wave op• Data kinds: none → image2d (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.wave_two_slit(wavelength_nm=550.0, slit_sep_um=20.0, distance_mm=200.0, shape=(256, 512), pixel_um=5.0, slit_width_um=2.0) (to call the implementation directly, import mathops; mathops.wave_two_slit(wavelength_nm=550.0, slit_sep_um=20.0, distance_mm=200.0, shape=(256, 512), pixel_um=5.0, slit_width_um=2.0); from the registry, opsmath.get("wave_two_slit"))
Two-slit interference on a screen — built from the physics, not the fringe formula.
Each slit is treated as a line source of the given width; the screen intensity
is `|sum over slit of exp(i k R) / sqrt(R)|**2 with R` the true distance
from each source point. **The textbook spacing `lambda D / d` is nowhere in
this computation** — which is the point: it is then available as an
independent prediction to check the picture against.
★Why this earns its place: :func:wave_fringe_period measures the period
of the produced image, and it must land on `lambda D / d` (in pixels,
`lambda D / (d * pixel)`). Two ways to the same number, only one of which
was used to draw.
Returns an `image2d` normalised to a peak of 1.
Raises `ValueError`: non-positive wavelength, separation, distance,
pixel or width; a grid over the cap; a geometry so coarse that fewer than
three fringes fit on the screen (reported, not silently aliased).
Limits: scalar, monochromatic, far-from-paraxial geometries are not modelled;
the slits are lines, so there is no vertical structure.
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
image2d as input)wave)wave_membrane_mode · wave_mode_frequencies · wave_nodal_lines · wave_fringe_period · wave_grating_orders
*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.