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A scheme for achieving high spatial resolution in soft X-ray microscopy with coherent broadband light sources is proposed, in which the chromatic aberration at a Fresnel zone plate lens can be canceled out by introducing time-delayed double pulses as an input light and by the Fourier transformation of recorded images with respect to the time delay. Numerical simulations of microscope images show that the spatial resolution of the proposed method is determined only by specifications of zone plates even when a broadband soft X-ray is used as a light source.