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.talbot_source_visibility(source_width_um, source_distance_mm, distance_mm, analyzer_period_um, profile='uniform', source_grating_period_um=None, duty=None, n_slits=None, wavelength_nm=None) (to call the implementation directly, import gratinginterf; gratinginterf.talbot_source_visibility(source_width_um, source_distance_mm, distance_mm, analyzer_period_um, profile='uniform', source_grating_period_um=None, duty=None, n_slits=None, wavelength_nm=None); from the registry, opsoptics.get("talbot_source_visibility"))
How much the fringe visibility drops for a given source size and source grating (Lau condition), in closed form as an incoherent sum.
> The detailed description below is the original text — the summary and the headings are translated.
線源の 1 点が格子の線に直交する向きに s ずれると、分析格子の上の縞は s·d/L だけ逆向きにずれる(L = 線源から第 1 格子、d = 第 1 格子から分析格子)。互いに干渉しない点の縞を足すので、可視度の倍率は線源の分布のフーリエ変換を周波数 d/(L p2) で読んだ値になる(Pfeiffer ら 2006, Nature Physics 2, 258):
"uniform" 幅 w: |sinc(π w d/(L p2))|(sinc x = sin x / x)
"gaussian" 半値全幅 w: exp(−2π² σ² d²/(L² p2²))、σ = w/(2√(2 ln 2))
線源格子(周期 p0、開口の割合 duty、開口 n_slits 本)を置くと、各開口は幅 duty·p0 の一様な線源、開口の並びは配列の因子 |sin(N β)/(N sin β)|、β = π p0 d/(L p2) を掛ける。β が π の整数倍(Lau の条件 p0 = p2·L/d)ですべての開口の縞が重なり、可視度は開口 1 本の |sinc(π duty)|(duty = 0.5 で 2/π)まで戻る。n_slits が None なら round(w/p0)(焦点 w に入る開口の数、1 以上)。線源格子はガウスの焦点とは組まない(拒否)。duty(開口の割合)は線源格子があるときだけ意味を持つ(None は 0.5)。線源格子なしで duty か n_slits を渡すと、黙って無視せずに拒否する(線源格子の周期を渡し忘れた呼び出しを見逃さない)。
wavelength_nm を渡すと、第 1 格子での横のコヒーレンス長 l_c = λ L/w [µm] も返す。
返り値 dict: visibility_factor / slit_factor / array_factor(線源格子なしは 1)/ lau_period_um(p2·L/d)/ lau_ratio(p0 / Lau の周期、線源格子なしは None)/ n_slits / projected_blur_um(w·d/L、分析格子の上での線源の影の幅)/ coherence_length_um(λ があるとき)。Raises ValueError: 正でない幅・距離・周期、未知の profile、ガウスと線源格子の組、duty が (0, 1] の外、n_slits が 1..100000 の外、線源格子なしでの duty・n_slits。
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
• poc_grating_interferometry — py -3.11 examples/poc_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 · darkfield_scatter_relation · talbot_carpet · 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.