spectral op• Data kinds: pairs → pairs
• Call: import fullseye as fs; fs.ledger.kubelka_munk_reflectance(absorption, scattering_per_mm=5.0, thickness_mm=1.0, background_reflectance=0.0, diffuse_factor=2.0) (to call the implementation directly, import spectralrad; spectralrad.kubelka_munk_reflectance(absorption, scattering_per_mm=5.0, thickness_mm=1.0, background_reflectance=0.0, diffuse_factor=2.0); from the registry, opsoptics.get("kubelka_munk_reflectance"))
Diffuse reflectance of a scattering layer in the Kubelka–Munk closed form (from an absorption-coefficient curve).
> The detailed description below is the original text — the summary and the headings are translated.
K = *diffuse_factor* · α(拡散光は斜めに通るので平行光の吸収係数の約 2 倍、Kubelka 1948)、S = *scattering_per_mm*。*thickness_mm*(既定 1 mm)が None なら無限厚 R∞ = 1 + K/S − √((K/S)² + 2K/S)、有限の厚さ X なら背景 R_g の上の層:
R = [1 − R_g (a − b coth(bSX))] / [a − R_g + b coth(bSX)], a = 1 + K/S, b = √(a² − 1)
(Kubelka, J. Opt. Soc. Am. 38, 448 (1948))。極限: X → ∞ で R∞、K → 0 で(SX(1 − R_g) + R_g)/(1 + SX(1 − R_g))、R_g = R∞ なら厚さに依らず R∞。逆は K/S = (1 − R∞)²/(2R∞)。
*absorption* は pairs(λ nm, α 1/mm)(materials.material_nir_absorption の返り値)。*scattering_per_mm* は数か、*absorption* と同じ波長の pairs。
返り値: pairs(λ nm, R)。界面の鏡面反射は含まない(spectral_reflectance_from_material が Saunderson の補正で足す)。
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.
• 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_hyperspectral_foreign_matter — py -3.11 examples/poc_hyperspectral_foreign_matter.py
pairs as input)mtf50 · energy_to_photons · spectral_product · spectral_integral · spectral_stats · hyperspectral_capture · film_thickness_fft · film_thickness_fit
spectral)blackbody_spectrum · cie_illuminant_a · led_spectrum · bandpass_spectrum · silicon_photodiode_qe · energy_to_photons · spectral_product · spectral_integral
*Provenance: spectralrad.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.