Numerical solution to the time-independent inhomogeneous photoacoustic wave equation using the Born series methods

The traditional Born series (TBS) and convergent Born series (CBS) methods to numerically solve the time-independent inhomogeneous photoacoustic (PA) wave equation are discussed. The performance of these algorithms is examined for a circular PA source (a disk of radius, a=5µm) in two dimensions. The speed of sound within the source region was gradually decreased from v_s=1950 to 1200 m/s, but the same quantity for the ambient medium was fixed to v_f=1500m/s. The PA fields were calculated over a large frequency band from f=7.3 to 2000 MHz. Accordingly, the wave number (k_f=2πf/v_f) varied from k_f=0.03 to 8.38µm^-1. The TBS method does not offer converging solutions when k_fa≥25 for v_s=1950m/s and k_fa≥9 for v_s=1200m/s. These have been observed in both the near and far fields. However, the solutions for the CBS technique converge in all cases. Both methods facilitate accurate solutions if the computational domain contains a collection of monodisperse/polydisperse disks considered in this study. Our numerical results suggest that the CBS protocol can provide accurate solutions under various test conditions.