Glossary

Angular harmonic

An integer Fourier channel \(m\) multiplying \(e^{im\theta}\).

Mode power

\(P_m=\int|\rho_m(r)|^2r\,dr\). PETAL2D power fractions are normalized by \(\sum_mP_m\).

Power centroid

The first spatial moment of \(|f|^2\), used by origin="centroid".

Domain consistency

Ratio of physical \(L^2\) weight in the analyzed polar domain to that in the supplied Cartesian domain.

Selected pair

An adaptive real-field selection unit \((m,-m)\). \(m=0\) and the even-grid Nyquist mode are singletons. Complex fields use singleton channels.

Nyquist mode

The highest discrete angular frequency class. For even Ntheta, NumPy represents it by -Ntheta/2.

Power-support radius

Smallest radius enclosing the configured fraction of integrated radial mode power.

Amplitude-support radius

Outermost radius where the mode amplitude remains above the configured fraction of its peak.

Cutoff radius

The larger of the power-support and amplitude-support radii. It marks a radius beyond which both configured radial-tail criteria are satisfied. It does not truncate the reconstruction.

Interpolation leakage

Spurious angular spectral weight introduced when a sampled Cartesian field is interpolated to a polar grid.