# Quantitative Reconstruction of Absorption Coefficients for Photoacoustic Tomography
## 4 Phantom Experiment  
Performances were also evaluated by a tissue-mimicking phantom with an embedded absorber, as illustrated in Figure 7a. The background of the tissue-mimicking phantom with a size of 0.6 (X) \(\times\) 0.6 (Y) \(\times\) 0.6(Z) cm\({}^{3}\) included (1%-2%) Intralipid and Arga powder. The absorption and scattering coefficients of the base phantom were 0.04 and 200 cm\({}^{-1}\) at a wavelength of 532 nm [26,34,43,44]. A 2 mm-diameter tube filled with 5% Indian ink as the absorber was inserted into a phantom-base. The \(\upmu\)a value of the Indian ink absorber was 112.5 cm\({}^{-1}\), and scattering coefficients was 100 cm\({}^{-1}\), we utilized a spectrophotometer to measure the optical properties of the phantom sample, and the absorption coefficient value was normalized to 100 for computational convenience [26,27,34]. In the phantom experiment, the light illumination was provided by a pulsed Nd:YAG laser source (Vigour-A-100S, Anshan Ziyu, China) with the wavelength of 532 nm, pulse repetition rate of 20 Hz and pulse duration 5 ns. A photoacoustic imaging system (Prodigy, S-Sharp, China) was exploited with a linear array transducer to acquire the PA signal. Figure 7b is a B-scan of the phantom reconstructed from PA signals obtained by the S-Sharp system, while Figure 7c demonstrates the corresponding fluence distribution of the phantom. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Target** & **Raw Data** & **Recovered** & **Ground Truth** & **SSIM1** & **SSIM2** & **Accuracy** \\ \hline target1 & 1.30 & 1.95 & 2.00 & 0.932036 & 0.999868 & 97.50\% \\ target2 & 0.96 & 5.97 & 6.00 & 0.627773 & 0.999995 & 99.50\% \\ target3- layer1 & 0.39 & 0.92 & 1.00 & 0.907882 & 0.998892 & 92.00\% \\ target3- layer2 & 0.20 & 3.02 & 3.00 & 0.539483 & 0.999917 & 99.33\% \\ target3- layer3 & 0.15 & 5.03 & 5.00 & 0.318427 & 0.999921 & 99.40\% \\ target3- layer4 & 0.10 & 7.01 & 7.00 & 0.220775 & 0.999925 & 98.57\% \\ target4 & 0.13 & 1.95, 3.97 & 2.00, 4.00 & 0.670044 & 0.999933 & 97.50\%, 99.25\% \\ target5 & 0.16 & 5.97 & 6.00 & 0.441811 & 0.999992 & 99.50\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results for quantitative recovery of absorption coefficient. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & **SSIM** & **RMSE** & **PSNR** \\ \hline Before recovery & 0.913498 & 1.45105 & 31.4724 dB \\ (Ground truth \& Raw data) & \\ After recovery & 0.999927 & 0.0253681 & 112.403 dB \\ (Ground truth \& Recovered) & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Algorithm performance evaluation. Figure 6: (a) Absorption energy distribution before iteration recovery; (b) Absorption coefficient distribution after iterative recovery; (c) The iteration error. The absorption coefficient of the phantom absorber was estimated by the proposed iteration method. Firstly, the initial absorption coefficient was obtained based on the 3D Monte Carlo model to execute light fluence compensation. In the iteration algorithm, the deviation was calculated between the detected and the computed distribution of absorbed energy at each iteration, which was used to update the estimated optical parameter. By minimizing the deviation in the absorbed energy, the final estimate was obtained as the value of the optimal absorption distribution. A-line profiles are selected to visualize the iteration recovery results, and the recovery results of absorption coefficients of the 3 rd, 6 th and 13 th iterations are shown in Figure 8a-c, respectively. After 13 iterations, the condition of iteration stopping was reached and the optimal quantitative estimate value could be outputted. The results show that the proposed algorithm can effectively reduce or even eliminate the influence of light fluence on the measured absorption distribution.