lockin op• Data kinds: table → table
• Call: import fullseye as fs; fs.ledger.lockin_ring_normals(demod, zenith_deg) -> 'dict' (to call the implementation directly, import lockin; lockin.lockin_ring_normals(demod, zenith_deg) -> 'dict'; from the registry, opsoptics.get("lockin_ring_normals"))
Surface normals from the first-harmonic response of a dipole-modulated ring -> dict of maps.
For a Lambertian pixel with unit normal n = (n_x, n_y, n_z) under a ring of sources at zenith angle zeta modulated with multipole 1, the response at the modulation frequency is z = A exp(j phi) = (rho / 2) sin(zeta) (n_x - j n_y) and the DC is rho cos(zeta) n_z (per unit ring power). The albedo rho cancels: (n_x - j n_y) / n_z = 2 z / (DC tan zeta). demod is the table of lockin_demodulate. The result has height_gradient_x / height_gradient_y (-n_x / n_z, -n_y / n_z), normal (H, W, 3), tilt_deg, azimuth_deg (direction of the height gradient) and valid. A pixel is valid only if no source of the ring is in shadow, which is A / DC < 1/2 (tilt below 90 - zenith_deg); the other pixels, and pixels with DC <= 0, are NaN in every map and False in valid: the model does not apply there.
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_lockin_imaging — py -3.11 examples/poc_lockin_imaging.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
lockin)lockin_demodulate · lockin_amplitude · lockin_phase · lockin_noise_floor · lockin_walsh_codes · lockin_separate · lockin_ring_synthesize · lockin_thermal_wave
*Provenance: lockin.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.