polarization op• Data kinds: stokes → table
• Call: import optics; optics.stokes_analyze(stokes) (or opsoptics.get("stokes_analyze"))
Read a Stokes vector: degree of polarisation, azimuth, ellipticity.
Returns a dict: `intensity S0 · dop` degree of polarisation
`sqrt(S1^2+S2^2+S3^2)/S0 · dolp linear part sqrt(S1^2+S2^2)/S0` ·
`docp circular part |S3|/S0 · azimuth_deg` orientation of the
polarisation ellipse `0.5*atan2(S2, S1) mapped into [0, 180)` ·
`ellipticity_deg 0.5*asin(S3/|S|) in [-45, +45]` ·
`handedness one of "right" / "left" / "linear"`.
**`azimuth_deg and ellipticity_deg are None` when they are
undefined** — azimuth when the linear part is exactly zero (circular or
unpolarised light has no orientation), ellipticity when the polarised part
is zero (unpolarised light has no ellipse). Returning 0.0 there would be a
fabricated angle; `None` says the truth and forces the caller to handle
it.
Ground truth it reproduces exactly: `[1,1,0,0]` -> dop 1, azimuth 0,
ellipticity 0, linear; `[1,-1,0,0] -> azimuth 90; [1,0,1,0]` ->
azimuth 45; `[1,0,0,1]` -> docp 1, ellipticity +45, right-handed;
`[1,0,0,0] -> dop 0 with both angles None`;
`[2,1,0,0]` -> dop 0.5 (a partially polarised beam, which is exactly the
case Jones algebra cannot express).
Raises `ValueError`: *stokes* is not a 1-D 4-vector, is complex /
masked / non-finite, is unphysical (`S0 < 0` or degree of polarisation
above 1 — which is how you find out a Mueller matrix was not physical), or
has `S0 == 0` (no light at all: every ratio would be 0/0, and "the
polarisation of darkness" is not a question with an answer).
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
• specular_photometric — py -3.11 examples/specular_photometric.py
table as input)abcd_matrix · wavefront_stats · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd · spot_diagram
polarization)jones_element · jones_apply · stokes_from_jones · mueller_element · mueller_apply
*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.