Hybrid methods for composite scattering from conductive target above a rough surface

. A hybrid method combining the method of moment (MoM) and physical optical (PO) is used to compute the scattering from 3D conductive target above a rough sea surface in this paper. Firstly, the composite model of 3D conductive target above the sea surface is constructed. The rough sea surface is simulated by the Pierson- Moscowitz spectrum and Monte- Caro method. The target is divided into MoM region and the rough sea surface is divided into PO region. Then, the current on the facet of target is obtained by MoM method and the current on the facet of rough surface is obtained by PO approximation. Compared to the method of moment, the hybrid MoM-PO method proves to be high accurate and efficient. Finally, composite scattering under different condition are studied in detained.


Introduction
The composite scattering from the target above the rough surface has been widely used in radar detection、ground remote sensing, et al [1] [2] . The fast multiple method (FMM) [3] and the forward and backward iterative algorithm [4] is of high accuracy for computing the composite scattering. However, they are hard to meet the need of computing the composite scattering with the electrically large size rough surface. The reciprocity theorem method combining the Kirchhoff approximation is of high efficiency for computing the composite scattering [5] . However, they are not accurate enough. The method of moment combining the Kirchhoff approximation (MoM-KA) is used to calculate the composite scattering from a 2D conductive target above a 1D rough surface by R Wang [6] , which is of high accuracy and efficiency. Nevertheless, more complex 3D problems for composite scattering are rarely studied in previews paper.
In this paper, a MoM-PO hybrid method is used to calculate the scattering from the 3D conductive target above a rough sea surface. The composite model is divided into MoM region for the method of moment and PO region for PO approximation. Compared to the traditional MoM, this hybrid method is accurate and efficient. The definition of the e L and h L is:

Composite Model
Where, The electric increment on rough sea surface that excited by the scattering field from the target is: Where, Hr is the incident magnetic field. By plugging the equation (1) into equation (6), the electric current coefficient on the rough sea surface is: Where,   S ,which contains the interaction between the incident waves and the rough sea surface. By solving the equation (15), the electric coefficient can be obtained, and then the electric current on the facet of target and rough surface are obtained furthermore. The remote composite scattering field for target above rough surface is obtained by Stratton-Chu equation [8] .

Numerical Results
In this paper, the parameter are set as: working frequency is f=0.3GHz, g=L/4, the polarization of the incident waves is VV polarization, the size of the rough surface is L x ×L y =100λ×100λ.

Validation Of Hybrid Method
As we see, the comparison results of the MoM method and the MoM-PO hybrid method for scattering from a cubic above a rough surface is shown in figure 2. In the example, the length of the cubic is l=2λ, altitude of the target from underlying rough surface is H=6λ, the polarization model is Verticval-to-vertical (VV) polarization, the incident angle is θ in =45 0 , the root mean square is δ=0.1λ, the correlation of rough surface is l x × l y =1.0λ. Compared to the method of moment, the MoM-PO hybrid method proves to be accurate and efficient. what's more, the MoM-PO hybrid method have great advantages in decreasing the computing time and storage requirement.  Figure 3. illumination of the composite scattering from target above the rough surface with different root mean square.

Numerical Results With Different Parameter Of Target
As we see, composite scattering from a cubic above a rough surface with different root mean square is shown in figure 3. The altitude of the target above rough surface is

 =
，the other parameter is as same as figure 2. As we see, with the root mean square of rough surface increases, the roughness of the rough surface increases, which contributes to specular scattering decreasing and backward scattering getting larger.

Conclusions
In this paper, a hybrid method combining the method of moment (MoM) and physical optic (PO) is proposed to solve the composite scattering from a 3D conductive target above a sea surface. Firstly, a composite model of target above the rough surface is constructed. The target is divided into MoM region, the rough surface is divided into PO region. Then, the electric current on the facets of target is obtained by MoM method, and the electric current on the facet of rough surface is obtained by PO method. Compared to MoM method, the hybrid method proves to be accurate and efficient. Finally, composite scattering from target above rough surface with different root mean square is analyzed in detain.