shape_from_polarization op• Data kinds: image2d → table
• Call: import fullseye as fs; fs.ledger.aolp_to_azimuth(aolp_deg, model='diffuse') (to call the implementation directly, import sfpolar; sfpolar.aolp_to_azimuth(aolp_deg, model='diffuse'); from the registry, opsoptics.get("aolp_to_azimuth"))
Turn the angle of linear polarisation into the two candidate azimuths of the surface normal (the pi ambiguity), diffuse and specular differing by 90 degrees.
Diffuse light leaves polarised in the plane of incidence, so the normal's image-plane azimuth is phi = psi or psi + 180; specular reflection is polarised across it, so phi = psi + 90 or psi + 270. Angles are measured from the image x axis (columns) toward the y axis (rows), the same sense as atan2(ny, nx) of a photometric normal map.
Returns a dict: azimuth_deg (2, *aolp.shape) in [0, 360) (row 1 is row 0 plus 180), offset_deg (0 or 90) and model. The pi ambiguity is a property of a linear polariser — psi and psi + 180 are the same measurement — and no setting of this operator removes it; that
is sfp_disambiguate's job.
Raises ValueError: non-finite or non-real *aolp_deg*; unknown *model*.
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
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
shape_from_polarization)sfp_dolp_model · dolp_to_zenith · 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.