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_grating_design(period_um=4.0, wavelength_nm=None, energy_kev=None, grating='pi', order=1, source_distance_mm=None) (to call the implementation directly, import gratinginterf; gratinginterf.talbot_grating_design(period_um=4.0, wavelength_nm=None, energy_kev=None, grating='pi', order=1, source_distance_mm=None); from the registry, opsoptics.get("talbot_grating_design"))
Grating-interferometer geometry: self-image distances of the first grating (fractional Talbot distances), fringe and analyser-grating periods, source-grating period (closed form).
> The detailed description below is the original text — the summary and the headings are translated.
第 1 格子(周期 period_um = p1)を通った波は、ある距離で格子の像(またはその周期の半分の像)を結ぶ。その距離に周期の合った吸収格子(分析格子)を置き、どちらかの格子を 1 周期ずらしながら撮ると、各画素で縞の正弦が取れる。この op はその距離と周期を返す。
grating:
"pi" 位相 π の格子(線の幅が周期の半分)。縞の周期 p1/2、距離 d_m = (m − 1/2)·p1²/(4λ)
(Weitkamp ら 2005, Opt. Express 13, 6296 の式 2)。
"pi_half" 位相 π/2 の格子。縞の周期 p1、d_m = (m − 1/2)·p1²/λ。
"absorption" 吸収格子。縞の周期 p1、d_m = m·p1²/λ(m = 2 がタルボ長 z_T = 2p1²/λ)。
order: m(1 以上の整数)。source_distance_mm: 線源から第 1 格子までの距離 L。None は平面波(L = ∞)。有限なら距離は d' = L·d/(L − d) に伸び(同じ文献)、縞は M = (L + d')/L 倍に拡大される。L ≤ d では自己像が結ばれない(分母が 0 以下)ので拒否する。
返り値 dict:
wavelength_nm / talbot_length_mm(z_T = 2p1²/λ、平面波)/ distance_plane_mm(d_m)/
distance_mm(d'、円錐ビームで伸びた距離。平面波なら d_m と同じ)/ magnification(M)/
fringe_period_um(第 1 格子の直後での縞の周期)/ analyzer_period_um(p2 = M × 縞の周期)/
source_grating_period_um(Lau の条件 p0 = p2·L/d'、Pfeiffer ら 2006。平面波なら None)/
angular_sensitivity(縞の位相 / 屈折角 = 2π d'/p2 [rad/rad])/
correlation_length_um(暗視野の自己相関長 ξ = λ d'/p2)/
relative_bandwidth(縞の振幅が 0 になるまでの波長の幅 Δλ/λ = 1/(2m − 1)。位相 π の格子だけ。
Weitkamp ら 2005 の式 3。他の格子は None)。
例(公表値): 14.4 keV、p1 = 4 µm、位相 π、m = 1 → d = 23.2 mm、p2 = 2 µm(平面波。Weitkamp ら 2005 の図 4 の装置)。Raises ValueError: 正でない周期・波長、wavelength_nm と energy_kev の両方(どちらも無ければ 28 keV)、未知の grating、order が 1..1000 の外、L ≤ d。
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)grating_stepping_simulate · grating_three_image_retrieve · darkfield_scatter_relation · 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.