interface op• Data kinds: none → measurement (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.critical_angle_deg(n1=1.5, n2=1.0) -> 'float' (to call the implementation directly, import glassmirror; glassmirror.critical_angle_deg(n1=1.5, n2=1.0) -> 'float'; from the registry, opsoptics.get("critical_angle_deg"))
Critical angle of total internal reflection [deg] = asin(n2/n1). Raises ValueError unless n1 > n2 (it does not exist otherwise).
> The detailed description below is the original text — the summary and the headings are translated.
ガラスから空気へ出るときだけ起きる。光ファイバ・プリズムの全反射面の設計値。
式: `degrees(asin(n2 / n1))`。入射角(法線からの角)がこれ以上なら屈折光が
存在せず全反射する。例: N-BK7 相当 `n1 = 1.5 → 空気 n2 = 1.0` で 41.8 度、
水 `n1 = 1.333` → 空気で 48.6 度。
• `n1: 光が出ていく側(密な媒質)の屈折率、n2`: 入る側(疎な媒質)の屈折率。
どちらも正の有限スカラ(`float()` で変換するので配列は受けない)。
• `n1 <= n2 は臨界角が存在しないので ValueError(NaN` や 90 度で
ごまかさない)。
• 返り値: float [deg]、`(0, 90)`。
• 波長依存は入れない。分散込みで評価するなら硝材の Sellmeier から求めた
`n1 を渡す(prism_min_deviation_deg` は内部でそれをやる)。
`fresnel_dielectric に臨界角以上の cos_i` を渡した場合の挙動はそちらを参照。
Brewster 角(p 偏光の反射が 0 になる角)は `brewster_angle_deg`。
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.
• glass_and_mirror_optics — py -3.11 examples/glass_and_mirror_optics.py
measurement as input)—
interface)fresnel_dielectric · fresnel_conductor · brewster_angle_deg
*Provenance: glassmirror.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.