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Phase autofocus is a significant step in translational motion compensation for inverse synthetic aperture radar (ISAR) imaging. Among the existing autofocus methods, contrast maximization-based algorithms are superior in accuracy and robustness. However, the existing maximum contrast autofocus methods are parametric, which significantly affects their convergence speed and, in some cases, limits their applicability. In this paper, a novel non-parametric maximum contrast ISAR autofocus algorithm based on Newton’s method is proposed to inherit the high level of accuracy and robustness of contrast-based algorithms and, at the same time, achieve faster convergence. The simplified Newton’s method, the modified Newton’s method, and the secant method are used to obtain a higher computational efficiency. The proposed method is then compared to a well-established non-parametric method, namely the minimum entropy autofocus method. It will be shown that the proposed method can improve the computational efficiency by a factor from 5 to 10 times in typical scenarios. Both simulated and real data will be used to test the proposed algorithm, particularly in terms of computational effectiveness. [ABSTRACT FROM AUTHOR]