coherent 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.triangulation_speckle_limit(wavelength_um=0.65, sin_u_obs=0.05, sin_theta=0.5, contrast=1.0) (to call the implementation directly, import coherent; coherent.triangulation_speckle_limit(wavelength_um=0.65, sin_u_obs=0.05, sin_theta=0.5, contrast=1.0); from the registry, opsoptics.get("triangulation_speckle_limit"))
Speckle floor of laser triangulation (table): δz = C λ / (2π sin u_obs sin θ).
Dorsch, Häusler & Herrmann, Appl. Opt. 33(7):1306, 1994: the centroid of a speckled spot cannot be located better than δx = C λ / (2π sin u_obs) in the observation plane, and triangulation turns a lateral shift into height through 1/sin θ. C is the speckle contrast reaching the detector (1 for fully developed speckle; lower with pixel integration or speckle_reduction). Also returns the speckle size (FWHM of the intensity autocorrelation, 0.5145 λ / sin u) in µm.
★For a centroid estimator C is *not* the pixel-integrated contrast: the centroid of a box-filtered intensity is the centroid of the intensity, so bigger pixels lower the contrast a viewer sees but not the centroid's error (gated exactly in the tests). Averaging the centroid along L µm of a line of 1/e² half-width w scales the error as √(w/L) (measured; Dorsch's spot-size independence is the L ≈ w case).
★The 2π factor is as quoted in secondary sources; the primary text was not read (only its abstract). tests/test_coherent.py gates the exponents (λ: +1, sin u: −1, sin θ: −1) against rendered speckled lines, not the constant.
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_laser_line_speckle_floor — py -3.11 examples/poc_laser_line_speckle_floor.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
coherent)coherent_image · speckle_field · speckle_statistics · laser_line_coherent · speckle_reduction
*Provenance: coherent.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.