lockin op• Data kinds: video → table
• Call: import fullseye as fs; fs.ledger.lockin_demodulate(video, f_ref, fps, window='rect') -> 'dict' (to call the implementation directly, import lockin; lockin.lockin_demodulate(video, f_ref, fps, window='rect') -> 'dict'; from the registry, opsoptics.get("lockin_demodulate"))
Per-pixel quadrature demodulation of an image sequence against a sinusoidal reference -> dict of maps.
For every pixel the sequence is correlated with cos and sin of the reference frequency:
x_k = DC + A cos(2 pi f_ref k / fps + phi). The table holds amplitude (A), phase (phi in radians, (-pi, pi]; 0 where A is 0), dc, in_phase (A cos phi), quadrature (A sin phi) and the scalars periods (reference periods in the sequence), window, leak_image and leak_dc.
The window is declared. rect is exact (a sinusoid of amplitude 2.5 and phase 0.7 rad is returned to 1e-15) but only for a whole number of periods; any other length is refused with the nearest frame counts named. hann takes any length of at least one period and states what it leaks:
leak_image (the conjugate image of the reference, relative to its amplitude) and leak_dc (a DC offset enters the quadrature sum by 2 leak_dc times its size).
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_amplitude · lockin_phase · lockin_noise_floor · lockin_walsh_codes · lockin_separate · 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.