geometric op• 数据种类:无 → table(仅由参数决定的算子 —— 不接受图像或数据输入)
• 调用: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"))
摄影景深:近界、远界与超焦距。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
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**。
• 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。
• 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。
• lightfield_depth — py -3.11 examples/lightfield_depth.py
• optics_imaging — py -3.11 examples/optics_imaging.py
table 作为输入)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 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.