Multi-step phase aberration compensation method based on optimal principal component analysis and subsampling for digital holographic microscopy.

Digital holographic microscopy (DHM) is a well-known powerful technique allowing measurement of the spatial distributions of both the amplitude and phase produced by a transparent sample. Nevertheless, in order to improve the transverse resolution of the DHM system, a microscope objective has to be introduced in the object beam path, which inevitably leads to phase aberration in the object wavefront. In recent decades, a multitude of techniques have been proposed to compensate for this phase aberration, and the principal component analysis (PCA) technique has proven to be one of the most promising approaches due to its high compensation accuracy, low computational complexity, and simplicity to implement. However, when it comes to high-order phase aberration, which is common for a mal-aligned DHM system, the PCA technique usually performs poorly since it is unable to fit the cross-terms of the standard Zernike polynomials. To address this problem, here we propose a multi-step phase-aberration-compensation method based on optimal PCA and sub-sampling where PCA is first applied to remove the non-cross-aberration terms, followed by sub-sampled fitting for the remaining cross-aberration correction. The key advantage of our approach is that it can handle both the conventional objective phase curvature and high-order aberrations such as astigmatism and anamorphism with very little computational overhead. Simulation and experimental results demonstrate that our method outperforms state-of-the-art approaches, and the compensation results are consistent with those obtained from the double-exposure method.