design op• Data kinds: table → table
• Call: import fullseye as fs; fs.ledger.seidel_coefficients(system, field=None) (to call the implementation directly, import raytrace; raytrace.seidel_coefficients(system, field=None); from the registry, opsoptics.get("seidel_coefficients"))
Third-order (Seidel) aberration sums per surface and total (table).
Uses the paraxial marginal ray (through the stop edge) and chief ray (through the stop centre) at the system's default field (or *field*), with Welford's refraction-invariant form: A = n(yc + u), Δ(u/n), Lagrange invariant H = n(ūy − uȳ)::
S_I = −Σ A² y Δ(u/n) spherical
S_II = −Σ A Ā y Δ(u/n) coma
S_III = −Σ Ā² y Δ(u/n) astigmatism
S_IV = −Σ H² c Δ(1/n) Petzval (field curvature)
S_V = −Σ (Ā/A)[Ā² y Δ(u/n) + H² c Δ(1/n)] distortion
C_L = −Σ A y Δ(δn/n), C_T = −Σ Ā y Δ(δn/n) axial / lateral colour
plus the aspheric deformation contribution 8 G (n'−n) y⁴ with G = k c³/8 + A4 (conic and fourth-order coefficient) to S_I (and its ȳ/y powers to S_II, S_III, S_V); higher aspheric orders are fifth order and above and do not enter the Seidel sums. Sums are in millimetres of wavefront times 8:
the third-order wavefront at the pupil edge is W040 = S_I/8, W131 = S_II/2, W222 = S_III/2, W220 = (S_III + S_IV)/4, W311 = S_V/2 (Welford's normalisation). waves gives the same numbers divided by the wavelength. Checked against the exact ray-traced OPD at small aperture (tests/test_raytrace.py).
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.
• lens_design_demo — py -3.11 examples/lens_design_demo.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · spot_stats · tolerance_analysis · wavefront_from_opd · spot_diagram
design)lens_system · thick_lens · glass · example_system · glass_catalog · sellmeier · paraxial_trace · spot_stats
*Provenance: raytrace.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.