Analytical Expression for Spherically Symmetric Photoacoustic Sources: A Unified General Solution (Theoretical Analysis and Derivation)

TL;DR

This paper derives a comprehensive analytical solution for the acoustic pressure generated by spherically symmetric photoacoustic sources, aiding in imaging system design and signal analysis.

Contribution

It provides a unified analytical expression for various spherically symmetric initial pressure distributions in photoacoustics, including implementation code.

Findings

Unified analytical expressions for multiple distributions

Applicable to arbitrary spherically symmetric sources

Provides tools for system design and signal analysis

Abstract

Here we present a comprehensive derivation of the analytical expression for the spatiotemporal acoustic pressure generated by photoacoustic sources with spherically symmetric initial pressure distributions. Starting from the fundamental photoacoustic wave equation, we derive a unified analytical solution applicable to arbitrary spherically symmetric initial distributions. Specific expressions are provided for several common distributions including uniform spherical sources, Gaussian distributions, exponential distributions, and power-law distributions. Far-field approximations are also discussed. The derived expressions provide valuable tools for photoacoustic imaging system design and signal analysis. We provide codes for ultrafast forward simulation using the general analytical spherically symmetric model, the implementation is available in the GitHub repository: \href{https://github.com/JaegerCQ/SlingBAG_Ultra}.