design op• Data kinds: table → table
• Call: import raytrace; raytrace.seidel_coefficients(system, field=None) (or 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 · paraxial_trace · spot_stats · tolerance_analysis · wavefront_from_opd · spot_diagram · ray_fan
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.