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The paper deals with the recent results of the experiments on soft X-ray imaging of various carbon-containing objects: biological samples, artificial carbon fibres, graphite slices, etc. The working wavelength was chosen to be 4.5 nm due to high penetration ability of these soft X-rays in the carbon materials. The experimental set-up included: laser plasma Xray source (generated with the 2nd harmonics of Nd:YAG laser), scandium-based thin-film filter and highly reflective spherical multilayer mirror. The Co/C multilayer's reflectivity was measured to be about 15 % at normal incidence that was high enough to produce soft X-ray images using single nanosecond exposure. The work demonstrates a possibility to produce high contrast images outside "water window" region for study of relatively thick (tens of microns) unstained samples that may lead to new fields of applications of the soft x-ray microscopy