Phase aberration compensation based on iteratively reweighted Zernike polynomial fitting for digital holographic microscopy

Phase aberration compensation is essential for quantitative imaging in digital holographic microscopy (DHM), as undesired background distortions severely degrade phase measurement reliability. Conventional Zernike polynomial fitting (ZPF) either relies on manually or automatically selected background regions, which restricts its applicability to samples with sparse or ambiguous background, or performs a global least-squares (LS) fit over all pixels, in which sample structures and outliers bias the estimated aberration. This work proposes a global iteratively reweighted ZPF (GIR-ZPF) method to overcome these issues. The proposed method performs global fitting using all valid pixels across the full field and introduces a Tukey-based iterative reweighting strategy to suppress structural and outlier interference, thereby eliminating the requirement for background selection. Simulation results show that, compared with the naive global ZPF (G-ZPF), GIR-ZPF reduces the RMSE and MAE of phase reconstruction by ∼13.3%, increases the PSNR from 24.8 to 26.0 dB, and improves the Zernike-coefficient estimation accuracy by nearly two orders of magnitude, while reaching an accuracy comparable to mask-based ZPF methods without requiring any mask prior. Experiments on microspheres and live A549 cells demonstrate that GIR-ZPF achieves flat phase backgrounds, clear sample contours, and well-preserved microstructural features. GIR-ZPF provides an effective and robust solution for phase aberration compensation of samples with sparse or ambiguous backgrounds in DHM.