grating_interf op• Data kinds: images × images → table
• Call: import fullseye as fs; fs.ledger.grating_three_image_retrieve(sample_stack, reference_stack=None, steps_per_period_sample=None, steps_per_period_reference=None, min_visibility=0.02, distance_mm=None, analyzer_period_um=None, reference_exposure=1.0) (to call the implementation directly, import gratinginterf; gratinginterf.grating_three_image_retrieve(sample_stack, reference_stack=None, steps_per_period_sample=None, steps_per_period_reference=None, min_visibility=0.02, distance_mm=None, analyzer_period_um=None, reference_exposure=1.0); from the registry, opsoptics.get("grating_three_image_retrieve"))
Separates transmission, differential phase and dark field from two phase-stepping stacks (with and without the sample).
> The detailed description below is the original text — the summary and the headings are translated.
各画素で I_k = a·(1 + V·cos(φ − 2πk/P)) をあて(P = 1 周期のステップ数。None は N 等分)、透過 T = a_s/a_r、微分位相 φ = wrap(φ_s − φ_r)、暗視野 D = V_s/V_r を返す(Pfeiffer ら 2008, Nature Materials 7, 134 の定義)。P = N のときは fringe.wrapped_phase と fringe.modulation (N 段の位相シフトの標準式)をそのまま使い、P ≠ N(1 周期の両端を含む走査など)は 3 項の最小二乗。2 組のステップ数は違ってよい(各組を別々にあてる)。
reference_stack が None なら、試料の画像列だけから a・V・φ を返す(比は取らない)。distance_mm と analyzer_period_um を渡すと、屈折角 α = φ·p2/(2π d) [µrad] も返す。reference_exposure: 基準を試料の何倍の露光(1 枚あたりの光子数)で撮ったか。透過は a_s/(a_r/reference_exposure)。暗視野と微分位相は比と差なので露光に依らない(透過だけが露光の比で化ける)。
min_visibility: 基準の可視度がこれ未満の画素(格子の欠陥・影)は位相が決まらないので NaN にし、数を返す。全画素が NaN になるときは値を返さずに拒否する。
返り値 dict: transmission / dpc_rad / darkfield(いずれも (H, W)、無効画素は NaN)/ visibility_sample / visibility_reference / refraction_urad(幾何があるとき)/ fit_residual_sample / fit_residual_reference(正弦をあてた残差の RMS / 平均の中央値。1 周期のステップ数を間違えると大きくなる)/ n_invalid。Raises ValueError: 画像列が 3-D でない・3 枚未満・NaN/Inf、2 組の画素の形が違う、P ≤ 0、P が小さすぎて正弦が分けられない、有効な画素が 1 つも無い、幾何の片方だけ、正でない reference_exposure。
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 · 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.