An improved axial approximation model for wide-angle sound field calculation of the underwater acoustic parametric array

As the difference-frequency of an underwater acoustic parametric array decreases, the beamwidth gradually increases. Although existing axial approximation models can simplify the calculation of the sound field of the parametric array, they are restricted by the axial approximation equation of geometric distance and cannot ensure the accuracy of wide-angle calculations in the entire frequency band. This paper proposes an improved axial approximation model to calculate the wide-angle sound field of the underwater acoustic parametric array. The model is based on the non-paraxial approximation of the Rayleigh integral and the virtual source integration. Furthermore, the Gaussian beam expansion method is applied to reduce the integration dimension. The accuracy of the wide-angle sound field calculation of the parametric array is analyzed by discussing the approximate assumptions and the calculation errors of each axis approximation model. The analysis results show that the accuracy of the wide-angle calculation of the existing axial approximation models is significantly dependent on the high-frequency directivity and the difference-frequency. A suitable model should be selected for calculating the wide-angle sound field depending on the application frequency band. The improved axial approximation model ensures accurate wide-angle calculations in any application frequency band. However, this model requires a large amount of computation and can therefore be used as a general calculation model for the wide-angle sound field of an underwater acoustic parametric array. Experimental data validate the effectiveness of the improved model and the accuracy of the wide-angle calculation analysis.