design op• Data kinds: table → table
• Call: import raytrace; raytrace.paraxial_trace(system) (or opsoptics.get("paraxial_trace"))
First-order properties of the prescription: focal lengths, pupils, image.
Returns a dict with `efl` (effective focal length, mm; negative for a
diverging system), `bfl (last vertex → paraxial focus), ffl` (first
vertex → front focus, negative when in front), `pp_front / pp_rear`
(principal planes measured from the first / last vertex), `image_mm`
(last vertex → paraxial image of the given object), `magnification`
(transverse; 0 for an object at infinity), `ep_position / ep_radius`
(entrance pupil from the first vertex), `xp_position / xp_radius`
(exit pupil from the last vertex), `fno` (image-space f-number,
`efl / (2·ep_radius)), na_image, lagrange` (the Lagrange invariant
for the system's default field), `marginal / chief` (the two paraxial
rays: heights and post-surface slopes at every surface).
Verified against the closed forms: single refracting surface
`n'/s' = n/s + (n' − n)/R`, the thick-lens lensmaker equation and its
thin-lens limit, and a mirror `f = −R/2 (see 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_defect_dataset_demo — py -3.11 examples/lens_defect_dataset_demo.py
• lens_design_demo — py -3.11 examples/lens_design_demo.py
table as input)abcd_matrix · wavefront_stats · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd · spot_diagram · ray_fan
design)lens_system · thick_lens · glass · example_system · glass_catalog · sellmeier · seidel_coefficients · 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.