imaging op• 数据种类:image2d → pairs
• 调用:import optics; optics.psf_to_mtf(psf, pixel_pitch_um=1.0)(或 opsoptics.get("psf_to_mtf"))
由实测点扩散函数得到径向平均的 MTF。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
`OTF = FFT{PSF}, MTF = |OTF| / |OTF(0)|`, then averaged over annuli of
constant spatial frequency out to the Nyquist limit `1/(2*pitch)`. This
is the measurement side of resolution: image a point source (or a slit, or
differentiate a knife edge), hand the spot here, and compare the curve with
the diffraction limit from :func:mtf_diffraction.
Returns an `(n, 2) float64 pairs` array: column 0 the spatial
frequency in cycles per millimetre, column 1 the MTF in [0, 1]. One row
per non-empty radial bin (a very anisotropic array can leave a bin empty;
those rows are dropped rather than filled with a NaN).
Ground truth it reproduces (measured): a delta PSF gives MTF == 1 at every
frequency exactly (max deviation 0.0); a Gaussian PSF of sigma pixels
gives the closed form `exp(-2*pi^2*sigma^2*f^2)` — the maximum absolute
deviation over the whole curve is 4.1e-4 at sigma = 2 px on 128x128,
8.3e-4 at sigma = 1.5 px on 64x64 and 2.4e-4 at sigma = 3 px on 256x256
(the residual is the radial average over a square grid, not an error in the
transform). Doubling *pixel_pitch_um* halves every reported frequency and
leaves the MTF column bit-identical.
The PSF is not re-normalised or re-centred: a PSF whose energy is not
centred carries a linear phase, which the modulus discards, so the MTF is
unaffected — but the *phase* transfer function, which is where a
decentred/asymmetric PSF shows up, is deliberately not summarised here.
Raises `ValueError`: *psf* is not 2-D / smaller than 2x2 / over the
size cap / complex / masked / non-finite; a PSF that sums to zero or less
(the DC normalisation would be 0/0 — an all-zero "PSF" is not a PSF);
non-positive or non-finite *pixel_pitch_um*.
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。
• measurement_uncertainty — 計測の不確かさと校正の知識 — 「測れている」を主張するために
• mv_cameras — 産業用カメラメーカー（センサとの紐付け・ラインスキャン / TDI）
• virtual_machine_vision — 仮想マシンビジョン — パラメータの洗い出しとオブジェクト模型
• 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_veiling_glare — py -3.11 examples/poc_veiling_glare.py
pairs 作为输入)—
imaging)mtf_diffraction · wavefront_stats
*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.