J. Eur. Opt. Society-Rapid Publ. 22, 32( 2026) 331
Figure 9. Calculation results of ship temperature distribution.( a) Spring.( b) Summer.( c) Autumn.( d) Winter.
both diffuse and specular reflection occurring on the object’ s surface [ 32 ].
Figure
10. The solar incident radiation.
determined by the target radiance. When the target does not completely cover a pixel, the radiation intensity of the pixel is the weighted average of the target and the background radiation, and the weight is determined by the area of the target in the pixel.
To verify the accuracy of the calculation model in this paper, the working conditions given in reference [ 31 ] are used to reproduce the ship deck temperature using the model in this paper. Four representative typical moments from the literature are selected for simulation, and the average deck temperature at the corresponding moments is calculated. The temperatures calculated in this study are 304.67 K and 280.51 K at 12:00 in summer and winter, respectively, with relative errors of 0.88 % and 0.53 % compared with the results in reference [ 31 ]. At the thermal crossover moment in summer( 07:00) and winter( 08:00), the temperatures calculated in this paper are 292.08 K and 274.88 K, respectively, with relative errors of 0.72 % and 0.04 %. The maximum relative error between the calculation results and the measurement data does not exceed 0.88 %.
3.2 BRDF modeling of ship target
The Cook-Torrance model is used to calculate the reflected radiation from the ship target surface, taking into account
BRDF t ðk; h i; u i; h r; u r
Þ ¼ k d I l ðn lÞþk s I l F D G
ð19Þ p ðn lÞðn vÞ
where k d and k s are the diffuse and specular reflection coefficients of the object surface, respectively; I l is ambient light intensity; F is the Fresnel reflection coefficient; D is the micro-facet distribution function; G is the shading factor; n is the normal direction of the micro-facet; l is the direction vector of the incident light; and v is the observation direction vector. F depends on the properties of the surface material.
4 Modeling of ambient light radiation characteristics
4.1 Modeling of solar radiation characteristics
Solar radiation is the primary energy source for the Earth ' s surface, and its intensity and distribution are influenced by latitude, time of day, and atmospheric conditions. In addition, changes in the incident angle and elevation angle of solar radiation, as well as the concentration of suspended particles such as dust and haze in the atmosphere, also play an important role in the intensity and propagation characteristics of radiation. When solar radiation passes through the atmosphere, it is attenuated by substances such as aerosols, clouds, water vapor, and dust, resulting in the absorption or scattering of some of the radiant energy. The solar altitude angle and azimuth angle are calculated based on the local time and the latitude and longitude of the scene [ 33 ].
sin h ¼ sin u sin d þ sin u cos d cos t ð20Þ
where h is the solar altitude angle; φ is the latitude of the observation point; δ is the solar declination; t is the local