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The paper introduces an adaptive-window-spectrogram-based method to directly estimate the phase derivative from a single fringe pattern. The proposed method relies on estimating the phase derivative using spectrogram peak detection for a set of different window lengths. Then the optimal window length is selected from the set by resolving the estimator's bias variance trade-off using the intersection of confidence intervals rule. Finally, the phase derivative estimate corresponding to the optimum window is selected. The method's applicability to phase derivative estimation is demonstrated using simulation and experimental results.