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_carpet(period_um=4.0, wavelength_nm=None, energy_kev=None, grating='pi', duty=0.5, z_max_mm=None, n_z=241, n_x=128, n_periods=2, n_harmonics=63, model='exact') (to call the implementation directly, import gratinginterf; gratinginterf.talbot_carpet(period_um=4.0, wavelength_nm=None, energy_kev=None, grating='pi', duty=0.5, z_max_mm=None, n_z=241, n_x=128, n_periods=2, n_harmonics=63, model='exact'); from the registry, opsoptics.get("talbot_carpet"))
Talbot carpet: the intensity I(x, z) behind a binary grating (π phase, π/2 phase or absorption) in closed form as a sum over diffraction orders.
> The detailed description below is the original text — the summary and the headings are translated.
格子 1 周期の透過 t(x)(線の幅の割合 duty で t_a、残りで t_b)のフーリエ係数 c_n は閉形式 c_n = (t_a − t_b)(1 − e^{−2πi n·duty})/(2πi n)、c_0 = t_a·duty + t_b(1 − duty)。平面波で照らした場は u(x, z) = Σ c_n e^{2πi n x/p} e^{i k_z(n) z}。
model:
"exact" k_z = 2π √(1/λ² − n²/p²)(角スペクトルの厳密な伝搬。1/λ < |n|/p の次数はエバネッセントで減衰)。
"paraxial" k_z ≈ 2π/λ − πλ n²/p²(Fresnel)。z_T = 2p²/λ で強度が z = 0 と厳密に同じになる(自己像)。
z_max での 1 次の位相誤差 πλ³z/(4p⁴)… が 0.1 rad を超えるときは拒否する("exact" を使う)。
縞の可視度 visibility(z ごと)は、縞の周期の次数 h(位相 π の格子は h = 2 = 周期 p/2、他は h = 1)の強度の係数 2|I_h|/I_0 で、係数の積から直接出す(x の標本化に依らない)。方形波の縞が完全に結ぶと 4/π。
z_max_mm: None ならタルボ長 z_T = 2p²/λ の 1 周期分。n_harmonics: 和を打ち切る次数 N(係数は 1/n で減るので、角の Gibbs の波打ちは残る —— 図用。距離と可視度は打ち切りにほぼ依らない)。
返り値 dict: intensity(n_z, n_x)/ z_mm / x_um / visibility(n_z)/ fringe_harmonic(h)/ talbot_length_mm / self_image_mm(talbot_grating_design の分数タルボ距離のうち z_max までのもの)/ wavelength_nm / model / paraxial_phase_error_rad(z_max での 1 次の近軸の位相誤差)。Raises ValueError: 正でない周期・波長・z_max、wavelength_nm と energy_kev の両方、未知の grating・model、duty が (0, 1) の外、n_z・n_x・n_periods・n_harmonics が範囲の外、近軸の誤差が大きすぎる。
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_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.