The dynamic modulation transfer function (MTF) for image degradation caused by sinusoidal vibration is formulated based on a Bessel function of the first kind. The presented method makes it possible to obtain an analytical MTF expression derived for arbitrary frequency sinusoidal vibration. The error obtained by the use of finite order sum approximations instead of infinite sums is investigated in detail. Dynamic MTF exhibits a stronger random behavior for low frequency vibration than high frequency vibration. The calculated MTFs agree well with the measured MTFs with the slant edge method in imaging experiments. With the proposed formula, allowable amplitudes of any frequency vibration are easily calculated. This is practical for the analysis and design of the line-of-sight stabilization system in the remote sensing camera.

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