Analysis of Negatively Focused Ultrasound Detectors in Optoacoustic Tomography

In optoacoustic tomography, negatively focused transducers may be used for improving the tangential image resolution while preserving a high signal-to-noise ratio. Commonly, image reconstruction in such scenarios is facilitated by the use of the virtual-detector approach. Although the validity of this approach has been experimentally verified, it is based on an approximation whose effect on optoacoustic image reconstruction has not yet been studied. In this paper, we analyze the response of negatively focused acoustic detectors in 2D in both time and frequency domains. Based on this analysis, tradeoffs between the detector size, curvature, and sensitivity are formulated. In addition, our analysis reveals the geometrical underpinning of the virtual-detector approximation and quantifies its deviation from the exact solution. The error involved in the virtual-detector approximation is studied in image reconstruction simulations and its effect on image quality is shown. The theoretical tools developed in this work may be used in the design of new optoacoustic detection geometries as well as for improved image reconstruction.