## 6 Conclusions  
In this paper, we introduce a semi-supervised Fourier ptychographic microscopy reconstruction network based on the FPT, termed SFPT. SFPT harnesses the sequence modeling capabilities of the FP-transformer to effectively reconstruct high-resolution amplitude and phase, integrates the FPM forward algorithm with Zernike modes for aberration correction and utilizes augmented datasets to learn the unwrapping phase.  
Through comparative reconstruction results on simulated and real data, we demonstrate that our method can efficaciously perform a super-resolution reconstruction of amplitude and phase even in the presence of aberrations and noise interference. By adjusting the distribution domain of a network's training dataset, we achieved phase unwrapping within a specified range and conducted comparative validation on real data, underscoring the effectiveness of the proposed method. However, the proposed method still has several limitations. For instance, SFPT demands substantial computational resources, with the computational cost of the transformer escalating rapidly as the image size increases. For larger images, it requires partitioning the image for reconstruction and subsequent stitching. Additionally, the method necessitates at least 12 GB of GPU memory for model training. Although the network demonstrates a certain degree of robustness, it needs to be fine-tuned when dealing with significant variations in aberrations, which incurs additional time costs. In future works, we will explore more lightweight reconstruction algorithms and effective strategies for real-time dynamic FPM reconstructions, which represents the mainstream trajectory for advancing the practical applicability of FPM.  
Conceptualization, X.Z., H.T., E.O., L.Z. and H.F.; methodology, X.Z.; software, X.Z.; validation, X.Z., H.T. and H.F.; formal analysis, X.Z.; investigation, X.Z.; resources, H.F.; data curation, X.Z.; writing--original draft preparation, X.Z.; writing--review and editing, X.Z. and E.O.; visualization, X.Z.; supervision, L.Z. and H.F.; project administration, H.F.; funding acquisition, H.F. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (12074268), the Shenzhen Science and Technology Major Project (KJZD02030923114601004) and the Scientific Instrument Developing Project of Shenzhen University (2023 YQ024).  
Not applicable.  
The code of this study will be publicly accessible in a GitHub repository at [[https://github.com/pilixiaohui/SFPT](https://github.com/pilixiaohui/SFPT)]([https://github.com/pilixiaohui/SFPT](https://github.com/pilixiaohui/SFPT)) (accessed on 27 December 2024).  
The authors declare no conflicts of interest. The funders had no role in the design of the study, in the collection, analyses, or interpretation of data, in the writing of the manuscript, or in the decision to publish the results.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Supervised** & **Zernike Modes** & **Pixel and Channel** & **Amplitude** & **Phase** \\
**Learning** & & **Self-Attention** & **PSNR/SSIM** & **PSNR/SSIM** \\ \hline \(\times\) & \(\times\) & \(\times\) & 17.97/0.2317 & 14.94/0.3168 \\ \hline \(\times\) & \(\times\) & \(\surd\) & 18.021/0.2326 & 15.74/0.3175 \\ \hline \(\times\) & \(\surd\) & \(\times\) & 27.16/0.8540 & 18.51/0.9014 \\ \hline \(\surd\) & \(\times\) & \(\times\) & 18.29/0.2261 & 15.00/0.2493 \\ \hline \(\surd\) & \(\surd\) & \(\times\) & 26.37/0.8595 & 21.07/0.9080 \\ \hline \(\surd\) & \(\surd\) & \(\surd\) & 26.53/0.8591 & 21.67/0.9176 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results of the SFPT key module ablation experiment.