noncoaxial op• Data kinds: table → table
• Call: import fullseye as fs; fs.ledger.ghost_analysis(system, coatings=None, field=None, rings=6, pupil_fill=0.98, pixel_mm=0.005, max_rows=None) (to call the implementation directly, import raytrace3d; raytrace3d.ghost_analysis(system, coatings=None, field=None, rings=6, pupil_fill=0.98, pixel_mm=0.005, max_rows=None); from the registry, opsoptics.get("ghost_analysis"))
Two-reflection ghosts of every surface pair (table): focus, size on the sensor and relative intensity.
For surface records i < j (refracting surfaces and beamsplitters; nominal mirrors only as the parts of the path they already are), the light runs to *j*, reflects, crosses *j−1 … i+1* backwards, reflects at *i* and runs on to the image plane — N(N−1)/2 paths. The nominal bundle (same launch as the image) is traced along each path with real rays. Per ghost:
• energy_ratio — ghost energy / image energy = R_i·R_j·Π T over the ghost path ÷ Π T over the image path; R from surface_reflectance (the media of the prescription and *coatings*:
a coating for all surfaces, or {record: coating}; records may carry their own coating), at the
angle of incidence of the field's chief ray on each surface (unpolarised; a 45° beamsplitter plate is not
treated as normal incidence);
• focus_offset_mm — the ghost's best focus relative to the image plane (along the image normal; negative = in front of the sensor), radius_mm (RMS) / max_radius_mm on the image plane, centroid_xy (image-plane local) and offset_xy (from the image's chief ray — where the false copy lands relative to the true image);
• point_ratio — ghost irradiance / image irradiance for a point source whose image fills one pixel_mm disk: energy_ratio · (pixel / max(pixel, radius))²;
• extended_ratio — the same for a uniform extended scene: energy_ratio · |det J_image| / |det J_ghost| (the ghost spreads the scene over its own magnification); jacobian is J_ghost (image-plane position of the ghost's chief ray per unit field, 2×2; image_jacobian the image's own).
Rows are sorted by point_ratio (ties by the declared order). n_pairs = N(N−1)/2.
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_example · noncoaxial_layout · noncoaxial_trace · noncoaxial_spot · image_orientation · beamsplitter_branches · tilted_plate_shift
*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.