polarization op• Data kinds: jones → stokes
• Call: import optics; optics.stokes_from_jones(state) (or opsoptics.get("stokes_from_jones"))
Jones vector -> Stokes vector (the four measurable intensities).
`S0 = |Ex|^2 + |Ey|^2 · S1 = |Ex|^2 - |Ey|^2` ·
`S2 = 2*Re(Ex*conj(Ey)) · S3 = 2*Im(Ex*conj(Ey))`.
In this convention (`exp(-i*omega*t) time dependence) S3 > 0` is
right-circular: the Jones vector `[1, -i]/sqrt(2)` maps to
`[1, 0, 0, +1]`. The convention is pinned by a test rather than left to
the reader, because every textbook picks a different one and a sign slip
here is invisible in intensity measurements.
Returns a `(4,)` float64 vector. A Jones vector always describes fully
polarised light, so the result always satisfies `S0^2 = S1^2+S2^2+S3^2`
exactly (degree of polarisation 1) — verified to 1e-15 in the tests. That
identity is also the reason Jones cannot represent a partially polarised
beam: for that, start from :func:mueller_element instead.
Raises `ValueError`: *state* is not a 1-D 2-vector, is masked, or is
non-finite.
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
stokes as input)mueller_apply · stokes_analyze
polarization)jones_element · jones_apply · 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.