Significance: Digital holographic microscopy is widely used to get the quantitative phase information of transparent cells.

Aim: However, the sample phase is superimposed with aberrations. To quantify the phase information, aberrations need to be fully compensated.

Approach: We propose a technique to obtain aberration-free phase imaging, using the derivative-based principal component analysis (dPCA).

Results: With dPCA, almost all aberrations can be extracted and compensated without requirements on background segmentation, making it efficient and convenient.

Conclusions: It solves the problem that the conventional principal component analysis (PCA) algorithm cannot compensate the common but intricate higher order cross-term aberrations, such as astigmatism and coma. Moreover, the dPCA strategy proposed here is not only suitable for aberration compensation but also applicable for other cases where there exist cross-terms that cannot be analyzed with the PCA algorithm.