polarization op• Data kinds: cimage × jones → jones
• Call: import optics; optics.jones_apply(jones, state) (or opsoptics.get("jones_apply"))
Push a Jones vector through a Jones matrix: `[Ex', Ey'] = J @ [Ex, Ey]`.
*jones* is a `(2, 2)` matrix (complex, or real which is promoted) and
*state* a 2-component complex Jones vector `[Ex, Ey]` of field
amplitudes. Returns a `(2,)` complex128 vector — chain it through further
elements, or hand it to :func:stokes_from_jones to get the observables.
Ground truth it reproduces exactly: Malus's law — a linear polariser at
*theta* on horizontal linear input returns amplitude `cos(theta)`, hence
intensity `cos^2(theta)`, matching to 1e-15 over the full angle sweep;
crossed polarisers return exactly `[0, 0]`; the identity matrix returns
the input bit-identically.
Note the zero vector is a legal result, not an error: light blocked by
crossed polarisers has zero amplitude. Downstream, :func:stokes_analyze
is the op that refuses a zero-intensity Stokes vector, because *there* the
degree of polarisation would be 0/0.
Raises `ValueError: *jones* is not (2, 2)`, *state* is not a
1-D 2-vector, either is masked or non-finite, or the product overflows.
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
jones as input)polarization)jones_element · stokes_from_jones · mueller_element · mueller_apply · stokes_analyze
*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.