polarization opmatrix → tableimport fullseye as fs; fs.ledger.mueller_checks(mueller, tol=1e-09) (実装を直接呼ぶなら import optics; optics.mueller_checks(mueller, tol=1e-09)、台帳から引くなら opsoptics.get("mueller_checks"))Say whether a 4x4 matrix is a physically realisable Mueller matrix, and how depolarising it is.
Returns a dict:
physical
True iff the coherency matrix H = 1/4 sum_ij M_ij (sigma_i (x) sigma_j^*)
is positive semidefinite — Cloude’s criterion (1986), the necessary and
sufficient condition for M to be a convex sum of pure (Mueller–Jones)
matrices (Gil, 2007). coherency_eigenvalues carries the four real
eigenvalues (descending) so the caller sees how far from physical.
pure
one non-zero eigenvalue: M comes from a single Jones matrix (no
depolarisation). Every element from :func:mueller_element except the
depolariser is pure.
depolarization_index
Gil–Bernabeu P_Delta = sqrt((sum_ij M_ij^2 - M_00^2) / (3 M_00^2)):
1 for a pure matrix, 0 for the ideal depolariser.
passive
the largest transmittance M_00 + sqrt(M_01^2 + M_02^2 + M_03^2) is
<= 1 — a passive element cannot amplify.
transmittance_max / transmittance_min
those two bounds of the transmitted intensity over all input states.
Ground truth in the tests: every :func:mueller_element kind is physical
and passive; the pure ones have eigenvalues (M_00, 0, 0, 0) to 1e-12 and
P_Delta = 1; the ideal depolariser has P_Delta = 0; a matrix with
M_11 > M_00 (more polarised output than input) is refused as
non-physical; a gain matrix (2 I) is physical but not passive.
Raises ValueError: not a real 4x4 matrix, non-finite, or
M_00 <= 0 (no transmitted intensity — every ratio would be 0/0).
Provenance: Cloude, S. R. (1986), Optik 75, 26; Gil, J. J. & Bernabeu, E.
(1986), Optica Acta 33, 185 (depolarisation index); the check set mirrors
what py-pol (del Hoyo & Sánchez Brea, MIT) exposes as is_physical /
is_pure / is_transmissive, re-implemented from the definitions.
optics の全 op は入力を検証してから計算する(黙って通さない):
_mm / _um / _deg / _mrad。mm と µm の取り違えは crash ではなく「もっともらしく間違った答え」なので、名前で防ぐ。大きさから単位を推測する処理は一切しない。ValueError — float('50') は成功してしまうため、未パースの設定値が長さとして通り抜ける(実測: thin_lens('50', '200') がもっともらしい 66.667 mm を返していた)。bool も True == 1 の暗黙昇格として拒否。ValueError(実数枠のみ。虚部の無言切り捨て・マスク剥がしを拒否)。NaN/Inf は全入力で ValueError。depth_of_field の過焦点距離以遠の far_mm = inf(それが過焦点距離の定義)と gaussian_beam のウエストでの wavefront_radius_mm = inf(平面波面の曲率半径)。どちらも有限の相棒(far_is_infinite / curvature_per_mm)を併せて返す。それ以外の無言 NaN/Inf は内部で検出して ValueError —「float64 が溢れた」と「答えが無限大」は別の主張なので、後者の顔で前者を返さない。optics.MAX_GRID(4096)、供給された場/PSF/開口は optics.MAX_FIELD_ELEMENTS(2^24)、ABCD 素子列は optics.MAX_SYSTEM_ELEMENTS(1024)、Zernike は MAX_ZERNIKE_TERMS(512)/ MAX_ZERNIKE_ORDER(40)/ MAX_ZERNIKE_BASIS(2^25)。小さな引数から巨大な内部確保が起きる経路(実測: n_max=40 × 4096² で 108 GB)を fail-closed で塞ぐ。| 物理的に不可能な状態も拒否: 偏光度 > 1 の Stokes ベクトル、負の透過率、負の強度、n- | m | が奇数などの不正な Zernike 添字。 |
py -3.11 examples/polarization_camera_pipeline.pytable を入力に取れる)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
polarization)jones_element · jones_apply · stokes_from_jones · mueller_element · mueller_apply · stokes_analyze · polarization_demosaic · polarization_demosaic_color
Provenance: optics.py — OPTICS operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.