The advantages of quantitative phase microscopy (QPM) such as label-free imaging with high spatial sensitivity, live cell compatibility and high-speed imaging makes it viable for various biological applications. The measurement accuracy of QPM strongly relies on the shape of the recorded interferograms, whether straight or curved fringes are recorded during the data acquisition. Moreover, for a single shot phase recovery high fringe density is required. The wavefront curvature for the high-density fringes over the entire field of view is difficult to be discerned with the naked eye. As a consequence, there is a quadratic phase aberration in the recovered phase images due to curvature mismatch. In the present work, we have implemented sampling moiré method for real-time sensing of the wavefront curvature mismatch between the object and the reference wavefronts and further for its correction. By zooming out the interferogram, moiré fringes are generated which helps to easily identify the curvature of the fringes. The wavefront curvature mismatch correction accuracy of the method is tested with the help of low temporal coherent light source such as a white light (temporal coherence ∼ 1.6 µm). The proposed scheme is successfully demonstrated to remove the quadratic phase aberration caused due to wavefront mismatch from an USAF resolution target and the biological tissue samples. The phase recovery accuracy of the current scheme is further compared with and found to better than the standard method called principle component analysis. The proposed method enables recording of the corrected wavefront interferogram without needing any additional optical components or modification and also does not need any post-processing correction algorithms. The proposed method of curvature compensation paves the path for a high-throughput and accurate quantitative phase imaging.