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.snell_window(depth_m, n_water=None, wavelength_um=0.55, view_angle_deg=0.0) -> 'dict' (to call the implementation directly, import watermedia; watermedia.snell_window(depth_m, n_water=None, wavelength_um=0.55, view_angle_deg=0.0) -> 'dict'; from the registry, opsoptics.get("snell_window"))
• GPU: none (CPU reference implementation only)
Snell's window seen from a point under the surface, and the apparent depth of a flat interface -> dict.
From a depth d below a flat surface the whole sky is squeezed into a cone of half angle theta_c = asin(1/n) (48.6 degrees for n = 1.333, a full angle of 97.2 degrees); on the surface it is a disc of radius d tan(theta_c). Looking down into water from the air at view_angle_deg from the vertical, an object at depth d seems to lie at d tan(theta_w) / tan(theta_a) with sin(theta_a) = n sin(theta_w), which is exactly d cos(theta_a) / (n cos(theta_w)): d / n for near-normal viewing (the paraxial value apparent_depth_factor_paraxial = 1/n) but smaller as the angle grows (the PoC shows the error). The table has critical_deg, window_full_angle_deg, window_radius_m, apparent_depth_factor_paraxial, apparent_depth_factor (at view_angle_deg), apparent_depth_m, paraxial_error (the relative error of the paraxial value) and n_water.
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_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 · 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.