Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors

Line detectors integrate the measured acoustic pressure over a straight line and can be realized by a thin line of a piezoelectric film or by a laser beam as part of an interferometer. Photoacoustic imaging with integrating line detectors is performed by rotating a sample or the detectors around an axis perpendicular to the line detectors. The subsequent reconstruction is a two-step procedure: first, two-dimensional (2D) projections parallel to the line detector are reconstructed, then the three-dimensional (3D) initial pressure distribution is obtained by applying the 2D inverse Radon transform. The first step involves an inverse problem for the 2D wave equation. Wave propagation in two dimensions is significantly different from 3D wave propagation and reconstruction algorithms from 3D photoacoustic imaging cannot be used directly. By integrating recently established 3D formulae in the direction parallel to the line detector we obtain novel back-projection formulae in two dimensions. Numerical simulations demonstrate the capability of the derived reconstruction algorithms, also for noisy measurement data, limited angle problems and 3D reconstruction with integrating line detectors.