Quantitative phase imaging (QPI) by differential phase contrast (DPC) with partially coherent illumination provides speckle-free imaging and lateral resolution beyond the coherent diffraction limit, demonstrating great potential in biomedical imaging applications. Generally, DPC employs weak object approximation to linearize the phase-to-intensity image formation, simplifying the solution to the phase retrieval as a two-dimensional deconvolution with the corresponding phase transfer function. Despite its widespread adoption, weak object approximation still lacks a precise and clear definition, suggesting that the accuracy of the QPI results, especially for samples with large phase values, is yet to be verified. In this paper, we analyze the weak object approximation condition quantitatively and explicitly give its strict definition that is applicable to arbitrary samples and illumination apertures. Furthermore, an iterative deconvolution QPI technique based on pseudo-weak object approximation is proposed to overcome the difficulty of applying DPC to large-phase samples without additional data acquisition. Experiments with standard microlens arrays and MCF-7 cells demonstrated that the proposed method can effectively extend DPC beyond weak object approximation to high-precision three-dimensional morphological characterization of large-phase technical and biological samples.