An Alternative Formulation for Plane-Polar Data Transformation

Author: Scott T. McBride
Publication: AMTA 2023
Copyright Owner: NSI-MI Technologies

There are several applications that require the Fourier transformation from data obtained on a regular polar grid to a regular sine-space grid, and one of these is the processing of plane-polar near-field data. The most common approach to this task is to interpolate from the polar grid to an X-Y grid and then use the conventional 2D Fourier transform.

This paper revisits an alternative algorithm, referred to herein as the polar-coordinate Fourier transform (PCFT), for doing the same transformation from polar input to a regular sine-space output grid. This PCFT has some advantages when processing data undersampled in their angular phi spacing, and appears to offer the possibility of probe correction without having to counter-rotate the probe.

The process of the PCFT is similar to that of the conventional 2D Fourier transform. These two processes are compared.

Rather than interpolating the polar data to the X-Y grid, the PCFT starts with a 1D transform along each diametric spoke of the polar wheel. Each spectral output is then rotated by the corresponding phi angle and interpolated to a common sine-space output grid. If probe-pattern correction is needed for a probe with no extra roll axis, then a notional approach is also described.

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