# Enhanced Phase Retrieval Method Based on Random Phase Modulation
## 4 Experiment and Analysis
In this work, we mainly analyzed the effect of different iteration numbers of the serial process \(n_{1}\) on the iteration number \(\hat{N}\) required for convergence and the corresponding reconstruction quality. Furthermore, the threshold condition \(\left|\left|S_{n+1}\right|-\left|S_{n}\right|\right|\leq 1^{-10}\) was used to determine the iteration convergence. The relationship between \(n_{1}\) and \(\hat{N}\), the number of iterations required for convergence, is plotted with a blue solid curve in Figure 10. With the increase in serial process iteration numbers, the number of iterations required eventually showed a downward trend and increased after encountering a minimum. When the minimum of \(\hat{N}\) was achieved, \(n_{1}\)\(=50\). In the convergence curve of the serial method, the point that the iteration number was equal to 50 can be considered a turning point, since the convergence speed was nearly reduced to 0 after the turning point. The convergence curve of the  
Figure 8: The experimental results. (**a**–**c**) Recovered amplitudes of the three methods; (**d**–**f**) reconstructed phases of the three methods. Figure 9: Cross-sections of the white lines marked in Figure 8a–c. serial method and the corresponding derivative curve are plotted in Figure 11 with a blue solid line and dotted orange line, respectively, while the positions of the turning points are marked with black dots. In the proposed serial-parallel cascaded method, when the iteration number of serial process \(n_{1}\) was set to the position of the turning point from the serial convergence curve, the iteration converged at the fastest speed. When the value of \(n_{1}\) was smaller than the value of the iteration number of the turning point, more parallel iterations were required later, since the iteration speed of the serial process was much faster than that of the parallel process. When \(n_{1}\) was greater than the iteration number of the turning point, any iteration numbers in excess constituted a waste, since the reconstruction quality hardly continued improving. Compared with the convergence speed, the effect of \(n_{1}\) on the reconstruction quality of the proposed serial-parallel cascaded method was relatively smaller. The dotted orange line in Figure 10 shows the relationship between serial iteration number \(n_{1}\) and the sharpness of the recovered amplitude. Although experimental errors made the relationship curve oscillatory and noisy, we could still find that a continuous increase of \(n_{1}\) caused the reconstruction quality to decrease in the convergent state. In particular, when \(n_{1}\) was greater than the iteration number of the turning point of the serial  
Figure 11: The convergence curve and the corresponding derivative curve of the serial method. Figure 10: The effect of the serial process iteration number on reconstruction performance of the proposed cascaded method. convergence curve, the degradation was even more serious. Therefore, we recommend that a value before the turning point of the serial method convergence curve should be used to set the iteration number of the serial process \(n_{1}\). It is worth noting that \(n_{1}\) cannot be too small since an initial result too far away from convergence would severely increase the number of iterations required for the subsequent parallel process.