Surface tolerance of a radar calibration sphere

The effect of small-amplitude surface irregularities on the backscattering properties of a metal sphere is examined using a full-wave boundary perturbation method. When the irregularities are resolved into their various spherical harmonics, it is shown that their total effect can be expressed as a weighted sum of their individual spectral amplitudes. The behavior of the weight coefficients as a function of both spectral order and frequency is described using graphs and various approximate formulas. This gives the complete description necessary for computing the effect of an arbitrary (small) surface variation for all frequencies from the Rayleigh region through the resonance region to the short wavelength region. The magnitude of the cross-polarized reflected power is included among the effects that can be computed.