shape_from_polarization op• Data kinds: normalmap → image2d
• Call: import fullseye as fs; fs.ledger.sfp_height(normals, mask=None, max_zenith_deg=88.0) (to call the implementation directly, import sfpolar; sfpolar.sfp_height(normals, mask=None, max_zenith_deg=88.0); from the registry, opsoptics.get("sfp_height"))
Integrate a normal map to a height map with Frankot-Chellappa on a mirror-extended domain, so the periodic boundary of the FFT does not bend the result.
Gradients p = -nx/nz, q = -ny/nz are formed inside *mask* (zero outside — the object stands on a flat background); slopes steeper than *max_zenith_deg* (the occluding rim, where nz -> 0 and the gradient diverges) are clamped to that zenith with the azimuth kept. The field is then reflected into a 2H x 2W even-symmetric domain (p changes sign under the mirror in x, q under the mirror in y) and handed to photometric.integrate_gradients — the same Frankot-Chellappa solver, without its wrap-around. Measured on a 64 x 80 tilted plane (slopes 0.3 and -0.2): largest height error 0.06 px here against 18 px with the periodic solver, which cannot represent a ramp at all (the residual 0.06 px is the kink of the half-sample mirror at the seam).
Returns (H, W) float64 heights in pixel units (multiply by the pixel pitch), with the background (outside *mask*) at mean 0, or the whole image at mean 0 when there is no mask.
Compared with photometric.integrate_normals (registered in ops3d):
that operator integrates as is (periodic, no validation, no rim clamp); this one validates the field (unit, finite, facing the camera) and fixes the boundary.
Raises ValueError: *normals* not a finite (H, W, 3) field of unit normals with nz >= 0; *mask* not boolean of shape (H, W) or empty; *max_zenith_deg* outside (0, 90).
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_phase_measuring_deflectometry — py -3.11 examples/poc_phase_measuring_deflectometry.py
• 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)sfp_dolp_model · dolp_to_zenith · aolp_to_azimuth · sfp_render · sfp_normals · sfp_disambiguate · sfp_estimate_index
*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.