Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction

An analytic explanation of the spatial resolution in thermoacoustic or photoacoustic reconstruction is presented. Three types of specific recording geometries, including spherical, planar, and cylindrical surface, as well as other general cases, are investigated. Analytic expressions of the point-spread functions (PSF's), as a function of the bandwidth of the measurement system and the finite size of the detector aperture, are derived based on rigorous reconstruction formulas. The analyses clearly reveal that the dependence of the PSF's on the bandwidth of all recording geometries shares the same space-invariant expression while the dependence on the aperture size of the detector differs. The bandwidth affects both axial and lateral resolutions; in contrast, the detector aperture blurs the lateral resolution greatly but the axial resolution only slightly.