Application of periodic structure scattering in Kelvin ship wakes detection

•An efficient approach to study ship wake detection in SAR by calculating the scattering from periodic surface is presented.•The Kelvin arm wake is simplified reasonably a sinusoidal surface by extracting the height data of ship wake.•The effects of parameters of ship and incident wave on the scattering intensity distribution are discussed, respectively. The traditional research on SAR imaging mechanism for ship wake mostly takes the wake as a whole for electromagnetic scattering simulation analysis. However, this method cannot obtain the scattering characteristics of wake structure effectively. Since the wake includes several types, such as Kelvin wake, turbulent wake, internal wave wake and so on, and each type have their own features, they can be studied according to the characteristics of different types of wakes, so as to enhance the detectability of wakes in remote sensing applications. This paper focuses on electromagnetic scattering of Kelvin wake. Considering the obvious periodic structure, the Kelvin wake model is established to extract the fluctuation data of Kelvin arms, which is approximated to sinusoidal periodic surface by non-linear fitting. Based on Floquet theory, T-matrix method and extended boundary condition method (EBCM), the formula of scattering cross section of a finite periodic dielectric surface is derived, and the correctness of the algorithm is proved by the law of conservation of energy. Furthermore, the scattering cross section of Kelvin arm is simulated by using this algorithm. The effects of ship speed, shape parameters and incident angle on the scattering intensity distribution of wake are analyzed and discussed, respectively.