imaging op• 資料種類:table → table
• 呼叫:import optics; optics.wavefront_stats(coeffs, radial=128, angular=192)(或 opsoptics.get("wavefront_stats"))
由 Zernike 展開得到的波前誤差統計:RMS、PV 與 Strehl。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
*coeffs* is exactly the dict :func: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
:data: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
:data: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 :data: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。
• 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
• 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。
• optics_imaging — py -3.11 examples/optics_imaging.py
table 作為輸入)abcd_matrix · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd · spot_diagram · ray_fan
imaging)*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.