moire_align 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.moire_magnification(p_mask_um=2.0, p_wafer_um=2.04, moving='wafer', twist_mrad=0.0) (to call the implementation directly, import moirealign; moirealign.moire_magnification(p_mask_um=2.0, p_wafer_um=2.04, moving='wafer', twist_mrad=0.0); from the registry, opsoptics.get("moire_magnification"))
Period and direction of the moiré fringes, the displacement magnification M and the capture range (closed form).
> The detailed description below is the original text — the summary and the headings are translated.
縞の周期 P = p_m p_w / |p_w − p_m|(格子を回すと周波数ベクトルの差の大きさの逆数 —— printpath の網点のモアレと同じ式なので、そちらを呼んで照合している)。拡大率はどちらの格子が動くかで違い、ウェハが動くなら M = p_m / |Δp|、マスクが動くなら M = p_w / |Δp|。捕捉範囲(読みが折り返すずれ)は動く格子のピッチ 1 つ分、逆向きのピッチ差の 2 対を使う差動では p_m p_w / (p_m + p_w)。
twist_mrad は 2 枚の格子の相対回転で、縞は大きく傾く(回転も拡大される)。0 以外では P は縮む。
返り値: dict(moire_period_um, fringe_angle_deg, magnification, magnification_wafer, magnification_mask, beat_frequency_per_um(符号つき)、fringe_direction(+1 / −1: ずれが正のとき縞が +x へ動くか)、capture_range_um, capture_range_differential_um)。Raises ValueError: ピッチが正でない・2 枚が同じピッチ(縞が無い)・moving の綴り違い。
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.
• poc_moire_alignment — py -3.11 examples/poc_moire_alignment.py
• poc_moire_screen — py -3.11 examples/poc_moire_screen.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
moire_align)moire_talbot_gap · moire_overlay_image · moire_phase · moire_phase_to_shift · moire_differential_shift · moire_mark_read · moire_phase_crlb
*Provenance: moirealign.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.