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Analysis of Dynamic Modulation Transfer Function for Complex Image Motion

In remote-sensing imaging, the modulation transfer function (MTF) for image motion relevant to the mixing of multiple forms of motions is hard to calculate because of the complicated image motion expression. In this paper, a new method for calculating the MTF for complex image motion is proposed. The presented method makes it possible to obtain an analytical MTF expression derived from the mixing of linear motion and sinusoidal motion at an arbitrary frequency. On this basis, we used the summation of infinitely many terms involving the Bessel function to simplify the MTF expression. The truncation error obtained by the use of finite order sum approximations instead of infinite sums is investigated in detail. In order to verify the MTF calculation method, we proposed a simulation method to calculate the variation of MTF in an actual optical system caused by image motion. The mean value of the relative error between the calculation method and the simulation method is less than 5%. The experimental results are consistent with the MTF curve calculated by our method.