geometric op• Data kinds: matrix → table
• Call: import optics; optics.abcd_trace(matrix, height_mm=1.0, angle_mrad=0.0) (or opsoptics.get("abcd_trace"))
Propagate one paraxial ray through an ABCD matrix.
Applies `[y', theta'] = M @ [y, theta] with y` in millimetres and
`theta` in radians internally; the API speaks milliradians because a
paraxial angle is small by definition and mrad keeps the numbers readable.
Returns a dict: `height_mm and angle_mrad` of the outgoing ray ·
`determinant of *M* (= n_in/n_out`; a value that is not 1 for a
same-medium system means the matrix is wrong, so it is reported rather than
assumed) · `imaging — True when |B| <= 1e-12 * (1 + |A| + |C| + |D|)`,
i.e. the output height does not depend on the input angle, which is the
definition of a conjugate (image) plane.
Ground truth it reproduces exactly: free space of length `d` gives
`y' = y + d*theta and theta' = theta; a thin lens leaves y`
untouched and bends the ray by `-y/f`; a ray parallel to the axis
(`angle_mrad = 0`) entering a lens crosses the axis exactly one focal
length behind it.
Raises `ValueError: *matrix* is not (2, 2)`, is complex or masked,
holds NaN/Inf, or has a determinant of 0 (a system that collapses every ray
to a point is not a ray-transfer matrix); non-finite *height_mm* /
*angle_mrad*; a result that overflowed float64.
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.
• optics_imaging — py -3.11 examples/optics_imaging.py
table as input)abcd_matrix · wavefront_stats · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd · spot_diagram
geometric)thin_lens · abcd_matrix · depth_of_field · relative_illumination
*Provenance: optics.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.