###### Abstract  
Fourier ptychographic microscopy (FPM) has recently emerged as an important non-invasive imaging technique which is capable of simultaneously achieving high resolution, wide field of view, and quantitative phase imaging. However, FPM still faces challenges in the image reconstruction due to factors such as noise, optical aberration, and phase wrapping. In this work, we propose a semi-supervised Fourier ptychographic transformer network (SFPT) for improved image reconstruction, which employs a two-stage training approach to enhance the image quality. First, self-supervised learning guided by low-resolution amplitudes and Zernike modes is utilized to recover pupil function. Second, a supervised learning framework with augmented training datasets is applied to further refine reconstruction quality. Moreover, the unwrapped phase is recovered by adjusting the phase distribution range in the augmented training datasets. The effectiveness of the proposed method is validated by using both the simulation and experimental data. This deep-learning-based method has potential applications for imaging thicker biology samples. F 2020  
improvements introduced by [PERSON] et al. [19], which incorporates multi-scale architectures, residual connections, attention mechanisms, and various other enhancements. [PERSON] et al. applied generative adversarial networks (GANs) to achieve high-resolution, artifact-free reconstructions with robust cross-explainability and clinical validation [20]. [PERSON] et al. proposed a linear-space-variant (LSV) model to achieve uniform full-field imaging while effectively eliminating vignetting-induced artifacts without segmenting the images [21]. [PERSON] et al. introduced a blind deep-learning-based preprocessing method (BDFP) that enhances noise robustness by modeling noise distribution for data augmentation [22]. These data-driven approaches achieve image reconstruction by learning complex mapping relationships, and most of them are supervised learning. Once trained, the rapid inference is allowed within the same experimental setup. The second type integrates the physical imaging model as prior knowledge, forming a physics-guided neural network architecture [23]. For instance, [PERSON] et al. [24] and [PERSON] et al. [25] simulated the forward imaging process of FPM using a neural network, with high-resolution amplitude and phase images as trainable parameters. By using optimization algorithms like gradient descent, the network is trained by its low-resolution amplitude output data distribution, which matches the experimentally collected data distribution. [PERSON] et al. [26] incorporated a single iteration of the FPM forward algorithm as a data preprocessing step, using the neural network for subsequent optimization to reduce network complexity [27]. [PERSON] et al. proposed the denoising diffusion probabilistic models for Fourier ptychography method [28], which combines diffusion models with Wirtinger gradient descent techniques, offering a new approach to FPM reconstruction. These physically guided methods typically do not require manual GT labels and can be considered self-supervised learning, offering the advantage of low-cost reconstruction; however, their parameter optimization process was often tailored to single sample, limiting the advantage of deep learning that can optimize results using large datasets. When encountering phase wrapping problem that arise with samples exhibiting significant phase distribution differences, FPM typically employs physical methods or phase unwrapping algorithms to address the problem, such as introducing solutions with varying refractive indices into the sample. And traditional unwrapping algorithms tend to exhibit substantial reconstruction errors when dealing with complex phase structures [29; 30]. The advancement of deep learning offers a novel approach to phase unwrapping in FPM [31].