Spatial resolution and sensitivity in photoacoustic tomography taking noise into account: from point-like detectors to large integrating detectors

As for any other imaging technique spatial resolution and sensitivity are important features for a photoacoustic imaging device. It is already well known that spatial resolution depends on the size and the bandwidth of the detectors. Therefore for photoacoustic image reconstruction usually small point-like and broadband detectors are assumed, which measure the pressure as a function of time on a detection surface around the sample. But in reality point-like detectors are not ideal at all: because of the small detector volume the thermodynamic fluctuations (= noise) get high and the signal amplitude is low, which results in a bad signal-to-noise ratio (SNR). For a bigger detector volume the fluctuations are less and the signal amplitude is better, which gives a better SNR. But on the other hand the photoacoustic pressure signal is averaged over the whole detector volume, which results in blurring and a reduced spatial resolution if reconstruction algorithms for point-like detectors are used. To characterize this trade-off between spatial resolution and sensitivity for a varying detector volume in a quantitative way the pressure is described by a random variable having the measured pressure as a mean value and noise as random fluctuations around that mean value ("stochastic process"). For a PVDF detector the optimum for the detector size is given.