  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.
