watervision 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.bottle_background_map(radius_mm, wall_mm, height_mm, fill_fraction, n_glass, n_liquid, background_distance_mm=150.0, camera_distance_mm=500.0, pixel_pitch_um=20.0, size=None, n_air=1.0) -> 'dict' (to call the implementation directly, import watervision; watervision.bottle_background_map(radius_mm, wall_mm, height_mm, fill_fraction, n_glass, n_liquid, background_distance_mm=150.0, camera_distance_mm=500.0, pixel_pitch_um=20.0, size=None, n_air=1.0) -> 'dict'; from the registry, opsoptics.get("bottle_background_map"))
• GPU: none (CPU reference implementation only)
Where on a flat patterned background each pixel of a (part-)filled bottle looks -> dict (the map u in mm).
The same bottle and camera as bottle_image (outer radius radius_mm, glass wall wall_mm, height height_mm, axis vertical, base at z = 0, pinhole camera_distance_mm from the axis, rows are the horizontal sections, pixel_pitch_um in the plane of the axis, row j at z = height - (j + 0.5) pitch), but instead of a brightness it returns the coordinate u (mm, along the image rows) at which the ray of every pixel meets a flat pattern background_distance_mm behind the axis. A pattern drawn on that plane (stripes, a checkerboard) is then seen at pattern(u): that is the distortion the bottle imposes. The liquid (n_liquid) fills the bottle to fill_fraction * height_mm with a flat surface; no meniscus, no bubbles. The ray of every row is traced through the circles of the section (outer wall, inner wall) with the vector form of Snell's law; the vertical position on the background is the row's own height (the rows are independent, as in bottle_image: no refraction at the shoulder or the base, no tilt out of the section).
The table has u_mm (rows, cols; NaN where the pixel cannot be used), valid (True where u_mm is a number), weight (the Fresnel transmittance product of the ray, 1 outside the bottle; multiply the pattern contrast by it), u_straight_mm (the column coordinate without a bottle, x (dc + db) / dc), x_mm, z_mm, pixel_pitch_mm, fill_row_from_top, liquid_rows, fill_z_mm, the counts tir_rays (rays that met a total internal reflection), backward_rays and unresolved_rays (all of them left NaN, never a guess) and the inputs echoed. Rows of equal geometry are computed once, so they are bit identical. n_glass <= 1, n_liquid <= 1, n_air < 1 or not below both, a fill outside [0, 1], a wall not thinner than the radius, a background not behind the bottle and a camera not further than one diameter 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_bottle_pattern_inverse — py -3.11 examples/poc_bottle_pattern_inverse.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
watervision)caustic_irradiance · bottle_image · fill_level_from_image · bottle_fit_from_pattern · wet_surface_appearance · wet_dry_inspection_pair · underwater_inspection_image · caustic_floor_segmentation
*Provenance: watervision.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.