lockin op• Data kinds: video → table
• Call: import fullseye as fs; fs.ledger.lockin_separate(video, codes) -> 'dict' (to call the implementation directly, import lockin; lockin.lockin_separate(video, codes) -> 'dict'; from the registry, opsoptics.get("lockin_separate"))
Separate coded lights and the uncoded rest by least squares against zero-mean codes -> dict of maps.
Models every pixel as x_k = dc + sum_l a_l code_l[k] and solves for dc and the coefficients a_l by least squares (so the codes need not be orthogonal, only independent of each other and of a constant). A light switched on where code is +1 and off where it is -1 with on-state image L has a = L / 2 (on_image = 2 a). The table holds coefficients (n_codes, H, W), on_image (the same times 2), dc (uncoded mean level: ambient plus half of every coded light), residual_rms (what the model does not
explain: a flicker or drift the codes do not carry) and condition (of the design matrix). Codes that are constant, of the wrong length, or so dependent that condition exceeds 1e8 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_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_ring_synthesize · lockin_ring_normals · 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.