To avoid exhaustive calibration of the shifter device in point diffraction interferometers, we present a dimensionreduction-based method to reconstruct the phase map from more phase-shifting fringe patterns with three or more frames. The proposed method assumes that the intensity space can be described adequately by the sine and cosine of multiple phase shifts introduced, which are the basis of the intensity space. Then, low-dimensional approximations of high-dimensional intensity spaces are determined by the newly developed reduced basis decomposition technique. Finally, the phase is reconstructed using the low-dimensional surrogates of the intensity spaces without the knowledge of accurate phase steps. Numerical and experimental studies demonstrated that the proposed method outperforms the existing popular phase reconstruction techniques in terms of accuracy and efficiency. Moreover, the performance of the proposed method is not limited by variations in the background and modulation, unlike the existing phase-shifting-algorithm-based approaches. (C) 2021 Optical Society of America