light_section op• Data kinds: image2d → table
• Call: import fullseye as fs; fs.ledger.laser_line_center_steger(image, sigma=1.5, min_peak_rel=0.1, max_iter=3) (to call the implementation directly, import lightsection; lightsection.laser_line_center_steger(image, sigma=1.5, min_peak_rel=0.1, max_iter=3); from the registry, opsoptics.get("laser_line_center_steger"))
• GPU: none (CPU reference implementation only)
Sub-pixel line centre by Steger's Hessian method (table).
> The detailed description below is the original text — the summary and the headings are translated.
ガウスの微分(scipy.ndimage.gaussian_filter、σ = sigma)で 1 次・2 次の微分を取り、Hessian の絶対値最大の固有値(明るい線では負)の固有ベクトル n を線の法線とし、2 次の Taylor 展開の極値 t = −(r_x n_x + r_y n_y) / (r_xx n_x² + 2 r_xy n_x n_y + r_yy n_y²) を線の中心とする(Steger 1998)。列ごとに平滑化した画像の最大の行から始め、t n が画素の外(|·| > 0.5)なら隣の画素へ移って max_iter 回まで繰り返し、|t n|∞ が最小の画素の値を採る(中心がちょうど画素の境にあると Newton の 1 歩の行き過ぎで 2 画素の間を往復するので、0.5 の厳密な判定だけでは拾えない —— 実測)。最小でも |t n|∞ > 1(隣の画素より遠い)・固有値が負でない列は valid=False。中心は 2-D の点(col も実数)。
Steger (1998): with Gaussian-derivative filters of scale sigma the line normal n is the eigenvector of the Hessian's largest-magnitude eigenvalue (negative for a bright line), and the centre is the extremum of the second-order Taylor polynomial along n. The point is 2-D (col is sub-pixel too). Also returns strength (−eigenvalue) and the normal nx, ny.
Ground truth (closed form of one Newton step on a Gaussian): for a Gaussian profile of total variance σ² = σ_line² + sigma² and a start pixel at offset δ from the centre, the error is −δ³ / (σ² − δ²) (≤ 0.125/σ² px for |δ| ≤ 0.5). Steger's condition sigma ≥ w/√3 (w = the line's half-width) keeps the profile's second derivative single-signed.
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_light_section_step_weld_floor — py -3.11 examples/poc_light_section_step_weld_floor.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
light_section)laser_line_center_centroid · laser_line_center_gauss · light_section_rig · light_section_targets · light_section_render · light_plane_calibrate · light_section_profile · light_section_scan
*Provenance: lightsection.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.