shape_from_polarization op• Data kinds: image2d → image2d
• Call: import fullseye as fs; fs.ledger.sfp_dolp_model(zenith_deg, refractive_index=1.5, model='specular') (to call the implementation directly, import sfpolar; sfpolar.sfp_dolp_model(zenith_deg, refractive_index=1.5, model='specular'); from the registry, opsoptics.get("sfp_dolp_model"))
Degree of linear polarisation of reflected (specular) or emitted (diffuse) light versus zenith angle, from the Fresnel equations.
*zenith_deg* is the angle between the surface normal and the viewing direction, in degrees, 0 <= zenith <= 90 (a scalar or an array of any shape — an (H, W) zenith map gives an (H, W) DoLP map).
model="specular": (R_s - R_p) / (R_s + R_p) for light reflected off a dielectric of index *refractive_index*. It rises from 0 at normal incidence to exactly 1 at Brewster's angle atan(n) (R_p = 0) and falls back to 0 at grazing incidence — so one DoLP value has two zenith angles.
model="diffuse": (T_p - T_s) / (T_p + T_s) for light scattered inside the body and refracted out through the surface. It rises monotonically from 0 to (n^2 - 1)/(n^2 + 1) at 90 degrees (0.385 for n = 1.5) — weaker, but one value has one angle.
Returns a float64 array of the input's shape (a 0-d array for a scalar).
Raises ValueError: zenith outside [0, 90] or non-finite; *refractive_index* not a finite real > 1; unknown *model*.
*refractive_index* (here and in every op of this module) may also be a material name of the shared table materials (e.g. "N-BK7", "PMMA", "WATER"): its index at the d line (587.56 nm) is used. Metals and materials that absorb there 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.
• 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_shape_from_polarization — py -3.11 examples/poc_shape_from_polarization.py
image2d as input)fraunhofer_pattern · pupil_psf · pupil_blur · psf_to_mtf · edge_spread · veiling_glare_index · emva_pair_statistics · emva_defect_pixels
shape_from_polarization)dolp_to_zenith · aolp_to_azimuth · sfp_render · sfp_normals · sfp_disambiguate · sfp_estimate_index · sfp_height
*Provenance: sfpolar.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.