  Most reconstruction algorithms for photoacoustic imaging assume that the
pressure field is measured by ultrasound sensors placed on a detection surface.
However, such sensors do not measure pressure exactly due to their non-uniform
directional and frequency responses, and resolution limitations. This is the
case for piezoelectric sensors that are commonly employed for photoacoustic
imaging. In this paper, using the method of matched asymptotic expansions and
the basic constitutive relations for piezoelectricity, we propose a simple
mathematical model for piezoelectric transducers. The approach simultaneously
models how the pressure waves induce the piezoelectric measurements and how the
presence of the sensors affects the pressure waves. Using this model, we
analyze whether the data gathered by piezoelectric sensors leads to the
mathematical solvability of the photoacoustic imaging problem. We conclude that
this imaging problem is well-posed in certain normed spaces and under a
geometric assumption. We also propose an iterative reconstruction algorithm
that incorporates the model for piezoelectric measurements. A numerical
implementation of the reconstruction algorithm is presented.
