appearance op• Data kinds: none → vector (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.grating_wavelengths(pitch_um, sin_in, sin_out, orders=(1, 2, 3)) -> 'np.ndarray' (to call the implementation directly, import matappear; matappear.grating_wavelengths(pitch_um, sin_in, sin_out, orders=(1, 2, 3)) -> 'np.ndarray'; from the registry, opsoptics.get("grating_wavelengths"))
Solve the grating equation d(sinθ_out − sinθ_in) = mλ for λ.
pitch_um: groove spacing d [µm]. 1.6 for CD, 0.74 for DVD (published standard values). sin_in / sin_out: sin of the in-plane component of the incident / outgoing direction along the grating (array allowed, broadcast).
orders: sequence of orders m (0 is excluded because it gives infinity).
Returns: wavelengths [nm] of shape (..., len(orders)). Solutions outside the visible range are returned as they are (if the caller passes them through the colour-matching functions they become 0 automatically — cutting them silently here would hide "why no colour appears").
Every optics op validates its input before computing (nothing slips through silently):
• Units are baked into the argument name — _mm / _um / _deg / _mrad. Confusing mm with µm does not crash; it yields a plausible-looking wrong answer, so the name prevents it. Nothing here guesses the unit from the magnitude.
• Strings raise ValueError — float('50') succeeds, so an unparsed configuration value would slip through as a length (measured: thin_lens('50', '200') returned a plausible 66.667 mm). bool is refused too, as the implicit promotion True == 1.
• complex / masked arrays raise ValueError (real-valued slots only; silently dropping the imaginary part or peeling off the mask is refused). NaN/Inf raises ValueError on every input.
• Division by zero and its relatives are refused by name: focal length 0, radius of curvature 0, refractive index <= 0, a fully opaque aperture (all zeros, so the normalisation is 0/0), a PSF whose sum is <= 0, a Stokes vector with S0 = 0, and an object sitting at the front focal point (the image is at infinity).
• Only two ops return a non-finite value, and both state it as a contract: depth_of_field returns far_mm = inf beyond the hyperfocal distance (that is what the hyperfocal distance means), and gaussian_beam returns wavefront_radius_mm = inf at the waist (the radius of curvature of a plane wavefront). Both also return a finite companion (far_is_infinite / curvature_per_mm). Any other silent NaN/Inf is detected internally and raises ValueError — "float64 overflowed" and "the answer is infinite" are different claims, so the first is never returned wearing the face of the second.
• Size caps: generated grids are capped by optics.MAX_GRID (4096); supplied fields/PSFs/apertures by optics.MAX_FIELD_ELEMENTS (2^24); ABCD element chains by optics.MAX_SYSTEM_ELEMENTS (1024); Zernike by MAX_ZERNIKE_TERMS (512) / MAX_ZERNIKE_ORDER (40) / MAX_ZERNIKE_BASIS (2^25). This closes, fail-closed, the paths where a small argument triggers a huge internal allocation (measured: n_max=40 × 4096² needs 108 GB).
• Physically impossible states are refused too: a Stokes vector with degree of polarisation > 1, negative transmittance, negative intensity, and invalid Zernike indices such as n-|m| odd.
• colorimetry — Colorimetry and spectra — colour is fixed only by spectrum × illuminant × observer
• mv_illumination_practice — Lighting in practice — wavelength, polarisation, drive modes, ambient light, safety
• 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.
• appearance_structural_colour — py -3.11 examples/appearance_structural_colour.py
• poc_beats_fringes_and_screens — py -3.11 examples/poc_beats_fringes_and_screens.py
vector as input)—
appearance)cie_xyz_from_wavelength · spectrum_to_srgb · thin_film_reflectance · grating_rgb · thin_film_rgb · ward_anisotropic
*Provenance: matappear.py — OPTICS 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.