noncoaxial op• 資料種類:table → table
• 呼叫: import fullseye as fs; fs.ledger.ghost_analysis(system, coatings=None, field=None, rings=6, pupil_fill=0.98, pixel_mm=0.005, max_rows=None)(要直接呼叫實作,import raytrace3d; raytrace3d.ghost_analysis(system, coatings=None, field=None, rings=6, pupil_fill=0.98, pixel_mm=0.005, max_rows=None);從台帳取用則 opsoptics.get("ghost_analysis"))
所有面對的兩次反射鬼影(table):焦點、在感測器上的大小與相對強度。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
For surface records i < j (refracting surfaces and beamsplitters; nominal mirrors only as the parts of the path they already are), the light runs to *j*, reflects, crosses *j−1 … i+1* backwards, reflects at *i* and runs on to the image plane — N(N−1)/2 paths. The nominal bundle (same launch as the image) is traced along each path with real rays. Per ghost:
• energy_ratio — ghost energy / image energy = R_i·R_j·Π T over the ghost path ÷ Π T over the image path; R from surface_reflectance (the media of the prescription and *coatings*:
a coating for all surfaces, or {record: coating}; records may carry their own coating), at the
angle of incidence of the field's chief ray on each surface (unpolarised; a 45° beamsplitter plate is not
treated as normal incidence);
• focus_offset_mm — the ghost's best focus relative to the image plane (along the image normal; negative = in front of the sensor), radius_mm (RMS) / max_radius_mm on the image plane, centroid_xy (image-plane local) and offset_xy (from the image's chief ray — where the false copy lands relative to the true image);
• point_ratio — ghost irradiance / image irradiance for a point source whose image fills one pixel_mm disk: energy_ratio · (pixel / max(pixel, radius))²;
• extended_ratio — the same for a uniform extended scene: energy_ratio · |det J_image| / |det J_ghost| (the ghost spreads the scene over its own magnification); jacobian is J_ghost (image-plane position of the ghost's chief ray per unit field, 2×2; image_jacobian the image's own).
Rows are sorted by point_ratio (ties by the declared order). n_pairs = N(N−1)/2.
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。
• poc_noncoaxial_optics — py -3.11 examples/poc_noncoaxial_optics.py
table 作為輸入)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
noncoaxial)noncoaxial_system · noncoaxial_example · noncoaxial_layout · noncoaxial_trace · noncoaxial_spot · image_orientation · beamsplitter_branches · tilted_plate_shift
*Provenance: raytrace3d.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.