polarization op• Data kinds: none → matrix (an op determined by its arguments alone — it takes no image or data input)
• Call: import optics; optics.mueller_element(kind='polarizer', angle_deg=0.0, retardance_deg=90.0) (or opsoptics.get("mueller_element"))
A 4x4 real Mueller matrix for one polarisation element.
*kind* is one of :data:MUELLER_KINDS — the same five as
:func:jones_element plus `"depolarizer" (ideal, diag(1, 0, 0, 0)`),
which has no Jones counterpart at all. That extra kind is the reason
this family exists: Jones algebra can only carry fully polarised light,
Mueller algebra carries partial polarisation, scattering and depolarisation
— which is what a real polarisation camera sees.
Angles are doubled inside (`c = cos(2a), s = sin(2a)`) because the
Stokes parameters live on the Poincare sphere, where a physical rotation by
`a is a rotation by 2a`.
Returns a `(4, 4) float64 matrix acting on [S0, S1, S2, S3]`; apply it
with :func:mueller_apply and compose a train as
`M_last @ ... @ M_first`.
Ground truth it reproduces exactly: an ideal polariser transmits exactly
half of unpolarised light (`[1,0,0,0] -> S0 = 0.5`) and fully polarises
it; two polarisers at relative angle theta transmit `0.5*cos^2(theta)`
(Malus); a rotator by 45 degrees turns horizontal into 45-degree linear;
the depolariser leaves `S0 and kills S1..S3`. Cross-checked against
the Jones family in the tests — for every kind and a sweep of angles, the
Jones path and the Mueller path return the same Stokes vector to 1e-14,
which is the only construction that catches a sign slip in either one.
Raises `ValueError`: an unknown *kind*; non-finite *angle_deg* or
*retardance_deg*.
Ideal, lossless (except the polariser's physical loss), normal-incidence
elements; no diattenuation-plus-retardance combinations, no depolarisation
other than the ideal case.
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
matrix as input)polarization)jones_element · jones_apply · stokes_from_jones · 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.