Abstract: A scanning measurement apparatus and method comprising a device under test for receiving or transmitting a signal, a measurement probe, a robot for moving the device or the probe relative to one another to scan continuously over a two-dimensional planar, cylindrical or spherical surface in a three-dimensional space, and a controller for obtaining measurement samples at generalized grid points on the two-dimensional surface computing characteristic coefficients from the measured values, wherein the characteristic coefficients are recovered using a conjugate gradient method, using in part an unequally spaced fast Fourier transform or using a conjugate gradient method and an unequally spaced fast Fourier transform.