geometric 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 optics; optics.depth_of_field(focal_mm=50.0, f_number=8.0, subject_mm=2000.0, coc_mm=0.03)(或 opsoptics.get("depth_of_field"))
攝影景深:近界、遠界與超焦距。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
The classical circle-of-confusion model. With `H = f^2/(N*c) + f` the
hyperfocal distance and `s` the focused subject distance:
`near = s*(H - f) / (H + s - 2f) and far = s*(H - f) / (H - s)`.
Returns a dict: `near_mm · far_mm · depth_mm (far - near`) ·
`hyperfocal_mm · far_is_infinite` (a bool, so a caller never has to
test for `inf` by accident).
**`far_mm is inf` at or beyond the hyperfocal distance, by contract,
not by accident** — focus at `H and everything from H/2` to infinity
is acceptably sharp, which is the whole point of the hyperfocal distance.
`depth_mm is then inf too. far_is_infinite` says so explicitly,
and the identity `near(H) == H/2` is exact (verified in the tests).
*coc_mm* is the acceptable circle of confusion in the image plane: the
35 mm convention is 0.03 mm, a machine-vision rule of thumb is 1-2 pixel
pitches. It is a *choice*, not a property of the lens — halve it and the
depth of field halves with it, which is why two depth-of-field calculators
disagree.
Ground truth: `f = 50, N = 8, c = 0.03 gives H = 10466.67 mm`; at
`s = H the near limit is exactly H/2 = 5233.33 mm` and the far limit
is `inf; the near/far limits bracket the subject for every s < H`.
Raises `ValueError`: non-positive or non-finite *focal_mm*,
*f_number*, *subject_mm*, *coc_mm*; `subject_mm <= focal_mm` (an object
inside the front focal length cannot be imaged by this lens — see
:func:thin_lens); a hyperfocal distance that is not greater than the
focal length (a degenerate combination of `N and c`).
Paraxial, thin, and blur-circle based: it ignores diffraction, which for
small apertures becomes the real resolution limit — compare with
:func:mtf_diffraction before trusting an `N = 22` calculation.
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。
• lightfield_depth — py -3.11 examples/lightfield_depth.py
• optics_imaging — py -3.11 examples/optics_imaging.py
table 作為輸入)abcd_matrix · wavefront_stats · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd · spot_diagram
geometric)thin_lens · abcd_matrix · abcd_trace · relative_illumination
*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.