wave op• Data kinds: none → table (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.wave_grating_orders(pitch_um=1.6, wavelength_nm=550.0, sin_in=0.0, orders=(-2, -1, 1, 2)) (to call the implementation directly, import mathops; mathops.wave_grating_orders(pitch_um=1.6, wavelength_nm=550.0, sin_in=0.0, orders=(-2, -1, 1, 2)); from the registry, opsmath.get("wave_grating_orders"))
Where a grating sends each order: `d (sin_out - sin_in) = m lambda` solved for the angle.
The companion to the existing `grating_wavelengths` (which solves the same
identity for *lambda*): given the pitch and the wavelength, this returns the
outgoing direction of each order, and marks the orders that are
evanescent — `|sin_out| > 1` means that order does not propagate, which
is why a CD shows fewer colours at grazing incidence.
★Why this earns its place: the two ops invert one another, so a round trip
must return the wavelength it started from; and the angles can be compared
against the peak positions of a *simulated* far field (the existing
`fraunhofer_pattern` of a real grating aperture), which knows nothing about
the grating equation.
Returns a `table: order, sin_out, angle_deg` (NaN when
evanescent), `propagates`.
Raises `ValueError: non-positive pitch or wavelength; |sin_in| > 1`;
order 0 alone with no others (it is always the specular direction — allowed,
but a caller asking only for it probably meant something else); non-finite input.
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.
• poc_beats_fringes_and_screens — py -3.11 examples/poc_beats_fringes_and_screens.py
table as input)wave)wave_membrane_mode · wave_mode_frequencies · wave_nodal_lines · wave_two_slit · wave_fringe_period
*Provenance: mathops.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.