noncoaxial op• 資料種類:無 → table(僅由參數決定的運算子 —— 不接受影像或資料輸入)
• 呼叫: import fullseye as fs; fs.ledger.noncoaxial_system(elements=None, stop=None, object_mm=inf, wavelength_um=0.58756, index_object=1.0, field=(0.0, 0.0), image_mm=None, image_tilt=(0.0, 0.0), object_tilt=(0.0, 0.0))(要直接呼叫實作,import raytrace3d; raytrace3d.noncoaxial_system(elements=None, stop=None, object_mm=inf, wavelength_um=0.58756, index_object=1.0, field=(0.0, 0.0), image_mm=None, image_tilt=(0.0, 0.0), object_tilt=(0.0, 0.0));從台帳取用則 opsoptics.get("noncoaxial_system"))
建構經過驗證的非共軸序列光學系統(table)——面、座標斷點、折轉、平板。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
*elements* is a list of dicts ("type" defaults to "surface"), or the dict returned by raytrace.lens_system (converted exactly; its traces then equal raytrace's to 1e-12):
• {"type": "surface", "R", "t", "n", "k", "ap", "mirror", "asph", "decenter", "tilt", "coating", "beamsplitter": {"R": r, "branch": "transmit"|"reflect"}} — as in raytrace.lens_system; decenter / tilt act on that surface only. coating is used by the ghost analysis (None / "bare", a material name = a quarter-wave single layer, [(material, nm), ...] from the incident side, or {"R": r}).
• {"type": "break", "decenter": (dx, dy), "tilt": (ax, ay, az), "order": "xyz"|"zyx", "t"} — a coordinate break (decenter, then rotate about x, the new y, the new z; degrees) that moves every later surface; {"type": "break", "undo": j} is the exact inverse of break record *j*.
• {"type": "return", "to": j, "t"} — go back to the coordinate system at the entry of record *j*.
• {"type": "fold_mirror", "tilt": (ax, ay), "t", "ap", "R", "reflectance"} — a mirror tilted by (ax, ay); the axis is reflected (45° folds by 90°) and t runs along the folded axis.
• {"type": "plate", "thickness", "n", "tilt": (ax, ay), "wedge": (wx, wy), "t", "beamsplitter": r, "branch", "coating_front", "coating_back"} — a tilted plane-parallel (or wedged) plate, or a plate beamsplitter; t is measured from the front vertex along the incoming axis (transmit branch) or along the reflected axis (reflect branch).
*stop* is the record index of the aperture stop (default: the first surface); *field* is (fx, fy) (degrees for an object at infinity, mm otherwise); *image_tilt* / *object_tilt* tilt the image / object plane about the local x and y axes (degrees; Scheimpflug). The last record's t is the distance to the image plane (None = the paraxial focus along the axis ray).
Default: a singlet f ≈ 100 mm followed by a 45° fold mirror (the image lands along +y).
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_example · noncoaxial_layout · noncoaxial_trace · noncoaxial_spot · image_orientation · beamsplitter_branches · tilted_plate_shift · scheimpflug_tilt
*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.