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_system(elements=None, stop=None, object_mm=inf, wavelength_um=0.58756, index_object=1.0, field=(0.0, 0.0), image_mm=None, image_tilt=(0.0, 0.0), object_tilt=(0.0, 0.0)) (to call the implementation directly, import raytrace3d; raytrace3d.noncoaxial_system(elements=None, stop=None, object_mm=inf, wavelength_um=0.58756, index_object=1.0, field=(0.0, 0.0), image_mm=None, image_tilt=(0.0, 0.0), object_tilt=(0.0, 0.0)); from the registry, opsoptics.get("noncoaxial_system"))
Build a validated non-coaxial sequential system (table) — surfaces, coordinate breaks, folds, plates.
*elements* is a list of dicts ("type" defaults to "surface"), or the dict returned by raytrace.lens_system (converted exactly; its traces then equal raytrace's to 1e-12):
• {"type": "surface", "R", "t", "n", "k", "ap", "mirror", "asph", "decenter", "tilt", "coating", "beamsplitter": {"R": r, "branch": "transmit"|"reflect"}} — as in raytrace.lens_system; decenter / tilt act on that surface only. coating is used by the ghost analysis (None / "bare", a material name = a quarter-wave single layer, [(material, nm), ...] from the incident side, or {"R": r}).
• {"type": "break", "decenter": (dx, dy), "tilt": (ax, ay, az), "order": "xyz"|"zyx", "t"} — a coordinate break (decenter, then rotate about x, the new y, the new z; degrees) that moves every later surface; {"type": "break", "undo": j} is the exact inverse of break record *j*.
• {"type": "return", "to": j, "t"} — go back to the coordinate system at the entry of record *j*.
• {"type": "fold_mirror", "tilt": (ax, ay), "t", "ap", "R", "reflectance"} — a mirror tilted by (ax, ay); the axis is reflected (45° folds by 90°) and t runs along the folded axis.
• {"type": "plate", "thickness", "n", "tilt": (ax, ay), "wedge": (wx, wy), "t", "beamsplitter": r, "branch", "coating_front", "coating_back"} — a tilted plane-parallel (or wedged) plate, or a plate beamsplitter; t is measured from the front vertex along the incoming axis (transmit branch) or along the reflected axis (reflect branch).
*stop* is the record index of the aperture stop (default: the first surface); *field* is (fx, fy) (degrees for an object at infinity, mm otherwise); *image_tilt* / *object_tilt* tilt the image / object plane about the local x and y axes (degrees; Scheimpflug). The last record's t is the distance to the image plane (None = the paraxial focus along the axis ray).
Default: a singlet f ≈ 100 mm followed by a 45° fold mirror (the image lands along +y).
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_example · 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.