light_section op• Data kinds: image2d → table
• Call: import fullseye as fs; fs.ledger.laser_line_center_gauss(image, min_peak_rel=0.1, half_window=2) (to call the implementation directly, import lightsection; lightsection.laser_line_center_gauss(image, min_peak_rel=0.1, half_window=2); from the registry, opsoptics.get("laser_line_center_gauss"))
• GPU: none (CPU reference implementation only)
Sub-pixel line centre per column by a Gaussian fit = weighted parabola on ln I (table).
> The detailed description below is the original text — the summary and the headings are translated.
列ごとに最大の行 p のまわり 2·half_window + 1 点で ln I = a + b y + c y² を重み I² の最小二乗で当て(Guo 2011)、中心 p − b / (2c) を返す。half_window=1 は古典の 3 点の対数放物線。正でない画素は外し、3 点未満・c ≥ 0(上に凸でない)・中心が窓の外に出た列は valid=False。
Fits ln I = a + b y + c y² with weights I² (Guo 2011) on 2·half_window + 1 rows around the column's peak; the centre is p − b / (2c). half_window=1 is the classic three-point log-parabola. Non-positive samples are dropped; columns with fewer than three samples, c ≥ 0 or a centre outside the window are valid=False.
★Saturation: as in laser_line_center_centroid the peak is the plateau of rows within 1e-9 of the column maximum; the window runs half_window rows beyond each end of it and the plateau's samples are left out of the fit (clipped values are not the Gaussian — censored). The flanks of a clipped Gaussian still give its centre exactly; a window that holds fewer than three unclipped samples is valid=False (it used to fit the flat top at its first row: −6.2 px, valid=True). saturated (and the plateau handling) uses the rule of laser_line_center_centroid: ≥ 3 rows, or ≥ 2 rows at the image's maximum; other columns are unchanged bit for bit. A two-row plateau at the ceiling cannot be told from an unclipped line centred exactly between two rows, so with fewer than three flank samples (half_window=1) its two samples stay in the fit. A plateau broken by a 1 LSB dip is not detected (see laser_line_center_centroid).
Ground truth (theorem): the log of a Gaussian is a quadratic, so a point-sampled Gaussian line comes back at its sub-pixel centre to 1e-9 px. ★Pixel-integrated (box-filtered) profiles are not exactly Gaussian; the bias is then measured, not zero. Also returns sigma_px (the fitted Gaussian's σ = sqrt(−1/(2c))).
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_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_steger · 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.