Аннотация:We used the optical spectra with resolution R=13000 obtained in the course of Cyg~X-1 spectral monitoring over 2003-2004, carried out with the echelle spectrometer of the 2-m telescope of Peak Terskol Observatory (3100 m, Caucasus). The high-precision spectra show clearly the sequence of line profile variations with orbital phases. The Doppler images were reconstructed by an improved Doppler tomography method developed by Agafonov (2004) (radioastronomical approach) on the base of HeII λ4686Å profiles of 2003 (”soft” X-ray state) and of 2004 (”hard” X-ray state). The main features of the reconstruction are: de-convolution in the image space with the introduction of the synthesized beam (equivalent summarized transfer function) and the removal of the distortions on the summarized image (after back projecting) caused by the sidelobes of this beam using CLEAN algorithm. The method is developed specially for a small number of irregularly distributed observations. The Doppler images and Roche lobe model allowed putting a limitation on the black hole to supergiant mass ratio 1/4\leM[X]/M[O]\le1/3. The emission may come from the accretion disk outer regions heated by the hot supergiant emission, from the ”hot line” discussed by Kuznetsov et al.(2001), or/and from the accretion stream (focused stellar wind).