# A Method to Obtain the Transducers Impulse Response (TIR) in Photoacoustic Imaging
## 4 Tests and Discussion
### The Effect of OPAS Length of the Transducer on Results  
To obtain the TIR more efficiently, it is discussed whether it is possible to obtain an accurate TIR by selecting the length of the OPAS obtained by the transducer. Because the above discussion has concluded that the TIR can be obtained by two transducers, the following discussion defaults to the calculation of the data of the two transducers. The calculation uses data on the length of 339 OPAS from two transducers. We chose two transducers, No. 1 and a transducer rotated 90\({}^{\circ}\) clockwise from its position around the center of the reconstructed area. Data of 100 and 200 signal lengths are selected from each of the two transducers' OPAS. When selecting the signals, they are selected sequentially, starting from the beginning of the OPAS.  
Compare the PAPS calculated by the algorithm with the original PAPS. As can be seen in Figure 7, when the OPAS length is 100 (Figure 7a), the calculated PAPS is incorrect. The calculated PAPS when the observed signal length is 200 (Figure 7b) is consistent with the original PAPS. This is because data tending to zero have little effect on the algorithm result, as the OPAS data tends to zero after approximately the 200 th signal. The length of TIR was assumed to be 30 or 40 to test whether the correct result could be obtained.  
Here, to verify the results, Figure 8 shows the result of calculating the LS algorithm when the OPAS length is 100, assuming that the TIR signal length is 30 or 40. Because the PAPS calculated by the algorithm is wrong, the TIR calculation is also wrong. The reason is that, when selecting OPAS data, it selects biological tissues that produce OPAS that are incomplete, and the selected data no longer satisfy the convolution equation of Equation (1). These data cannot be used to solve the PAPS and TIR.  
Figure 5: It uses two transducer data to obtain the PAPS.  
Figure 6: Results after the algorithm is corrected. (**a**) Corrected the PAPS. (**b**) The TIR is calculated after correcting the PAPS.  
When continuing to calculate the OPAS length of 200, assuming the TIR length is 30 or 40, the TIR is also calculated with the LS algorithm. As the PAPS was correct earlier, the result of the TIR calculation would also have been correct. The result obtained is shown in Figure 9a,b. It can be seen that the result is not much different from the set TIR. The missing data in Figure 9a are data which are more likely zero, which did not affect the outcome. So, if this article is taken as an example, a signal length of about 200 should be selected for each transducer to obtain an accurate TIR. According to this conclusion, in practice, when solving the TIR by selecting the OPAS length, intact OPAS produced by biological tissues should be selected to obtain the correct TIR.  
Figure 8: TIR results with an OPAS length of 100. (**a**) The TIR length is 30. (**b**) The TIR length is 40.  
Figure 7: (**a**) The calculated PAPS when the OPAS is 100 signal lengths is compared to the original PAPS. (**b**) The calculated PAPS when the OPAS is 200 signal lengths is compared to the original PAPS.  
Figure 9: TIR results with an OPAS length of 200. (**a**) The TIR length is 30. (**b**) The TIR length is 40.