transform op• Data kinds: image2d → table
• Call: import fullseye as fs; fs.ledger.hankel_image(image, *, center=None, spacing: 'float' = 1.0, n: 'int' = 256, r_max: 'float | None' = None) -> 'dict' (to call the implementation directly, import mathtransforms; mathtransforms.hankel_image(image, *, center=None, spacing: 'float' = 1.0, n: 'int' = 256, r_max: 'float | None' = None) -> 'dict'; from the registry, opsmath.get("hankel_image"))
Obtains the 2-dimensional Fourier transform of an axisymmetric image (a round aperture, a Gaussian blob, diffraction rings) with 1 radial Hankel transform.
The image is split into rings 1 pixel wide by distance from the centre and averaged (radial profile), then passed to hankel_transform (order 0). If axisymmetric, the 2-D transform takes just 1 integral (averaging over rings also reduces noise by 1/√(pixels per ring)), and how far it departs from axial symmetry is returned as a number (asymmetry). The frequency step is about 1/(2·radius), as with the 2-D FFT; it does not get finer.
Args:
image: 2-D real image.
center: centre (row, col). If omitted, the brightness centroid.
spacing: length of 1 pixel (sets the frequency unit).
n: number of samples of the Hankel transform.
r_max: upper limit of the radius used (default = shortest distance from the centre to the image edge; rings with missing corners are not used).
Returns:
nu (frequency), F (radial cross-section of the 2-D Fourier transform, the value of ∬ f e^{−2πi k·x} dx), r, profile (radial profile),
center, asymmetry = ‖image − axisymmetric image rebuilt from the profile‖ / ‖image‖ (0 means axisymmetric; not diluted by a dark background).
Gate: a disc of radius R gives F(ν) = R J₁(2πνR)/ν (Airy), exp(−π r²/σ²) gives σ² exp(−π σ² ν²) (self-dual scaling), and it matches the radial cross-section of the 2-D FFT.
Every mathops op validates its input before computing (nothing slips through silently):
• complex input raises ValueError — coercing to float64 silently discards the imaginary part (numpy only emits a ComplexWarning and returns a plausible-looking wrong real number). State .real/.imag/abs() explicitly, or use complexops, which handles complex data.
• masked arrays with masked elements raise ValueError — the implicit conversion that peels off the mask and uses the raw values underneath is refused. Say explicitly whether to fill or to drop.
• NaN/Inf raises ValueError on every input (refused with the count stated — it propagates through the whole result).
• Shapes are strict: 1-D and 2-D are never implicitly promoted or broadcast (a matrix in a vector slot, or a vector in a matrix slot, raises ValueError; reshape explicitly).
• Size cap: ops that take a matrix, and the stat_histogram bins, raise ValueError beyond mathops.MAX_ELEMENTS (2^26 ≈ 67 million elements).
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• transforms_tour — py -3.11 examples/transforms_tour.py
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
transform)abel_transform · abel_inverse · abel_inverse_image · abel_revolve · hankel_transform · tf_poles_zeros · tf_freq_response · tf_impulse_response
*Provenance: mathtransforms.py — MATH operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.