The polar FFT is a special case of the NFFT, where one computes the Fourier
transform on particular grids.
Of course, the polar as well as a so-called pseudo-polar FFT can be computed
very accurately and efficiently by the NFFT.
Furthermore, the reconstruction of a
signal from its Fourier transform
samples on a (pseudo-)polar grid by means of the inverse nonequispaced FFT is
possible under certain density assumptions.
For details see [21] and for further applications
[3].