harmonic frequencies in addition to the fundamental frequency. To account for the nonlinear effects in the medium a frequency domain solution of Burgers equation is used. The model also accounts for the attenuation of the waveform as it propagates through the medium. The results of the simulations of linear and nonlinear propagation are compared to relevant results presented in a selection of articles to verify the correctness of the simulator. The non-linearly generated second harmonic frequency is often used in medical ultrasound imaging. Due to the fact that medical ultrasound mainly is used in imaging the human body, the field only has to be propagated over small distances (no larger than 1 meter). Since sonar technology is based on the same principles as medical ultrasound there is reason to believe that second harmonic imaging also could be of great interest in sonar. One of the main differences between sonar technology and medical ultrasound is the fact that the acoustic field is propagated over much larger distances in sonar. Taking into account the large number of harmonics which are often involved in the simulation of nonlinear field propagation and the fact that the field has to be propagated over much larger distances (from several meters to several kilometers), the simulation of nonlinear acoustics can be very time consuming in sonar. In this thesis we look into the possibility of estimating the second harmonic by linear propagation of two times the fundamental frequency.