grating_interf 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.darkfield_scatter_relation(darkfield=None, sigma_urad=None, distance_mm=23.2, analyzer_period_um=2.0, thickness_mm=None, wavelength_nm=None) (to call the implementation directly, import gratinginterf; gratinginterf.darkfield_scatter_relation(darkfield=None, sigma_urad=None, distance_mm=23.2, analyzer_period_um=2.0, thickness_mm=None, wavelength_nm=None); from the registry, opsoptics.get("darkfield_scatter_relation"))
Converts between the dark field D (a visibility ratio) and the width σ of the scattering-angle distribution (published formula for Gaussian scattering).
> The detailed description below is the original text — the summary and the headings are translated.
散乱角の分布がガウス(標準偏差 σ、格子の線に直交する向きの成分)なら、縞の可視度は D = exp(−2π² σ² d²/p2²)(Strobl 2014, Sci. Rep. 4, 7243 の式 7 をガウスで積分した形 = Bech ら 2010, Phys. Med. Biol. 55, 5529 の線拡散係数の式)。d は試料(第 1 格子)から分析格子までの距離、p2 は分析格子の周期。逆に σ = (p2/(π d √2))·√(−ln D)。
darkfield と sigma_urad のどちらか一方を渡す(スカラーか配列)。thickness_mm を渡すと線拡散係数 ε = σ²/t [µrad²/mm] を返す(σ² が厚さに比例する、という仮定の下で)。wavelength_nm を渡すと自己相関長 ξ = λ d/p2 [µm] を返す(暗視野が感じる構造の大きさの目安)。
配列の D で (0, 1] の外の画素(雑音で 1 を超えた・0 以下)は σ を NaN にして数を n_invalid に返す。スカラーで (0, 1] の外なら拒否する(黙って 0 や負の σ を返さない)。
返り値 dict: darkfield / sigma_urad / diffusion_coeff_urad2_per_mm(t があるとき)/ correlation_length_um(λ があるとき)/ angular_sensitivity(2π d/p2)/ n_invalid。Raises ValueError: darkfield と sigma_urad の両方 / どちらも無い、σ < 0、スカラーの D が (0, 1] の外、正でない距離・周期・厚さ・波長、NaN/Inf。
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.
• grating_interferometry — py -3.11 examples/grating_interferometry.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
grating_interf)talbot_grating_design · grating_stepping_simulate · grating_three_image_retrieve · talbot_carpet · talbot_source_visibility · grating_step_period_estimate · dpc_integrate
*Provenance: gratinginterf.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.