General equation Given the heating function H(\boldsymbol{r},t), the generation and propagation of photoacoustic wave pressure p(\boldsymbol{r},t) in an acoustically homogeneous inviscid medium is governed by :\nabla^2p(\boldsymbol{r},t)-\frac{1}{v_s^2}\frac{\partial^2}{\partial{t^2}}p(\boldsymbol{r},t)=-\frac{\beta}{C_p}\frac{\partial}{\partial t}H(\boldsymbol{r},t) \qquad \qquad \quad \quad (1), where v_s is the speed of sound in medium, \beta is the thermal expansion coefficient, and C_p is the specific heat capacity at constant pressure. Eq. (1) holds under thermal confinement to ensure that heat conduction is negligible during the laser pulse excitation. The thermal confinement occurs when the laser pulsewidth is much shorter than the thermal relaxation time. The forward solution of Eq. (1) is given by :\left.p(\boldsymbol{r},t)=\frac{\beta}{4 \pi C_p} \int \frac{d \boldsymbol{r}'} \frac{\partial H(\boldsymbol{r}',t')}{\partial t'} \right|_{t'=t-|\boldsymbol{r}-\boldsymbol{r}'|/v_s} \qquad \quad \,\,\,\,(2). In stress confinement, which occurs when the laser pulsewidth is much shorter than the stress relaxation time, This method is suitable for three imaging geometries: planar, spherical, and cylindrical surfaces. The universal back projection formula is {{center|1=\left.p_0(\boldsymbol{r})=\int_{\Omega_0} \frac{d \Omega_0}{\Omega_0} \left [2 p(\boldsymbol{r},v_s t) - 2 v_s t \frac{\partial p(\boldsymbol{r}_{0},v_s t)}{\partial (v_s t)} \right]\right|_{t=|\boldsymbol{r} - \boldsymbol{r}_{0}|/v_s},\qquad \quad(4), }} where \Omega_0 is the solid angle subtended by the entire surface S_0 with respect to the reconstruction point \boldsymbol{r} inside S_0, and {{center|1=d \Omega_0 = \frac{d S_0}. }}
Simple system A simple PAT/TAT/OAT system is shown in the left part of Fig. 3. The laser beam is expanded and diffused to cover the whole region of interest. Photoacoustic waves are generated proportional to the distribution of optical absorption in the target, and are detected by a single scanned ultrasonic transducer. A TAT/OAT system is the same as PAT except that it uses a microwave excitation source instead of a laser. Although single-element transducers have been employed in these two systems, the detection scheme can be extended to use ultrasound arrays as well.
Biomedical applications Intrinsic optical or microwave absorption contrast and diffraction-limited high spatial resolution of ultrasound make PAT and TAT promising imaging modalities for wide biomedical applications:
Brain lesion detection Soft tissues with different optical absorption properties in the brain can be clearly identified by PAT.
Hemodynamics monitoring Since HbO2 and Hb are the dominant absorbing compounds in biological tissues in the visible spectral range, multiple wavelength photoacoustic measurements can be used to reveal the relative concentration of these two
chromophores. Thus, the relative total concentration of hemoglobin (HbT) and the hemoglobin
oxygen saturation (sO2) can be derived. Therefore, cerebral hemodynamic changes associated with brain function can be successfully detected with PAT.
Breast cancer diagnosis By utilizing low scattered microwave for excitation, TAT is capable of penetrating thick (several cm) biological tissues with less than mm spatial resolution. Since cancerous tissue and normal tissue have about the same responses to radio frequency radiation, TAT has limited potential in early breast cancer diagnosis. ==Photoacoustic microscopy==