The possibility of using compound refractive lenses as elements of X-ray optics designed to form an image on an X-ray resist in the soft X-ray wavelength range is discussed. For this purpose, a mathematical simulation of the transformation of the wave front as it passes through the optical system under consideration was carried out. The intensity distribution of the X-ray radiation wavefront with a wavelength varied from 2 to 14 nm at the input/output of a compound refractive lens and in the plane of the substrate with X-ray resist is calculated. Promising materials (Si, Be, diamond) of compound refractive lenses, which have high transparency for the selected wavelengths, are considered. It has been shown that the transition to diffractive and kinoform lenses minimizes the degree of absorption of X-ray radiation in the lens material by several orders of magnitude, which makes it possible to increase the resolution up to 14 nm. The results of the study can be used in the development of new optical systems based on a transparent mask and a compound refractive lens, which are applicable for X-ray nanolithography tasks. Keywords: X-ray nanolithography, X-ray radiation, compound refractive lens, kinoform lenses, resolution, numerical aperture.

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