noncoaxial 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.noncoaxial_example(name='folded_singlet') (to call the implementation directly, import raytrace3d; raytrace3d.noncoaxial_example(name='folded_singlet'); from the registry, opsoptics.get("noncoaxial_example"))
A named non-coaxial example system (table): folds, a periscope, a beamsplitter, a tilted plate, Scheimpflug.
"folded_singlet" (plano-convex BK7 f ≈ 100 mm, then a 45° fold mirror 40 mm behind it — the image lands along +y), "periscope" (two parallel 45° mirrors:
an even number of reflections), "coaxial_doublet" (raytrace's cemented doublet converted — traces equal raytrace), "tilted_plate" (a 5 mm BK7 plate tilted 30° in the converging beam of an f/10 singlet), "epi_beamsplitter" (a coaxial epi-illumination inspection lens: object → 45° plate beamsplitter, 3 mm BK7, R = 0.5 on the front face → doublet → sensor), "scheimpflug" (the doublet imaging a 30°-tilted object at 1:1-ish with the image plane tilted by the closed form) and "off_axis_parabola" (a paraboloid R = −200 used 36 mm off its axis, folded by its own tilt).
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_noncoaxial_optics — py -3.11 examples/poc_noncoaxial_optics.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
noncoaxial)noncoaxial_system · noncoaxial_layout · noncoaxial_trace · noncoaxial_spot · image_orientation · beamsplitter_branches · tilted_plate_shift · scheimpflug_tilt
*Provenance: raytrace3d.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.