watermedia op• Data kinds: none → table (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.fresnel_water_air(theta_deg, wavelength_um=0.55, polarization='s', direction='air_to_water', n_water=None) -> 'dict' (to call the implementation directly, import watermedia; watermedia.fresnel_water_air(theta_deg, wavelength_um=0.55, polarization='s', direction='air_to_water', n_water=None) -> 'dict'; from the registry, opsoptics.get("fresnel_water_air"))
• GPU: none (CPU reference implementation only)
Fresnel reflectance and transmittance of the air-water interface -> dict.
theta_deg is the angle of incidence (0 to 90, an array is accepted) on the side the light comes from; direction is air_to_water or water_to_air. The index of water is the real part of the material table at wavelength_um (dispersion included: 1.3435 at 0.40 um, 1.3347 at 0.55 um, 1.3305 at 0.70 um) unless n_water is given. The amplitude coefficients are r_s = (n1 cos i - n2 cos t) / (n1 cos i + n2 cos t) and r_p = (n2 cos i - n1 cos t) / (n2 cos i + n1 cos t); the reflectance is |r|^2 and the transmittance is computed from the transmitted amplitude, T = n2 cos t / (n1 cos i) |t|^2, so R + T = 1 is a check and not a definition. Beyond the critical angle (water to air) the light is totally reflected: R = 1, T = 0, tir is True and the refracted angle is NaN. The table has R, T (for polarization: s, p or their mean unpolarized), R_s, R_p, T_s, T_p, theta_t_deg, tir, n_water, brewster_deg (atan n) and critical_deg (asin(1/n)).
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. Exception, declared: the u_map of bottle_fit_from_pattern takes pixels that could not be measured as NaN (infinity is still refused).
• 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. Exception, declared: bottle_background_map returns NaN in u_mm for pixels whose ray is unusable (total internal reflection and the like), together with a valid mask and the counts.
• 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_water_inspection_images — py -3.11 examples/poc_water_inspection_images.py
• poc_water_transparent_media — py -3.11 examples/poc_water_transparent_media.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
watermedia)ocean_spectrum · ocean_height_field · snell_window · refracted_view · water_attenuation · underwater_image · phase_function_hg · scattering_phase_petzold
*Provenance: watermedia.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.