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A novel and cost-effective method is developed for the roll alignment automation for out-of-plane coupling between a laser and an angled facet single-mode fiber. The method is based on an approximated closed-form analytical formula for the functional dependence of out-of-plane laser-fiber coupling efficiency on relative rotational angle between fiber and laser. In this method, only three measurements are needed to locate maximum optical power coupling position in the presence of initial fiber-laser relative rotational angular misalignments. This intelligent searching method can easily be incorporated into any conventional fiber-optic alignment optimization algorithms and is sufficiently general for alignment automation of even more complicated out-of-plane fiber-optic alignment in the presence of initial nonplanar misalignments.