polarization opsignal → matriximport fullseye as fs; fs.ledger.mueller_from_intensities(intensities, psg, psa, rank_tol=1e-09) (実装を直接呼ぶなら import optics; optics.mueller_from_intensities(intensities, psg, psa, rank_tol=1e-09)、台帳から引くなら opsoptics.get("mueller_from_intensities"))Recover a Mueller matrix from intensities measured through known generator / analyser states (polarimetric least squares).
Model: the detector behind a polarisation-state analyser sees
I_i = (A_i @ M @ G_i)[0, 0] = a_i^T M g_i where g_i = G_i[:, 0] is
the Stokes vector the generator emits from unpolarised light and
a_i = A_i[0, :] is the analyser’s first row. That is linear in the 16
entries of M: I_i = w_i . vec(M) with w_i = outer(a_i, g_i).ravel().
Stacking the N measurements gives W (N x 16), solved by least squares.
intensities is (N,) (one detector) or (N, ...) (an image per
state: the same system solved per pixel, so the result is (4, 4, ...)).
psg and psa are sequences of N Mueller matrices (4x4) — build them with
:func:mueller_element and matrix products.
Fail-closed on an under-determined design: if W has rank < 16 the
design cannot see every entry (the classic case — linear polarisers only,
no retarder — leaves the S3 row and column unobservable, rank 9) and the
function raises with the rank instead of returning a pseudo-inverse answer
that would look plausible and be wrong in the unobserved entries.
Ground truth in the tests: a known M (retarder then polariser),
36 generator/analyser pairs with quarter-wave plates, intensities computed
by the forward model → M recovered to 1e-10; the same with polarisers
only → rank 9, refused.
Raises ValueError: shapes disagree, fewer than 16 measurements,
non-finite input, or rank < 16.
Provenance: the observation matrix outer(a, g) is the standard
formulation (Chipman, “Polarimetry”, Handbook of Optics ch. 15); the
pinv variant is what Polanalyser’s calcMueller does. Re-implemented
with an explicit rank check.
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.pymatrix を入力に取れる)abcd_trace · emva_filter_distortion · mueller_apply · mueller_checks · pixel_shift_capture · pixel_shift_merge · pixel_shift_motion_mask · oct_from_spectra
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.