imaging op• 数据种类:table → table
• 调用: import fullseye as fs; fs.ledger.wavefront_stats(coeffs, radial=128, angular=192)(要直接调用实现,import optics; optics.wavefront_stats(coeffs, radial=128, angular=192);从台账取用则 opsoptics.get("wavefront_stats"))
由 Zernike 展开得到的波前误差统计:RMS、PV 与 Strehl。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
*coeffs* is exactly the dict match3d.fit_zernike returns — {(n, m): coefficient}, coefficients in waves — and this op re-uses match3d's own basis builder, so the two cannot drift apart in normalisation or in the (n, m) convention. Fit with fit_zernike, characterise here.
The wavefront is reconstructed on a polar grid (*radial* x *angular*) over the unit pupil and reduced with the area element rho d(rho) d(theta) — an unweighted mean over a uniform-in-rho grid over-counts the centre and is a real, silent, ~10% error.
Returns a dict: rms_waves (piston removed — piston is not an aberration) · pv_waves peak-to-valley over the pupil · strehl the Marechal estimate exp(-(2*pi*rms)^2) · marechal_valid whether rms_waves <= MARECHAL_RMS_LIMIT (0.1), because past that the estimate is optimistic and reporting the number without the caveat is the dishonest option · terms and n_max of the expansion.
Ground truth it reproduces (measured at the defaults): pure defocus {(2, 0): 0.1} — for which Z = 2*rho^2 - 1 has an exact pupil RMS of 1/sqrt(3) — gives rms_waves = 0.0577422 against the exact 0.0577350, a relative error of 1.2e-4 from the discrete quadrature (3.1e-5 at radial=256), and pv_waves = 0.2 exactly; the Strehl is 0.8766676 against the exact 0.8766962. Pure astigmatism {(2, 2): 0.1} (exact RMS 1/sqrt(6)) gives 0.0408280 against 0.0408248. Piston alone ({(0, 0): c}) gives rms 0 and Strehl 1 for any c, and RMS scales exactly linearly in the coefficients (doubling them doubles the RMS to machine precision).
Raises ValueError: *coeffs* is not a dict, is empty, holds more than MAX_ZERNIKE_TERMS terms, has a key that is not an (n, m) int pair or is not a valid Zernike index (n >= 0, |m| <= n, n-|m| even), or a non-finite coefficient; a radial order above MAX_ZERNIKE_ORDER (40 — the shared basis builder's factorial recurrence breaks its own |Z| <= 1 bound at n = 46, measured, and the same bound is re-checked at runtime); *radial* / *angular* outside [8, MAX_GRID].
The radial quadrature is discrete, so its error grows with the order being
integrated: measured, the relative RMS error tracks (n_max/radial)^2 within a factor 2 — 1.2e-4 at n_max=2, 1.7e-3 at n_max=6 and 4.3e-2 at n_max=20, all at the default radial=128. Below radial >= 16*n_max a RuntimeWarning says so rather than letting a 12%-wrong Strehl look authoritative. Raising *radial* fixes it at O(1/radial^2), but note the basis is built for *all* orders up to n_max, so the working set grows as n_max^2 * radial * angular and is capped by MAX_ZERNIKE_BASIS.
Marechal is a small-aberration approximation and the RMS is over the *fitted* expansion, so it says nothing about wavefront structure finer than n_max — and fit_zernike itself discloses ~10% inter-mode crosstalk at its default sampling. Both limits compound; treat the Strehl as an indicator, not a measurement.
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 — 测量不确定度与校准知识 —— 为了能主张“测得准”
• mv_cameras — 工业相机厂商(与传感器的对应、线扫描 / TDI)
• virtual_machine_vision — 虚拟机器视觉 —— 梳理参数与对象模型
• 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_zernike_aberrations — py -3.11 examples/poc_zernike_aberrations.py
table 作为输入)abcd_matrix · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd · spot_diagram
imaging)psf_to_mtf · mtf_diffraction · edge_spread · sfr_from_edge · mtf50 · veiling_glare_index
*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.