## 3 Experimental Results and Discussion
### Simulation Analysis of POSE  
To measure the ability of the proposed strategy to suppress local extrema, POSE was compared with the improved hill-climbing search (IHCS) [29] in simulation experiments. The Gaussian equation \(F_{i}^{(j)}\) (\(i=1\), 2, \(\ldots\), 25, \(p=13\)) in (5) generates sets of simulated sharpness evaluation curves [36], where \(j\), \(p\), \(\sigma_{f}\) and \(\alpha\) denote the image stack index, focus position, Gaussian standard deviation, and offset, respectively. A normally distributed random number _noise_(\(\varepsilon_{f}\)) generates the noise bias with mean 0 and standard deviation \(\varepsilon_{f}\) to simulate local extrema. The above hyperparameters are obtained by Gaussian fitting of the clinically collected curves.  
\[F_{i}^{(j)}=A\exp\left(-\frac{(i-p)^{2}}{2\sigma_{f}^{2}}\right)+\alpha+noise \left(\varepsilon_{f}\right) \tag{5}\]  
The experiment generates 10,000 sets of simulation curves, and their peak positions are estimated through the above strategies (with \(i=1\) as the start point). As shown in Table 1, compared with IHCS, POSE has 2.73 fewer local extrema in the search path, and the search success rate is increased by 21.84%. Hence, the proposed strategy holds stronger robustness to the noise.  
Some search results were further visualized to explain this performance improvement of POSE. Even if the curve oscillates violently near the start point or peak (Figure 7a,b), POSE can still obtain an accurate search path utilizing the error smoothness and data awareness of EWMA, while IHCS only judges the convergence based on the original data, resulting in spurious peaks. Furthermore, POSE fails when the curve exhibits a significant dip (Figure 7c) near the start point. Since the historical statistical value of EWMA in the early search stage appears unreliable, the convergence condition is met once the search path enters the 'valley'. However, such cases are rarely observed in practical fundus focus. This limitation can be overcome by optimizing imaging conditions or conducting autonomous searches within partitions.  
Due to individual differences in eye diopter, the curve peak often occurs in off-center positions (\(p\
eq 13\)). To demonstrate the applicability of POSE, the peak position (let \(p=8\), 9, \(\ldots\), 18, corresponds to [+10 D, \(-10\) D] diopter, respectively) in (5) is changed, and the search process is repeatedly performed to obtain the curves shown in Figure 8. It can be seen that the search success rate of POSE is higher than that of IHCS in all cases. As the diopter changes from positive to negative, the defocused range of the curve widens, and  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Quantitative Criteria** & **IHCS** & **POSE** \\ \hline Average number of local extrema & 3.38 & 0.65 \\ Average search success rate & 71.56\% & 93.40\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation results on search strategies.  
the disturbance introduced by noise bias becomes more pronounced. Hence, the overall success rate tends to decline. However, POSE exhibits an 85% search success rate, even with a \(-\)10 D diopter, which proves the proposed strategy applies to different individuals.