The developed software model environment allows to estimate the power characteristics of background radiation. A method of this model implementation makes it possible to obtain solar radiation indicatrices taking into account scattered radiation from the water surface. The high level of versatility of the model environment enables us to make calculations for any aircraft under different conditions of the water surface in several spectral ranges.

Разработанная программная модельная среда позволяет оценить мощностные характеристики фонового излучения. Метод ее реализации позволяет получать индикатрисы излучения Солнца с учетом отраженного излучения от водной поверхности. Высокий уровень универсальности модельной среды дает возможность проводить расчеты для любых летательных аппаратов при различных состояниях поверхности воды в нескольких спектральных диапазонах.

Aircraft radiation makes a major contribution to spatial energy distribution when simulating background-target environment. Now, there are some studies devoted to calculations and simulation of aircraft engine radiation characteristics [

This study is a follow-up of paper [

Solar radiation is supposed to make a major contribution to background radiation. Solar radiation spectrum I(λ, T) is assumed to correspond to radiation of an absolute black body with the temperature of 6000 K [

(1)

where h – Planck constant, с – light velocity in vacuum, k – Boltzmann constant; Т – temperature, λ – wavelength.

The specific feature of calculation of background radiation above water surface is that it requires simulation of radiation scattered by fogs and mists. Parameters of radiation that has passed through a layer of aqueous aerosols drastically differ from parameters of radiation that has passed through the atmospheric layer consisting of gas molecules only. Hence, they require specific calculation. Scattering of solar radiation by aqueous aerosols is considered as per the Mie theory and formulas (2) and (3) described in [

where Qэкст, Qрас – coefficients of extinction efficiency and radiation scattering by aerosols, respectively, to be calculated using Mie coefficients an, bn; аnd x – parameter defining the ratio of aerosol particle size to radiation wavelength.

Another important factor contributing to the final radiation distribution is radiation reflection from the water surface. In a computational model, the water surface is divided into surface elements, and the resulting reflection is calculated as the sum of reflections from each element. Reflection of each surface is supposed to be the Lambertian reflection, with the reflection coefficients calculated by the Fresnel formulas (4) [

where r||, r ┴ – longitudinal and lateral components of reflected wave amplitude, τ||, τ┴ – longitudinal and lateral components of propagated wave amplitude, α1 – incident angle, α2 – angle of reflection, n1 – refractive index of medium with light propagated before reflection, n2 – refractive index of medium with light propagated after reflection.

The use of surface elements of variable size allows to take into account different grades of water surface swell during simulation. Fig. 1 illustrates an example of water surface formation.

Fig. 1. An example of the water surface divided into polygons for reflection calculation (green, red and blue lines are the axes of Cartesian coordinate system)

In order to demonstrate the simulation results, there is an option for visualization of the resulting radiation. Reflection coefficients were calculated to take into account the intensity of light reflected from different types of water surfaces in several optical ranges. Obtained results (Fig. 2) are used for further simulation of the background-target environment.

The method described in [

Fig. 3. Spectra of solar radiation reaching water surface with account for absorption by the atmospheric air and aerosols, in the range of: а) 0.3–1.0 µm, b) 2–6 µm, c) 8–14 µm

Fig. 4. Dependence of reflected radiation distribution on azimuth at different angles of observation point: а) 30°, b) 40°, c) 60° at 1-grade water surface swell, d) 30°, e) 40°, е) 60° at 5-grade water surface swell

Fig. 5 shows the resulting spectrum of reflected radiation making a major contribution to the background-target environment with the target located above the sea surface. These spectra are determined for nonspecular reflection from the sea surface at the observation angle of 45°, at the distance of 1 km from the surface of reflecting element.

Fig. 5. Spectra of solar radiation reflected by water surface, in the range of: а) 0.3–1.0 µm, b) 2–6 µm, c) 8–14 µm

The software environment which makes it possible to estimate power characteristics of background radiation depending on the observation angle was developed.

The developed software environment is very flexible and allows to conduct calculations with water and solid surfaces being in different states. The developed software environment can be used for creating optoelectronic systems.

The authors declare that there are no conflicts of interest present.