itof op• Data kinds: table → table
• Call: import fullseye as fs; fs.ledger.itof_multipath_separate(phasors, frequencies_hz=None, n_paths=2, pencil=None) (to call the implementation directly, import itof; itof.itof_multipath_separate(phasors, frequencies_hz=None, n_paths=2, pencil=None); from the registry, opsoptics.get("itof_multipath_separate"))
Phasors measured at equally spaced frequencies → depth and strength of each path (matrix pencil). Returns a table.
> The detailed description below is the original text — the summary and the headings are translated.
画素に経路 p(距離 d_p、強さ a_p)の光が入ると、周波数 f のフェーザは m(f) = Σ_p a_p e^{i 4π f d_p / c}。周波数が等間隔 f_k = f_0 + kΔf なら m_k = Σ_p α_p z_p^k(z_p = e^{i 4π Δf d_p / c}、α_p = a_p e^{i 4π f_0 d_p / c})という減衰しない指数の和になり、行列ペンシル(Hua & Sarkar 1990)で z_p が閉形式に出る:
1. 粗い距離 d_p = arg(z_p) · c / (4π Δf)(周期 c/(2Δf) の剰余)。
2. Vandermonde の最小二乗で α_p。|α_p| が強さ。
3. 細かい距離: 中央の周波数 f_c を原点にした arg(α_p) は周期 c/(2f_c) の剰余を教えるので、粗い距離に最も近い次数を選んで精密化する(粗い距離の誤差が c/(4 f_c) を越えると次数を誤る —— 雑音が大きいときは depth_coarse も見ること)。
経路は距離の近い順に並べる。経路が 1 本しか無い画素では、2 本目の強さが 0 近くに出る。★分けられるのは、2 つの経路の距離の差がおおよそ帯域の分解能 c / (2 F Δf) より大きいときだけ(等間隔 F 周波数の幅が帯域)。それより近い経路は雑音があると 1 本に潰れる。
*phasors* は itof_phase_amplitude の表(phasor と周波数を使う)か、複素の (F, ...) 配列。*pencil* はペンシルの幅 L(既定 F // 2、n_paths <= L <= F − n_paths)。
返す dict: depth (P, ...)、depth_coarse、amplitude (P, ...)、residual(当てはめの相対残差)、ambiguity_coarse(c/(2Δf))、resolution(c/(2FΔf))。
Raises ValueError: 周波数が等間隔でない・2·n_paths 個未満 / 形が合わない / n_paths が 1〜8 でない / pencil が範囲外 / 画素数が上限を超える。
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_unwrap_error_rate · 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.