polarization op• 数据种类:无 → matrix(仅由参数决定的算子 —— 不接受图像或数据输入)
• 调用: import fullseye as fs; fs.ledger.mueller_element(kind='polarizer', angle_deg=0.0, retardance_deg=90.0)(要直接调用实现,import optics; optics.mueller_element(kind='polarizer', angle_deg=0.0, retardance_deg=90.0);从台账取用则 opsoptics.get("mueller_element"))
• GPU:无(仅 CPU 参考实现)
单个偏振元件的 4x4 实 Mueller 矩阵。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
*kind* is one of MUELLER_KINDS — the same five as 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 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, for kind="retarder", non-finite *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. A polariser with a finite extinction ratio
is mueller_partial_polarizer.
Per-pixel fields (2026-10-23). An array *angle_deg* (or, for kind="retarder", an array *retardance_deg*) returns (*shape, 4, 4), one matrix per entry of the broadcast shape — an isoclinic angle map and a retardance map of a photoelastic part give the whole field in one call, ready for mueller_apply's field form. Before this the call raised ValueError and the photoelasticity PoC had to assemble (H, W, 4, 4) by hand. Scalars take the original code path untouched (scalar results are bit-for-bit what they were; pinned by a test against a verbatim copy of the old code). Output capped at MAX_FIELD_ELEMENTS numbers.
Angle convention. *angle_deg* is measured from +x (along a row) toward +y (down the rows): clockwise on a displayed image — the sense of atan2(ny, nx) of a normal map and of 0.5 * atan2(2 txy, sxx - syy) for image-coordinate stresses. See the polarisation section comment of this module.
optics 的每个算子都先校验输入再计算(不让任何东西无声通过):
• 单位写进参数名 —— _mm / _um / _deg / _mrad。把 mm 和 µm 弄混不会崩溃,而是给出「看着合理却是错的答案」,所以用命名来防。这里绝不从数值大小去猜单位。
• 字符串一律 ValueError —— float('50') 会成功,于是未解析的配置值会被当成长度混进来(实测:thin_lens('50', '200') 曾返回看着合理的 66.667 mm)。bool 也按 True == 1 的隐式提升拒绝。
• complex / masked array 一律 ValueError(仅接受实数槽位;拒绝无声丢弃虚部或剥掉掩码)。所有输入中的 NaN/Inf 一律 ValueError。但已声明的缺测除外:bottle_fit_from_pattern 的 u_map 以 NaN 接收未能测得的像素(∞ 仍被拒绝)。
• 逐项点名拒绝除零及其近亲:焦距 0、曲率半径 0、折射率 <= 0、全不透明光阑(全为 0,归一化变成 0/0)、总和 <= 0 的 PSF、S0 = 0 的 Stokes 矢量、物体位于前焦点(像在无穷远)。
• 只有两个算子会返回非有限值,而且都写进了契约:depth_of_field 在超焦距以外返回 far_mm = inf(这正是超焦距的定义),gaussian_beam 在束腰处返回 wavefront_radius_mm = inf(平面波前的曲率半径)。两者都同时返回一个有限的搭档(far_is_infinite / curvature_per_mm)。除此之外的无声 NaN/Inf 都在内部检出并 ValueError ——「float64 溢出了」和「答案是无穷大」是两种不同的主张,不能拿后者的脸去交付前者。但已声明的缺测除外:bottle_background_map 对光线不可用的像素(全反射等)在 u_mm 中返回 NaN,并同时返回 valid 掩码和数量。
• 尺寸上限:生成网格受 optics.MAX_GRID(4096)限制,传入的场/PSF/光阑受 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「小参数引发巨大内部分配」的路径(实测:n_max=40 × 4096² 需要 108 GB)。
• 物理上不可能的状态同样拒绝:偏振度 > 1 的 Stokes 矢量、负透过率、负强度、n-|m| 为奇数等非法 Zernike 指标。
• 示例数据目录(下载 URL / 许可证) —— 2-D 用 skimage.data(BSD/公有领域)加合成图,3-D 给出真实数据源(Stanford/PDS 等)的下载 URL。
• 算子来历与参考文献 —— 该算子族所依据的研究/方法出处。
• 算法的正典(作者、年份)与用途见上面的族使用指南。
• optics_imaging — py -3.11 examples/optics_imaging.py
• poc_mueller_dofp_observability — py -3.11 examples/poc_mueller_dofp_observability.py
• poc_photoelasticity — py -3.11 examples/poc_photoelasticity.py
• polarization_camera_pipeline — py -3.11 examples/polarization_camera_pipeline.py
matrix 作为输入)abcd_trace · emva_filter_distortion · mueller_apply · mueller_checks · equirect_rotate · pixel_shift_capture · pixel_shift_merge · pixel_shift_motion_mask
polarization)jones_element · jones_apply · stokes_from_jones · mueller_partial_polarizer · mueller_apply · stokes_analyze · polarization_demosaic · polarization_demosaic_color
*Provenance: optics.py — OPTICS 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.