# 3D Photoacoustic Tomography System Based on Full-View Illumination and Ultrasound Detection
## 3 Results
### Performance Test of the 3D-PACT
#### 3.1.3 The Superiority of Photoacoustic Coplanar Configuration and Virtual Point Detection  
In the photoacoustic tomography system proposed herein, the narrow sound beam of dual-foci virtual point ultrasonic transducer and the annular illumination beam were coupled to form a photoacoustic coplanar mode based on the quartz bowl with the characteristics of laser transmission and ultrasonic reflection. To prove the advantages of the virtual-point ultrasonic detection and photoacoustic coplanar mode, a comparative experiment was performed using a conventional unfocused ultrasonic transducer (V310, Olympus, Tokyo, Japan). The results of the comparative experiment are shown in Figure 6. In the experiment, the black tape was evenly wrapped around a steel column with a diameter of 25 mm as an imaging phantom, as shown in Figure 6a. The number of sampling points per imaging section was 90, and it took about 9 s to complete a photoacoustic data acquisition of a cross section. Figure 6c,d showed the reconstruction images from the dual-foci virtual point ultrasonic transducer and unfocused ultrasonic transducer, respectively. From a qualitative point of view, it is obvious that the quality of the reconstructed image with the dual-foci transducer was better than its counterpart in terms of qualities such as shape-similarity and image-purity. In order to quantitatively analyze the reconstruction quality of Figure 6c,d, the simulation result of the imaging target (shown in Figure 6b) was used as a reference standard. The photoacoustic raw data of Figure 6b was obtained using a K-wave simulation, and then reconstructed using the improved back projection algorithm mentioned above. The performance indicators, such as MSE (mean squared  
Figure 6: (**a**) Phantom of the comparative experiment. (**b**) Reference standard image by K-Wave simulation. Reconstructed PA images obtained with (**c**) the dual-foci transducer and (**d**) the traditional unfocused transducer. (**e**) A-Line plots from dual-foci transducer and traditional unfocused transducer. (**f**) Absorption intensity distribution at the centerline of (**a–c**). error), PSNR (peak signal to noise ratio), and SSIM (structural similarity) [40; 41; 42] were calculated separately according to the following formulae. The MSE index is given as:  
\[MSE=\frac{1}{mn}{\sum\limits_{i=1}^{m}{\sum\limits_{j=1}^{n}{\left\|{I(i,j)-K(i, j)}\right\|^{2}}}} \tag{7}\]  
The \(I(i,j)\) and \(K(i,j)\) in the formula represent the reconstructed image and the reference standard image, which refer to the reconstructed photoacoustic image and the K-Wave simulation image in this paper, and the parameters \(m\) and \(n\) represent the length and width of the image. _PSNR_ is defined as:  
\[PSNR=20*\log_{10}(\frac{MAX_{1}}{\sqrt{MSE}}) \tag{8}\]  
where \(MAX_{1}\) is the gray level of the image. Lastly, the \(SSIM\) is given as:  
\[SSIM(x,y)=\frac{(2\mu_{x}\mu_{y}+c_{1})(2\sigma_{xy}+c_{2})}{(\mu_{x}^{2}+\mu_{ y}^{2}+c_{1})(\sigma_{x}^{2}+\sigma_{y}^{2}+c_{2})} \tag{9}\]  
where \(x\) and \(y\) represent the two images for comparison, \(\mu_{x}\) and \(\mu_{y}\) are the mean of the image, \(\sigma_{x}\) and \(\sigma_{y}\) represent the variance of image, \(\sigma_{xy}\) is the covariance of \(x\) and \(y\), \(c_{1}=(k_{1}L)^{2}\) and \(c_{2}=(k_{2}L)^{2}\) are two constants used to avoid division by zero in the formula, \(L=2^{B}\)-1 is the range of pixel values, and \(k_{1}=0.01\), \(k_{2}=0.03\) are default values. The results of the above three performance indexes are shown in the following Table 2.  
It can be seen form Table 2 that the performance indicators \(SSIM\) and \(PSNR\) of the reconstructed images were greatly improved in the case of virtual-point ultrasound detection, while the value of \(MSE\) was obviously reduced. The three performance indicators of the reconstructed photoacoustic image under the dual-foci virtual point transducer were better than those under the unfocused transducer that verified the reliability of the proposed system.