Noise-robust phase compensation using principal component analysis with guided parameter adjustment

Phase compensation by principal component analysis (PCA) is a fast and fully automatic numerical technique for removing the background phase in digital holographic microscopy. However, the effectiveness of this method assumes that the object is thin and localized in small areas within the field of view. We propose a multi-step numerical method for phase compensation by PCA on objects with low signal-to-background ratio (SBR) and presence of speckle noise. We demonstrate that these conditions limit the effectiveness of the conventional phase compensation method by PCA because they introduce phase discontinuities in the first principal component. Consequently, a poor estimation of the tilt and curvature coefficients of the background phase estimate is obtained. To avoid this, we identify and remove error points in the unwrapped first principal component vectors, followed by guided adjustment of the curve-fitted coefficients to compensate for the phase jump due to phase discontinuities. The effectiveness of the proposed method was demonstrated on a simulated object wave with a known background phase, and on a reconstruction of a complex object obtained using multiple-plane phase retrieval. Results show that optimal adjustment of the curve-fitted coefficients to compensate for the phase jump leads to the best estimation of the background phase in a least-squares sense.