Dyadic point spread functions for 3D inverse source imaging based on analytical integral solutions

Imaging is a valuable tool for solving inverse source problems. The achievable image quality is determined by the imaging system. Its performance can be evaluated by using the concept of point spread functions (PSFs). It is common to compute the PSFs using a numerical algorithm. However, in some cases the PSFs can be derived analytically. In this work, new analytical PSFs are presented. The results apply to scalar and dyadic scenarios in 3D originating from acoustics and electromagnetics. Data sets with narrow angular acquisition or complete spherical coverage are considered, where broadband and narrowband frequency domain data is supported. Several visualizations accompany the resulting formulas. Finally, the analytical PSFs are verified using a numerical implementation of the imaging process.