AbstractWe consider the scattering of plane, time‐harmonic electromagnetic waves by a perfect conductor D. We first show that the set ℱλconsisting of the span of a fixed linear combination of the electric and magnetic far‐field patterns is dense in the space of square‐integrable tangential vector fields defined on the unit sphere for all values of the wave number k ≠ 0 provided that Im k ≥0. We next consider the affine hull