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.refracted_view(points_xyz, eye_xyz, surface='flat', n_water=None, wavelength_um=0.55) -> 'dict' (to call the implementation directly, import watermedia; watermedia.refracted_view(points_xyz, eye_xyz, surface='flat', n_water=None, wavelength_um=0.55) -> 'dict'; from the registry, opsoptics.get("refracted_view"))
Where an underwater point appears to a camera above a flat or wavy surface (Fermat's principle) -> dict.
points_xyz is (M, 3) (or one point), z up and the mean water level z = 0; eye_xyz is the camera, above the surface. A point with z >= surface height is in the air and is returned unchanged (in_air True, no refraction point). For an underwater point the path from the point to the eye is the one of stationary optical length n |R - P| + |E - R| over the crossing point R on the surface; at that point Snell's law n sin(theta_w) = sin(theta_a) holds. Flat surface: the crossing lies in the vertical plane through the point and the eye and is the unique root of the Snell condition (found by bisection to machine precision); the apparent position is the point seen along the eye ray continued below the surface to the horizontal position of the true point: its depth is x h / (s - x) and tends to d / n for a camera straight above. Wavy surface: surface is a table with height (square, periodic) and extent_m, as returned by ocean_height_field; the crossing is found by Newton iteration on the gradient of the optical path with bicubic heights and normals, started from the flat solution; the vector Snell condition n (d_w x N) = d_a x N is verified at the result and a point that fails it (or does not converge) is returned as NaN with converged False. The table has apparent (M, 3), refraction_point (M, 3), converged, in_air, snell_residual (flat: |n sin(theta_w) - sin(theta_a)|, wavy: the norm of the vector residual), apparent_depth_m and n_water. A caustic can make several paths possible; the one found is the stationary point nearest the flat solution, or (when the Newton iteration fails on steep ripples) the shortest optical path on a local grid.
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_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 · fresnel_water_air · snell_window · 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.