Development of analytical solution for Photoacoustic Imaging of an Extended line source with acoustic lens based reconstruction strategy

Photoacoustic imaging has proved itself as a swiftly emerging hybrid imaging technique that can be employed for studying soft tissues. A major challenge in the field of photoacoustic imaging is to reduce the time and computational complexity, associated with image reconstruction while maintaining the quality of the reconstructed PA images. Traditionally, reconstruction has been tackled using several backpropagation approaches. However, these approaches are limited by factors like computational and memory overheads. Further, they often require a large number of PA acquisitions for achieving acceptable accuracy. Acoustic lens-based Photoacoustic imaging system attempts to mitigate these issues by developing a lens-based reconstruction strategy that creates a high-quality image of the Photoacoustic source on the sensor. This strategy eradicates the need for computationally exhaustive post-processing steps and hence can be deployed in real-time environments. Although researchers primarily focused their attention on developing and studying mathematical models for point source systems in photoacoustic lensing, complex source geometries are usually encountered in actual real-life Photoacoustic imaging. Thin cylindrical geometries are an important aspect of employing photoacoustic imaging to study blood vessels. We present an analytical framework for the impulse response of a photoacoustic lensing system and extend the same towards incorporating infinitesimally thick cylindrical sources or extended line sources. We verify our analytical solutions numerically.