This Letter proposes a new method for the estimation of the first-and second-order phase derivatives corresponding to strain and curvature from a single fringe pattern in digital holographic interferometry. The method is based on a discrete energy separation algorithm, which provides a biased phase derivative estimate in a noisy environment. Subsequently, the least-squares spline approximation with optimal number of knots selection technique is used to obtain the accurate estimation of phase derivatives. The accuracy and computational efficiency of the proposed method is validated with simulation and experimental results. (C) 2014 Optical Society of America