The multi-plane phase retrieval method provides a budget-friendly and effective way to perform phase imaging, yet it often encounters alignment challenges due to shifts along the optical axis in experiments. Traditional methods, such as employing beamsplitters instead of mechanical stage movements or adjusting focus using tunable light sources, add complexity to the setup required for multi-plane phase retrieval. Attempts to address these issues computationally face difficulties due to the variable impact of diffraction, which renders conventional homography techniques inadequate. In our research, we introduce a novel Adaptive Cascade Calibrated (ACC) strategy for multi-plane phase retrieval that overcomes misalignment issues. This technique detects feature points within the refocused sample space and calculates the transformation matrix for neighboring planes on-the-fly to digitally adjust measurements, facilitating alignment-free multi-plane phase retrieval. This approach not only avoids the need for complex and expensive optical hardware but also simplifies the imaging setup, reducing overall costs. The effectiveness of our method is validated through simulations and real-world optical experiments.

翻译：多平面相位恢复方法提供了一种经济高效的相位成像途径，但由于实验中沿光轴方向的偏移常面临对齐挑战。传统方法，例如使用分束器替代机械位移台或通过可调光源调节焦距，增加了多平面相位恢复所需光学系统的复杂性。而试图通过计算方式解决这些问题的尝试，则因衍射效应的影响变化导致传统单应矩阵技术失效。本研究提出一种新型自适应级联校准策略，用于克服多平面相位恢复中的不对齐问题。该技术可在重聚焦样本空间内检测特征点，并实时计算相邻平面的变换矩阵以数字方式调整测量数据，从而实现无对齐多平面相位恢复。该方法不仅避免了对复杂昂贵光学硬件的依赖，还简化了成像系统结构，降低了整体成本。通过仿真与实际光学实验验证了该方法的有效性。