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The process of spherical scanning in the near field of an antenna to infer the far field can be drastically simplified, both in theory and in practice. The three cartesian components of the electric field are measured separately. For example, to measure Ex the small dipole probe of an optically modulated scatterer is set parallel to Ox and is moved over a sphere by the use of pre-programmed xyz translational motions; thus it is automatically kept aligned in the same direction. This contrasts with conventional spherical scanning, where a directional receiver is kept pointing toward the centre. To distribute the sampled points evenly over the sphere a new method, based on the Fibonacci series, is suggested. The results are extrapolated to infer the far field for Ex. Further scans deal with the components Ey and Ez. Only the scalar wave equation need be used, no spherical vector components are necessary, and there is no probe correction to make, because there is virtually no interaction between the probe and the system being measured. The same near-field scanning method can be used to infer the far field of a passive scatterer, simply by subtraction of the incident field. The method has been tested with both simulated and real data for the scattering of a parallel beam by a metal strip, and with simulated data for a spherical scan around a four-point source.