The transport-of-intensity equation (TIE) enables quantitative phase imaging (QPI) under partially coherent illumination by measuring the through-focus intensities combined with a linearized inverse reconstruction algorithm. However, overcoming its sensitivity to imaging settings remains a challenging problem because of the difficulty in tuning the optical parameters of the imaging system accurately and because of the instability to long-time measurements. To address these limitations, we propose and experimentally validate a solution called neural-field-assisted transport-of-intensity phase microscopy (NFTPM) by introducing a tunable defocus parameter into neural field. Without weak object approximation, NFTPM incorporates the physical prior of partially coherent image formation to constrain the neural field and learns the continuous representation of phase object without the need for training. Simulation and experimental results of HeLa cells demonstrate that NFTPM can achieve accurate, partially coherent QPI under unknown defocus distances, providing new possibilities for extending applications in live cell biology.

中文翻译：

---

神经场辅助强度传输相位显微镜：未知离焦距离下的部分相干定量相位成像


强度传输方程 (TIE) 通过测量离焦强度并结合线性逆重建算法，可以在部分相干照明下实现定量相位成像 (QPI)。然而，克服其对成像设置的敏感性仍然是一个具有挑战性的问题，因为精确调整成像系统的光学参数很困难，而且长时间测量不稳定。为了解决这些限制，我们通过在神经场中引入可调散焦参数，提出并通过实验验证了一种称为神经场辅助强度传输相位显微镜（NFTPM）的解决方案。 NFTPM无需弱物体近似，结合部分相干图像形成的物理先验来约束神经场，无需训练即可学习相位物体的连续表示。 HeLa细胞的仿真和实验结果表明，NFTPM可以在未知离焦距离下实现准确、部分相干的QPI，为扩展在活细胞生物学中的应用提供了新的可能性。