MATLAB Code Implementation for Calculating Spherical RCS

In electromagnetic scattering analysis, Radar Cross Section (RCS) serves as a key metric for quantifying target reflectivity. For spherical target RCS calculations, MATLAB enables implementation through two primary approaches: the exact analytical method based on Mie series, and the Physical Optics (PO) method suitable for high-frequency approximation scenarios.

Exact Analytical Method (Mie Theory) The Mie series solution provides a rigorous analytical approach for computing sphere RCS, applicable to spheres of arbitrary size and material parameters. Its core principle involves expanding incident plane waves using spherical harmonic functions and solving scattering field coefficients through boundary conditions. MATLAB implementation requires handling series summation of complex Bessel functions and Legendre polynomials, with truncation order determined by the sphere's electrical size (ka, where k is wavenumber and a is radius). Key functions include besselj() for Bessel functions and legendre() for Legendre polynomials, with convergence typically achieved when truncation order exceeds ka + 10.

Physical Optics Method (PO) The PO method assumes surface currents exist only in illuminated regions (neglecting shadowing and multiple reflections), approximating scattered fields through surface current integration. For spheres, symmetry can simplify integration, though high-frequency approximations lose details like edge diffraction, reducing accuracy at large scattering angles. MATLAB implementation involves discretizing spherical surface meshes using sph2cart() conversions and performing numerical integration with trapz() or integral(). Surface current calculation typically employs tangent plane approximation using cross products of incident wave vectors and surface normals.

Method Comparison Accuracy: Mie solution provides unconditional precision; PO method applies when target size significantly exceeds wavelength, with backscatter RCS (θ=180°) results approaching exact solutions. Efficiency: PO computations require significantly less resources than Mie series (especially for large spheres), but necessitate precision trade-off considerations. Applicability: Mie theory suits academic validation; PO method better aligns with engineering scenarios (e.g., stealth design).

Practical applications often combine both methods: using Mie solutions to validate PO algorithm effectiveness thresholds, then employing PO for accelerated computation of electrically large targets. Extension directions may include bistatic RCS analysis, material coating effects, and polarization-dependent implementations through additional MATLAB function modifications.