itof op• Data kinds: table → table
• Call: import fullseye as fs; fs.ledger.itof_phase_amplitude(samples, frequencies_hz=None, phase_offsets_rad=None, read_noise_e=None) (to call the implementation directly, import itof; itof.itof_phase_amplitude(samples, frequencies_hz=None, phase_offsets_rad=None, read_noise_e=None); from the registry, opsoptics.get("itof_phase_amplitude"))
• GPU: none (CPU reference implementation only)
K-step raw signal → phase, amplitude, offset, wrapped depth and a per-pixel depth-noise estimate (table).
> The detailed description below is the original text — the summary and the headings are translated.
*samples* は itof_capture の dict、または (F, K, ...) の配列(周波数 F、段 K が先頭。1 周波なら samples[None])。段 k のバケットを m_k = B + A·cos(φ − θ_k) とみなし、[1, cos θ_k, sin θ_k] の最小二乗で B・A cos φ・A sin φ を解く(θ_k が等間隔 2πk/K なら DFT と同じ。4 段なら φ = atan2(m1 − m3, m0 − m2)、A = ½√((m0 − m2)² + (m1 − m3)²)、B = Σm_k / 4)。θ_k は *phase_offsets_rad*(既定は等間隔、dict ならその値)。
距離の雑音の見積もり: 各バケットの分散を B + read_noise²(ショット雑音は平均に等しい)とみなすと、最小二乗の共分散から位相の標準偏差 σ_φ が出る(4 段・等間隔なら σ_φ = √((B + σ_r²)/2) / A)。σ_d = c σ_φ / (4π f)。★小さい雑音の近似で、A ≈ √B 程度まで SNR が落ちると実際の散らばりはこれより大きい。
返す dict: kind("itof_phase")、phase (F, ...) [0, 2π)、amplitude、offset、phasor (A·e^{iφ}、複素)、frequencies_hz(分かれば)、wrapped_depth と ambiguity_range(周波数が分かれば)、phase_sigma、depth_sigma(周波数が分かれば)。
★振幅が無い画素・飽和の印(2026-11-09):
• A ≤ 1e-9 · max_k |m_k|(その画素のバケットの大きさに対して丸め屑)の画素は A = 0 と同じに扱い、phase 0・phase_sigma / depth_sigma は inf。全バケットが等しい(完全に飽和した) 画素は A が丸め屑 6e-13 で A > 0 を通り、位相 0.49 rad・距離 0.59 m というでたらめの値を有限の depth_sigma(1e14)つきで返していた。
• offset B ≤ 0 で読み出し雑音が 0 の画素(暗電流を引いたデータ)は分散を見積もれないので phase_sigma inf(以前は 0 =「雑音ゼロ」と主張していた)。
• saturated (F, ...) bool: その画素のどれかのバケットが配列全体の最大値と等しく、かつその最大値に 2 つ以上の標本が並ぶ(= 天井がある)。full well を知らないので天井から推す印で、valid は無い(値は変えない)。バケットの 40 % がクリップされた画素は距離が最大 12 cm ずれても depth_sigma は 3.3 cm のまま(式は飽和を知らない)—— この印を見て捨てる。★雑音のない整数の画像で、飽和していないのに最大値がたまたま 2 回出ると誤って印が付く(雑音ありの 240×320 で 10 枚中 1 枚・2 画素)。★見逃しは黙る(独立レビュー 2026-11-09): クリップの後に画素ごとの暗電流を引いたデータは天井が 1 つの値でなくなり、5 画素中 1 画素にしか印が付かない。天井より明るい画素が 1 つでもある(露光を合成した HDR など)と最大値が天井でなくなり、印は全部消える。どちらも飽和の判定は補正前の生データ(または full well を知る呼び手)でする。
Raises ValueError: 配列が 2 次元未満・非有限 / 段の数が 3〜32 でない / 段の位相が退化 / 周波数の数が F と合わない・範囲外 / dict が生信号でない。
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. Exception, declared: the u_map of bottle_fit_from_pattern takes pixels that could not be measured as NaN (infinity is still refused).
• 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. Exception, declared: bottle_background_map returns NaN in u_mm for pixels whose ray is unusable (total internal reflection and the like), together with a valid mask and the counts.
• 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_3d_sensor_modalities — py -3.11 examples/poc_3d_sensor_modalities.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
itof)itof_capture · itof_noise_budget · itof_unwrap_multifreq · itof_unwrap_error_rate · 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.