# Wavefront Shaping and Its Application to Enhance Photoacoustic Imaging
## 3 Photoacoustically-Guided Wavefront Shaping (PAWS)
\begin{table}
\begin{tabular}{c c c c} \hline
**Character** & **LCoS-SLM** & **DM** & **DMD** \\ \hline Working principle & Electrically controlled liquid & Piezoelectric arrays and flexible & Tilting of micro-mirror arrays \\  & crystal arrays & reflective surface & \\ \hline Max pixel number & High (1920 \(\times\) 1080) & Low (10–1000) & High (3000 \(\times\) 2000) \\ \hline Refreshing rate & Slow (10–100 Hz) & Fast (1–10 kHz) & Fast (up to 23 kHz) \\ \hline Diffraction efficiency & High (60–90\%) & High (–100\%) & Low (<50\%) \\ \hline Enhancement factor \(\alpha\) & \(\pi/4\) & \(\pi/4\) & 1/(2\%) \\ \hline Major manufacturer & Holoeye Photonics (German) & Boston Micromachines (USA) & Texas Instruments (USA) \\ \hline Cost (in US dollar) & Moderate (–20 k) & Moderate (–20 k) & High (–50–100 k) \\ \hline \end{tabular} \({}^{1}\)LCoS, liquid-crystal-on-silicon; SLM, spatial light modulator; DM, deformable mirror; DMD, digital micromirror device.  
\end{table} 
Table 1: Representative commercial wavefront modulators \({}^{1}\) (modified from [79]). Using PA signals as the virtual internal guide star has many advantages for biomedical applications. They are noninvasive, label-free, and nontoxic. By translating the ultrasound transducer outside the tissue sample, dynamic optical focusing can be achieved within a large field of view. Moreover, ultrasound has orders of magnitude weaker scattering than light does, and it allows deep penetration and precise pinpointing to the targeted position. Therefore, photoacoustically-guided wavefront shaping has rapidly gained attention and been followed by several other research teams [26; 28; 45; 46; 47]. However, since the diffused optical energy is maximized within the ultrasonic focus, the dimension of the resultant optical focal spot is typically ultrasonic-diffraction limited. For example, the full width of half maximum (FWHM) of the focal zone is \(\sim\)50 \(\upmu\)m for a 50 MHz focused transducer. Within this region, many optical modes exist, resulting in a large M (on the order of 104 considering fully developed speckles) and a limited peak intensity enhancement ratio (inversely proportional to M). Another promising feature of using photoacoustic signals as the virtual guide star is the capability to break the acoustic diffraction limitation and generate finer resolutions, if nonlinearity in PA signal generation and detection is exploited. For example, it has been demonstrated that sub-acoustic diffraction-limited optical focusing is possible when the detected PA signals (which are broadband) are spectrally filtered and then used as the feedback [26; 45]. From the perspective of generation nonlinearity, [PERSON] et al. developed a dual-pulse excitation approach (Figure 3a), firing two consecutive, yet identical, optical pulses to generate two individual PA signals--the difference between them create a nonlinear PA response that can be used as a nonlinear feedback [48]. The hypothesis was built upon a so-called Grueneisen effect [49]. Recall that the PA signal is proportional to the Grueneisen parameter \(\Gamma\) (Equation (3)). For many materials, including water and blood, the value of this parameter increases with in situ temperature within the ultrasonic focus. In this dual-pulse excitation approach, the first laser pulse heated the sample, generating a first PA signal, denoted as PA1; before the first pulse dissipated completely, the second laser pulse was fired, generating a second PA signals denoted as PA2, whose amplitude was larger than PA1 as the value of the corresponding \(\Gamma\) was higher due to the lingering heat. The difference between PA2 and PA1, denoted as \(\Delta\)PA, is proportional to F2, the square of the optical fluence, instead of F, within the ultrasonic focus. As seen, higher concentration of optical energy onto fewer speckle grains leads to a higher F2 and, hence, a stronger nonlinear PA signal amplitude \(\Delta\)PA.