polarization op• 資料種類:signal → matrix
• 呼叫: import fullseye as fs; fs.ledger.mueller_from_intensities(intensities, psg, psa, rank_tol=1e-09)(要直接呼叫實作,import optics; optics.mueller_from_intensities(intensities, psg, psa, rank_tol=1e-09);從台帳取用則 opsoptics.get("mueller_from_intensities"))
從已知起偏器/檢偏器狀態下量得的強度恢復 Mueller 矩陣(偏振量測的最小平方)。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
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 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 的每個運算子都先檢驗輸入再計算(不讓任何東西無聲通過):
• 單位寫進參數名 —— _mm / _um / _deg / _mrad。把 mm 和 µm 弄混不會當掉,而是給出「看似合理卻是錯的答案」,所以用命名來防。這裡絕不從數值大小去猜單位。
• 字串一律 ValueError —— float('50') 會成功,於是未解析的設定值會被當成長度混進來(實測:thin_lens('50', '200') 曾回傳看似合理的 66.667 mm)。bool 也按 True == 1 的隱式提升拒絕。
• complex / masked array 一律 ValueError(僅接受實數槽位;拒絕無聲丟棄虛部或剝掉遮罩)。所有輸入中的 NaN/Inf 一律 ValueError。
• 逐項點名拒絕除零及其近親:焦距 0、曲率半徑 0、折射率 <= 0、全不透明光闌(全為 0,正規化變成 0/0)、總和 <= 0 的 PSF、S0 = 0 的 Stokes 向量、物體位於前焦點(像在無窮遠)。
• 只有兩個運算子會回傳非有限值,而且都寫進了契約:depth_of_field 在超焦距以外回傳 far_mm = inf(這正是超焦距的定義),gaussian_beam 在束腰處回傳 wavefront_radius_mm = inf(平面波前的曲率半徑)。兩者都同時回傳一個有限的夥伴(far_is_infinite / curvature_per_mm)。除此之外的無聲 NaN/Inf 都在內部檢出並 ValueError ——「float64 溢位了」和「答案是無窮大」是兩種不同的主張,不能拿後者的臉去交付前者。
• 尺寸上限:生成網格受 optics.MAX_GRID(4096)限制,傳入的場/PSF/光闌受 optics.MAX_FIELD_ELEMENTS(2^24),ABCD 元件序列受 optics.MAX_SYSTEM_ELEMENTS(1024),Zernike 受 MAX_ZERNIKE_TERMS(512)/ MAX_ZERNIKE_ORDER(40)/ MAX_ZERNIKE_BASIS(2^25)。以 fail-closed 堵住「小參數引發巨大內部配置」的路徑(實測:n_max=40 × 4096² 需要 108 GB)。
• 物理上不可能的狀態同樣拒絕:偏振度 > 1 的 Stokes 向量、負穿透率、負強度、n-|m| 為奇數等非法 Zernike 指標。
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• 演算法的正典(作者、年份)與用途見上面的族使用指南。
• polarization_camera_pipeline — py -3.11 examples/polarization_camera_pipeline.py
matrix 作為輸入)abcd_trace · mueller_apply · mueller_checks
polarization)jones_element · jones_apply · stokes_from_jones · mueller_element · mueller_apply · stokes_analyze · polarization_demosaic · polarization_demosaic_color
*Provenance: optics.py — OPTICS 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.