itof 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.itof_unwrap_error_rate(frequencies_hz=(80000000.0, 100000000.0, 120000000.0), phase_sigma_rad=0.05, max_range_m=None) (to call the implementation directly, import itof; itof.itof_unwrap_error_rate(frequencies_hz=(80000000.0, 100000000.0, 120000000.0), phase_sigma_rad=0.05, max_range_m=None); from the registry, opsoptics.get("itof_unwrap_error_rate"))
Estimated probability that multi-frequency unwrapping (maximum-likelihood decoding) picks the wrong wrap order. Returns a table.
> The detailed description below is the original text — the summary and the headings are translated.
周波数を共通の基本周波数の整数倍 f_i = n_i f_g と書くと、非曖昧距離は U = c / (2 f_g)、周期は p_i = U / n_i。折り返さない位相を並べたベクトルは距離 v に比例する直線 v·g(g_i = 2π/p_i)の上にあり、折り返しはこれを 2π m(m は整数のベクトル)だけずらした平行な直線の族を作る。最尤の復号(itof_unwrap_multifreq の "ml")が誤るのは、測った位相が別の直線 v·g + 2πm の方に近いとき。位相雑音 σ_i で割った空間での 2 本の直線の距離を D_m とすると、その 2 仮説の誤りは Q(D_m / 2)(ガウス)。
• union_bound = Σ_m Q(D_m/2)(範囲内で出会う m すべての和。上界)、nearest_term = max_m Q(D_m/2)。
• Wang–Xia(2007)の保証: 周期を p_i = Γ M_i と書く(Γ = U / lcm(n_i))。全周波数の剰余の誤差が Γ/4 未満なら次数は決して誤らない(最も長い周期を錨にする residue_crt の保証)。guaranteed_phase_rad = 各周波数でその境界に当たる位相の誤差 2π (Γ/4) / p_i —— 低い周波数ほど小さい。
*phase_sigma_rad* はスカラ(全周波数で同じ)か周波数ごと。*max_range_m* は探す範囲(既定 U)。
返す dict: unambiguous_range、periods、integers(n_i)、gamma、guaranteed_phase_rad、union_bound、nearest_term、min_distance(最小の D_m)、offsets(m の配列、(M, F))、distances。
Raises ValueError: 周波数が 2 個未満・通約できない・比が細かすぎる / σ が正でない・形が合わない / max_range_m が U より広い。
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_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
itof)itof_capture · itof_phase_amplitude · itof_noise_budget · itof_unwrap_multifreq · itof_multipath_separate · itof_flying_pixel_mask · itof_wiggling_correct
*Provenance: itof.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.