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.cylinder_lens_caustic(radius_mm, n_glass, n_fill=1.0, thickness_wall_mm=0.0, n_rays=41) -> 'dict' (to call the implementation directly, import watermedia; watermedia.cylinder_lens_caustic(radius_mm, n_glass, n_fill=1.0, thickness_wall_mm=0.0, n_rays=41) -> 'dict'; from the registry, opsoptics.get("cylinder_lens_caustic"))
• GPU: none (CPU reference implementation only)
The paraxial focus and the real-ray caustic of a cylinder (a rod or a bottle) in a collimated beam -> dict.
thickness_wall_mm = 0 is a solid rod of index n_glass and outer radius radius_mm; thickness_wall_mm > 0 is a hollow tube of that wall thickness filled with a medium of index n_fill (1.0 = empty, 1.333 = water). The light travels along +z across the axis (at the origin) and is bent in the plane of the section. The paraxial focus comes from the 2x2 ray-transfer matrix of the surfaces (efl = -1/C, back focal distance -A/C); for a solid rod it is the closed form f = n R / (2 (n - 1)) measured from the axis, and for a thin-walled tube filled with n_fill the two-interface limit n_fill R / (2 (n_fill - 1)). The real rays are traced surface by surface with the exact vector form of Snell's law at parallel heights from the axis up to 95 % of the clear aperture (the rod, or the fill); focus_z_mm is where each leaves the cylinder and crosses the axis (distance from the axis, NaN if it does not cross), caustic_z_mm / caustic_y_mm the envelope of neighbouring exit rays. The marginal focus (the highest ray that leaves the cylinder before it crosses the axis) is shorter than the paraxial one (positive spherical aberration). The table also has paraxial_focus_mm (from the axis), efl_mm, power_per_mm (C; an empty thin tube has almost none), efl_closed_form_mm, marginal_focus_mm, longitudinal_aberration_mm, heights_mm, paths_z_mm / paths_y_mm (the ray points from the start to the exit) and exit_dir_z / exit_dir_y. n_glass <= 1, n_fill < 1 and a wall as thick as the radius are refused.
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 · snell_window · refracted_view · water_attenuation · underwater_image · phase_function_hg
*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.