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In this study, we are aimed to analyze the possibilities of timely visualization of the aircraft wake (for the flight safety) using the measurement of radiobrightness contrast of the wake against the ambient atmosphere. The theoretical model and numerical code are developed and the calculations of radiobrightness temperature are performed for typical conditions of the atmosphere and the wake of Boing 707 aircraft in the spectral range 1-1000 GHz. It is shown that water vapor is a proper exhaust gas to visualize the wake in the microwave region. The narrow spectral intervals are selected to detect the wake at different altitudes of flight. Simple analytical model is developed for rapid estimation of radiobrightness contrast in different ambient conditions. On the base of this model the method was proposed to raise the sensitivity of aircraft wake detection. S. Ivanov received financial support from the Ministry of Science and Higher Education within the State assignment FSRC «Crystallography and Photonics» RAS and Russian Science Foundation (Project No.18-55-16006).