interface op• Data kinds: signal → signal
• Call: import fullseye as fs; fs.ledger.fresnel_dielectric(cos_i, n1=1.0, n2=1.5, polarization='unpolarized') -> 'np.ndarray' (to call the implementation directly, import glassmirror; glassmirror.fresnel_dielectric(cos_i, n1=1.0, n2=1.5, polarization='unpolarized') -> 'np.ndarray'; from the registry, opsoptics.get("fresnel_dielectric"))
Fresnel reflectance at a dielectric interface (array-capable, total internal reflection included).
cos_i: cos of the angle of incidence (scalar or array, 0–1).
n1/n2: real refractive index of the incident / transmitted side.
polarization: "unpolarized" (default, mean of s and p) / "s" / "p".
Returns: reflectance R (same shape as cos_i, 0–1). Incidence beyond the critical angle gives exactly 1.0 (total internal reflection).
Cross-check (fixed in tests): at normal incidence ((n1−n2)/(n1+n2))² (air→BK7 = 0.04), at the Brewster angle p polarization is 0 (below 1e-15), beyond the critical angle 1.0. Transmittance is 1 − R (an interface without absorption, so energy is conserved).
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
• poc_pv_thermal_survey — py -3.11 examples/poc_pv_thermal_survey.py
signal as input)emva_photon_transfer · emva_quantum_efficiency · emva_linearity_error · emva_snr_curve · emva_dark_current · cie_xyz_from_wavelength · spectrum_to_srgb · thin_film_reflectance
interface)fresnel_conductor · brewster_angle_deg · critical_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.