light_section 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.light_section_uncertainty_budget(wavelength_um=0.65, sin_u_obs=0.1, sin_theta=0.5, line_width_um=40.0, pixel_um=1.0, length_um=None, n_patterns=1, polarizations=1, noise_rel=0.0, peak_dn=None, window_rows=160, calib_rms_um=0.0, calib_dof=inf, speckle_contrast=None) (to call the implementation directly, import lightsection; lightsection.light_section_uncertainty_budget(wavelength_um=0.65, sin_u_obs=0.1, sin_theta=0.5, line_width_um=40.0, pixel_um=1.0, length_um=None, n_patterns=1, polarizations=1, noise_rel=0.0, peak_dn=None, window_rows=160, calib_rms_um=0.0, calib_dof=inf, speckle_contrast=None); from the registry, opsoptics.get("light_section_uncertainty_budget"))
• GPU: none (CPU reference implementation only)
Uncertainty budget of a light-section height as a GUM table (table).
> The detailed description below is the original text — the summary and the headings are translated.
成分(行)/ components:
• speckle: u = C λ / (2π sin u_obs) · √(w/L) [µm、観察面の横ずれ]、感度 1/sin θ。
• read_noise: 列全体の重心に加法の白色雑音(頂に対する比 noise_rel、peak_dn を与えれば量子化 1/12 LSB² も)が入れる分散を線形化した閉形式 Σ (y − y0)² / (Σ I)² · σ²、L / pixel 列の平均で割る。単位は µm、感度 1/sin θ。
• calibration: 光面の校正の残差 calib_rms_um、感度 1、自由度 calib_dof。
列は source / u / sensitivity / dof / delta_z_um(= |c|·u)で、spc.gum_propagate / spc.gum_expanded にそのまま渡せる(相関なしを仮定)。combined_u_z_um(二乗和の平方根)と dominant(最大の成分)も返す。
★The read-noise term is the linearised variance of the whole-column centroid (the estimator
of laser_line_center_centroid with half_window=None over window_rows rows); other estimators have other noise gains. speckle_contrast overrides the contrast (default 1/√(n_patterns · polarizations), fully developed speckle; 0 = a smooth surface). The √(w/L) speckle averaging is a measured rule (see coherent), not part of Dorsch's closed form.
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_gauss · laser_line_center_steger · light_section_rig · light_section_targets · light_section_render · light_plane_calibrate · light_section_profile
*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.