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References in periodicals archive ?
FIAFTA relates the plane wave spectrum and the near-field samples using the diagonal translation operator [T.sub.L]([??], [r.sub.M]) (known from the Fast Multipole Method [24]) according to
The error in the plane wave spectrum [[??]'.sub.err] computed by solving
Therefore, the estimated error in the plane wave spectrum for the same inaccuracy in the probe output can differ for different measurement surfaces.
The use of the synthetic approach allows us to compare the estimated error with that of the observed error in the plane wave spectrum. The reference plane wave spectrum [[??]'.sub.ref] using ideal near-field data is compared with the erroneous plane wave spectrum Jo and the "reference" maximum and mean error is computed as
Another realization but using the same standard deviation is used to compute the error in the plane wave spectrum. The observed error in the plane wave spectrum using perturbed near-field data and the estimated error using only the error distribution in the probe output for spherical measurements are then compared.
The erroneous plane wave spectrum [J'.sub.o] is determined using the perturbed probe pattern.
The plane wave spectrum on the plane z = [z.sub.0] is given as
The resultant plane wave spectrum of the intensity pattern is shown in Figure 7, with the required spectrally filtered data highlighted.