appearance op• Data kinds: signal → signal
• Call: import matappear; matappear.thin_film_reflectance(nm, thickness_nm=350.0, n_film=1.33, n_sub=1.0, cos_theta=1.0, n_out=1.0) -> 'np.ndarray' (or opsoptics.get("thin_film_reflectance"))
The spectral reflectance of a thin film (thickness d, index n_film). The closed Airy (multiple-reflection) form.
> The detailed description below is the original text — the summary and the headings are translated.
nm: 波長 [nm] (配列可)。
thickness_nm: 膜厚 [nm]。シャボン玉なら 200–800、陽極酸化被膜なら 50–300。
n_film/n_sub/n_out: 膜 / 基板 / 入射側の屈折率(実数、吸収なし)。
cos_theta: 入射側での入射角の cos(配列可、nm とブロードキャストできる形)。
返り値: 反射率 R(0–1)。nm と cos_theta のブロードキャスト形。
物理: 膜内の伝搬による位相差 δ = 2π·(2 n_film d cosθ_film)/λ。境界のフレネル係数
(s 偏光と p 偏光の平均 = 無偏光)を r1, r2 として R = |r1 + r2 e^{-iδ}|² / |1 + r1 r2 e^{-iδ}|²。
λ/4 の奇数倍で反射が極大(n_film > n_sub のとき)になり、厚みを変えると色が動くのが
シャボン玉の色。膜厚 0 では R が基板単体のフレネル反射に一致する(テストで確認)。
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 — 測色と分光の知識 — 色は「分光 × 光源 × 観測者」でしか決まらない
• mv_illumination_practice — 照明の実務知識 — 波長・偏光・点灯方式・外光・安全
• 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
signal as input)cie_xyz_from_wavelength · spectrum_to_srgb · fresnel_dielectric · fresnel_conductor · metal_optical_constants · beer_lambert_transmittance · slab_transmittance · prism_min_deviation_deg
appearance)cie_xyz_from_wavelength · spectrum_to_srgb · grating_wavelengths · 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.