Stationary Phase Derivation for RCS of an Ellipsoid

This letter derives a factor needed to correct an omission in Ruck et al., Radar Cross Section Handbook, Vol. I & II, eq. (5.1-54), for the RCS of an ellipsoid. The derivation goes back to first principles to calculate geometrical optics (GO) expression for the RCS of an ellipsoid by evaluating the physical optics (PO) integral using the stationary phase method. It is shown there is a factor missing from Ruck´s expression. Once this factor is included, the new expression for the bistatic RCS of an ellipsoid correctly reduces to the stated monostatic expression. The new expression also agrees with other published results for the bistatic RCS of the prolate spheroid published Crispin and Siegel, methods of radar cross-section analysis, and Bowman, Senior, and Uslenghi, electromagnetic and acoustic scattering front simple shapes. It also reduces to the special case for RCS of a sphere when the major and minor axes are made equal. This new expression provides a consistent solution that corrects the previous omission and matches (for the special cases) all other previously published bistatic expressions.