Consider an extended irregularly shaped region of energy deposition. A broad pulsed laser beam (H = 10 [J/cm2]) illuminates a nonscattering strongly medium with moderate background absorption (μa = 5 [cm-1], a 2-mm penetration depth) and a 1-mm-diameter sphere with three-fold stronger absorption (μa = 15 [cm-1]). Integrating the contributions of W/(|r' - rdetector|) to the velocity potential observed at rdetector yields the velocity potential at time t. The velocity potential is calculated as a function of time. Then the negative time derivative of the velocity potential normalized by the density yields the time-resolved pressure.
Map of energy deposition, W. The object is heated on its front surface by irradiation from below and casts a shadow behind itself. Detector is behind the object in its shadow. The background medium is also absorbing.
Velocity potential versus time observed at the detector.
(BOTTOM) Pressure versus time observed at the detector. Positive (compressive) and negative (tensile) components of stress are apparent. Tensile components arise from the edge of the object.
Both with and without the object, the drop in pressure at about 1.2 us is due to the arrival of the tensile release wave from the front surface of the medium (optical discontinuity, mechanically matched, i.e., water).
black = no object, background only
red = with object plus background
The noise of these simulations can be improved by convolving the impulse response against a finite pulse duration.
Clearly, signals are complex. A reliable forward calculation to predict φ signals from a given W distribution is the first step toward implementing optoacoustic image reconstruction.