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_speckle_floor(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, method='centroid', n_trials=12, n_columns=1024, n_rows=160, n_patterns=1, polarizations=1, noise_rel=0.0, pixel_oversample=2, seed=0, center_kw=None, smooth_surface=False) (to call the implementation directly, import lightsection; lightsection.light_section_speckle_floor(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, method='centroid', n_trials=12, n_columns=1024, n_rows=160, n_patterns=1, polarizations=1, noise_rel=0.0, pixel_oversample=2, seed=0, center_kw=None, smooth_surface=False); from the registry, opsoptics.get("light_section_speckle_floor"))
• GPU: none (CPU reference implementation only)
Speckle floor of a light-section height, simulated and in closed form side by side (table).
> The detailed description below is the original text — the summary and the headings are translated.
シミュ: coherent.laser_line_coherent で粗面のスペックル込みの光条を n_trials 枚(高さは乱数、部品ごとに別の位相スクリーン)描き、method の中心抽出で列ごとの中心を取り、長さ length_um(既定 = 光条の幅)ごとに平均して高さに直す(z = Δrow · pixel / sin θ、coherent の三角測量の約束)。真の高さとの差の標準偏差が sim_delta_z_um(95 % の χ² 区間つき)。
閉形式の側: δz = C λ / (2π sin u_obs sin θ) · √(w/L)、C = 1/√(n_patterns · polarizations) (coherent.speckle_reduction)。★前半 C λ / (2π sin u sin θ) が Dorsch らの式(dorsch_delta_z_um)で、後ろの √(w/L)(averaging_factor)は長さ L の平均の 実測の規則であって Dorsch の式の一部ではない。closed_form_delta_z_um はその積(L < w では Dorsch の式より大きい: w 173.2 µm・L 50 µm で 1.86 倍)。読み出し雑音 noise_rel(光条の頂の平均に対する比)は
シミュに入り、閉形式の側は light_section_uncertainty_budget の雑音の項と合わせて closed_form_total_um に入る。
Simulates n_trials speckled lines with coherent.laser_line_coherent, extracts the centre per column with method, averages over length_um (default = the line width) and converts to height (z = Δrow · pixel / sin θ). Returns the simulated standard deviation (with its χ² 95 % interval), the closed form closed_form_delta_z_um = Dorsch × √(w/L) (the √(w/L) averaging over length_um is a measured rule, not part of Dorsch's formula), the pure Dorsch value dorsch_delta_z_um with averaging_factor = √(w/L) and ratio_sim_to_dorsch, the ratios, and the additive-noise term. smooth_surface=True renders a mirror-smooth part (phase 0: no speckle, contrast 0) so that only noise_rel is left — the gate for the budget's read-noise term. center_kw overrides the estimator's settings (defaults: centroid over the whole column without clipping; gauss with half_window = the line's 1/e² half-width in pixels; steger with sigma = w/(pixel·√3)). ★Columns within one block share speckle; blocks are treated as independent samples (the χ² interval assumes that). ★The 2π constant is from the open-access Ettl et al. 2014, which cites Dorsch et al. 1994; the primary text was not read.
★The fine step pixel_um / pixel_oversample must be at most the intensity's Nyquist λ/(4 sin_u_obs) (|E|² has bandwidth 2 sin_u/λ), else ValueError naming the smallest pixel_oversample; up to λ/(5 sin_u_obs) a RuntimeWarning (the floor converges from there). Checking only the field's band let steps of up to λ/(2 sin u) through and the simulated floor came out 0.5–0.8 of its converged value (2026-11-09). Both numbers are returned as fine_step_um / intensity_nyquist_um.
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_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.