Superresolution optics, employing Gaussian apodization, is rigorously treated at the soft X-ray wave-length(λ=0.013 ${mu}{ extrm}{m}$) region. In the diffraction integral, the line integral along the imaginary axis is found small, and it is ignored, so that the diffraction integral consists of the integration along the real axis. The resolution of the diffracted image is not effected by the pupil angular frequency bandwidth $2{omega}_0$, which is one of the most important the characteristic features of Gaussian apodization ($e^{-o^2x^2}$ optics. The superresolution optics has resolution ($frac{1}{2}{ imes}FWHM)$=$Delta$x=0.008 $mu$m which is smaller than the Rayleigh criterion of 2λ=0.026 ${mu}{ extrm}{m}$ for NA=0.25. The optical system has ${omega}_0{ge}frac{1}{2}{sigma}$, which gives the peak intensity of the diffracted image larger than $e^{-2}$ times intensity obtainable by the infinite sperture.