Piezoelectric Sensors' Electric Response When Used as Detectors for Short Time Photo Acoustic Pulses with Heat Transport Included

Abstract

In this work we report a description of the heat transport that is generated alongside the photoacoustic pressure pulses generation. This issue is significant because of the applications of this physics' field to biomedical applications in specific to photoacoustic signal detection, photoacoustic tomography, photothermal processes, when these signals are registered either by transducer methods or either by optical holography or interferometric methods. The paper should be of interest to readers in the areas of photoacoustic imaging, optical coherence tomography, laser induced ultrasound in condense media and laser-pulse induced photoacoustic and photothermal phenomena. The significance of the work is to provide a model based on first principles such as the energy conservation principle, and the concept of the Free Helmholtz energy, that is capable of describing the thermal process involved in the photo acoustic phenomenon. We are solving the problem of generating an acoustic pulse induced by the incidence of a light pulse of time duration of order of nano seconds upon a flat slab modeled as an elastic material. In our model we are including the thermal response, and comparing the equations resulting from the heat transport approach, with those of the trending photoacoustic applications, showing clearly the kind of approximations involved in the trending models. In this work we make an important application of the Landau's formalism to deal with the thermoelastic expansion, in order to provide a better modeling of the thermal response of the photoacoustic pulse generation at time scale of nanoseconds, here we show that the inclusion heat transport considerations, implies the existence of a slow pressure pulse not present in the trending models of the photoacustic phenomena. The people who will be interested in this research will be those working in the area of photoacustic tomography, they will receive the benefit of a better data acquisition interpretation, and gaining a better understanding of physics concepts involved. Once the model that describes the generation of photoacoustic pulses has been established, then we introduce a model for a piezoelectric material in order to detect pressure signals converted to voltage signals. Then we investigate theoretically and experimentally the performance of these low-noise capacitive sensors based on Polyvinylidene Fluoride piezoelectric films to sense ultrasound signals for their use in photoacoustic detection. Then we model a generic piezoelectric detector consisting of an acoustic layered medium containing a piezoelectric material coupled to two metallic electrodes that convert the acoustic signal into a voltage signal. Then we calculate the transfer voltage function for a piezoelectric capacitor, which multiplied by the Fourier transform of the acoustic incident pulse yields the voltage electric response. We invert the voltage Fourier transform of the pulse to recover the actual pressure signal. We take special attention to the thermal aspects of the problem. Also numerical examples are provide and finally we compare the pulses modeled with our own experimental results.