In the practice of visual navigation, the observer’s orientation on colored lights (constant or flashing with different flashing characteristics), observed on a colored uneven background, allows establishing a confident visual contact with the Earth. She gives the pilot a course of landing, a glide path of decline, the position of the horizon. The brightness of the background is determined both by external natural and artificial sources of illumination, and by the brightness of the navigation complex scattered in the atmosphere. The ratio of these brightnesses is determined by the conditions of observation (the time of day, the meteorological visibility, the presence of extraneous sources, etc.). In general, this can be characterized as the observation of a colored object on a colored background with an uneven distribution of brightness over their surfaces. To estimate the visibility of the fire of navigational complexes, a threshold model of the visual analyzer (eye) is currently used which is based on comparing the illumination of the visual organ with threshold values, on the basis of which a decision is made about the visibility of the observed fire. Since the threshold model can not fully take into account the physiology of the visual process and, therefore, give an accurate result for analyzing the observation of the fire, a statistical model of the visual analyzer can be used. Its application is relevant in the case of an observer’s orientation on the light field of a sector navigation complex consisting of multi-colored sectors that are adjacent to each other and differing in flashing characteristics. The model makes it possible to estimate the probability of detecting the color fire of a sector-based navigation complex on a colored background with an arbitrary distribution of brightness over their surface .
To determine the structure of the light field: the shape of the contour of the monochromatic sector, within which the fire of the complex is perceived with a probability not less than specified, a method of successive images is used. The method is based on the representation of the radiation field in the form of a series of source images located at different distances from the optical system. The propagation of radiation from the source to the image is determined by the transfer functions of the elements of the radiation propagation path having different physical nature , the optical system, the scattering and turbulent atmosphere. At altitudes up to 2–3 km in the atmosphere, there is always a surface layer of a natural aerosol with a particle size of 0.1–10 µm . Passage of radiation through the atmospheric layer is described in the framework of the small-angle approximation (SAA). This approach can be used for direct observation of the fire of the complex. Firstly, due to the functional characteristics of the radiating device, it is only necessary to take into account that fraction of radiation that is scattered forward in the range of angles from 0 to 10°–15°. Secondly, SAA gives accurate results of optical distances within which the working region of the complex lies, for optical distances up to τ ≤ 10 (where: τ = ε · R – is the optical distance, R – is the removal, ε – is the attenuation index of the medium ). In Fig. 1 the working areas of the sector navigational complex on superbright light-emitting diodes and the representations of radiation transfer in the atmosphere, defined within the framework of SAA, are presented. On the basis of the proposed method, a calculation of the sector diagram was carried out, taking into account the influence of various external factors. The proposed method makes it possible to refine the parameters of the radiation pattern of the monochromatic sector at a remote section of the light field, which amounts to 30% of the range of visibility of the fire (for a meteorological visibility of 50 km) with probability of detection of ρ = 1. Data obtained by the standard method adopted to estimate the range of visibility of navigation lights are known . Fig. 2 compares the diagrams of the monochromatic sector for different probabilities and quality of the optical system obtained by the proposed method and used by the traditional method. The characteristic shapes of the obtained diagrams of the monochromatic sector for the values of the meteorological visibility are 50; 4 and 0.2 km (for the value of the coupling coefficient, the aberration values with the parameters of the optical system Kos = 4183.3 and the probability of detection ρ = 0.5 and ρ = 1) are shown in Fig 3. The effect of atmospheric turbulence on the light field of the sectoral navigation complex is expressed in the shift of the position of the boundaries between sectors and the broadening of sectors. The displacement of the boundary of the sector, because of the turbulence of the atmosphere at the propagation distance di, is determined by the variance σr2 or the standard deviation σr (uncertainty of the visual positioning of the fire of the complex ≈ 2σr) . The results of calculations for wavelengths l = 505 nm and l = 630 nm are shown in Fig.4. They show that in the operating wavelength range the influence of turbulence is manifested almost uniformly for all wavelengths, and the magnitude of the standard deviation is determined only by the degree of turbulence in the atmosphere and does not depend on the wavelength. Figure 5 shows the dependence of the broadening of the sector diagram on the degree of turbulence. Calculations showed that, on the whole, turbulence does not affect the accuracy of the orientation of the light field of the sector navigation complex (SNC) on the basis of super-bright LEDs. The change in the shape of the diagram of the monochromatic sector for different values of meteorological visibility and the level of background illumination (time of day) is shown in Figs. 6 and 7, respectively. An analysis of the results of numerical calculations makes it possible to draw an important conclusion that the parameters of the atmosphere and the brightness of the background practically do not affect the angular sizes of the sectors. The specified level of fire detection probability also does not affect the choice of sector sizes. Such independence of the operating parameters of the complex ensures accurate formation of the light field boundaries in any conditions throughout the entire range of action (Zdd, in Fig. 8) of the complex’s fire. The conclusion was confirmed by the experimental data obtained during observations, which were carried out with the number of independent observers from 3 to 5 people and the number of independent observations at a selected range for each observer equal to five. To determine the width of the transition zones at different distances from the complex, the width of the transition zones was determined from the range of action. The initial data for it were the dimensions of the diagram of the monochromatic sector, the emitting surface of the fire and the range of the complex. The application of this dependence makes it possible to optimize the light field according to the criterion of "range of action – the minimum width of the transition zones" and gives a reference point for adjusting the mutual position of the sectors of the navigation complex. The width of the transition zones between sectors is determined by a change in color or a flash characteristic (Fig. 8). CONCLUSIONS Determination of the spatial distribution of illumination taking into account the visually perceived average brightness of the sector navigation light in the cross section of the sectors making up its light field made it possible to observe that for the considered observation conditions, the width of the transition zones between the sectors of the light field of the SNC is kept within 4–6 angles. min throughout the range. This indicates that there is no noticeable influence of external factors on the angular width of the transitional zones of the light field of the sector navigation complex operating on super-bright LEDs. That is, confirms the high efficiency of the application of the sector navigation system for solving the problems of visual navigation in transport.