light_transport op• Data kinds: table → table
• Call: import fullseye as fs; fs.ledger.predict_fringe_phase_error(transport, period=16.0, triangulation_deg=20.0, projector_width=None, irradiance=1.0) (to call the implementation directly, import lighttransport; lighttransport.predict_fringe_phase_error(transport, period=16.0, triangulation_deg=20.0, projector_width=None, irradiance=1.0); from the registry, opsoptics.get("predict_fringe_phase_error"))
Predict, per camera pixel, the fringe-phase bias and height error that interreflection causes in phase-shifting profilometry, from the light-transport matrix.
A sinusoid of *period* projector pixels illuminates patch i with the complex amplitude ζ_i = n_i·d · mean_footprint(e^{i 2π x / period}). The camera sees Z = T (irradiance · ζ); its direct part is ρ_i · irradiance · ζ_i and the rest is the global phasor. The decoded phase is the argument of the sum (fringe_multipath_phase_error). The height error follows from u = x cos β − z sin β:
Δz = −Δu / sin β with Δu = bias · period · pitch / (2π) (*pitch* = projector pixel in scene units).
*transport* from transport_matrix_radiosity; *projector_width* (default: the number of patches) must match the pattern width given to render_transport for the two to agree.
Returns a dict (a table): bias (rad, (P,)), height_error (scene units, (P,)), direct_amplitude, direct_phase, global_amplitude, global_phase, ratio, worst_case, pitch and x (patch centres).
Raises ValueError: not a transport table; *period* <= 2; *triangulation_deg* outside (0, 80] or a shadowed patch; *projector_width* not an integer in [2, 1<<16]; *irradiance* <= 0.
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
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 · micro_phase_decode
*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.