fiber 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.fiber_lp_modes(v_number=6.0, max_modes=None) (to call the implementation directly, import fiberoptics; fiberoptics.fiber_lp_modes(v_number=6.0, max_modes=None); from the registry, opsoptics.get("fiber_lp_modes"))
LP_lm modes of a weakly guiding step-index fibre: solves the characteristic equation and returns u, w and the normalised propagation constant b of each mode (table).
> The detailed description below is the original text — the summary and the headings are translated.
u J_{l−1}(u)/J_l(u) = −w K_{l−1}(w)/K_l(w)、u² + w² = V²(Gloge 1971)。l ごとに u の区間を J_l の零点と J_{l−1} の零点(= 遮断)で区切り、符号の変わる区間を二分法で解く(80 回、区間幅の 1e-24 倍)。
返り値: dict(modes = [{"l", "m", "u", "w", "b", "cutoff_v", "degeneracy"}], n_modes(縮退込みの総数)、count_approx = V²/2)。縮退: l = 0 は 2(偏光)、l ≥ 1 は 4(偏光 × cos/sin)。
★限界: LP0m(m ≥ 2)は遮断の直上で束縛が指数関数的に弱い(w ∝ e^{−1/(…)}、V − u が e^{−数百})ので、遮断から V で約 0.05 以内では浮動小数で根が表せず、数えない(n_modes が 2 少ない)。LP_lm(l ≥ 1)の近づき方は代数的なので遮断の 0.001 上から解ける(PoC poc_fiber_light_guide の門)。
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_fiber_light_guide — py -3.11 examples/poc_fiber_light_guide.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
fiber)material_group_index · material_gvd · fiber_numerical_aperture · fiber_v_number · fiber_mode_field_diameter · fiber_bundle_coupling
*Provenance: fiberoptics.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.