light_transport op• Data kinds: none → table (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.tof_multipath_phase(amplitudes, path_lengths, modulation_hz=20000000.0) (to call the implementation directly, import lighttransport; lighttransport.tof_multipath_phase(amplitudes, path_lengths, modulation_hz=20000000.0); from the registry, opsoptics.get("tof_multipath_phase"))
Continuous-wave time-of-flight depth when several light paths reach one pixel: the phase of the phasor sum, and its bias against the direct path.
Path k with amplitude a_k and round-trip length L_k (metres) contributes a_k e^{i 2π f L_k / c}; the sensor reports the phase of the sum and converts it to depth c φ / (4π f) (modulo the ambiguity range c / (2f)). Path 0 is the direct one (true depth L_0 / 2). With two paths the bias is atan2(r sin Δ, 1 + r cos Δ) · c/(4π f) (r = a_1/a_0, Δ = the extra phase), positive while 0 < Δ < π.
*amplitudes* and *path_lengths* are (K, ...) (paths first) and broadcast against each other.
Returns a dict (a table): phase ([0, 2π)), depth, true_depth, bias (depth units, from the wrapped phase difference), amplitude and ambiguity_range.
Raises ValueError: non-finite values, fewer than one path, a negative amplitude or a zero direct amplitude, a non-positive path length, shapes that do not broadcast, *modulation_hz* outside (0, 1e10].
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_interreflection_fringe_error — py -3.11 examples/poc_interreflection_fringe_error.py
• poc_itof_multifreq — py -3.11 examples/poc_itof_multifreq.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
light_transport)groove_profile · form_factors_2d · transport_matrix_radiosity · high_frequency_patterns · render_transport · separate_direct_global · fringe_multipath_phase_error · predict_fringe_phase_error
*Provenance: lighttransport.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.