imaging optable → tableimport fullseye as fs; fs.ledger.wavefront_stats(coeffs, radial=128, angular=192) (実装を直接呼ぶなら import optics; optics.wavefront_stats(coeffs, radial=128, angular=192)、台帳から引くなら opsoptics.get("wavefront_stats"))Wavefront error statistics from a Zernike expansion: RMS, PV and Strehl.
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 の全 op は入力を検証してから計算する(黙って通さない):
_mm / _um / _deg / _mrad。mm と µm の取り違えは crash ではなく「もっともらしく間違った答え」なので、名前で防ぐ。大きさから単位を推測する処理は一切しない。ValueError — float('50') は成功してしまうため、未パースの設定値が長さとして通り抜ける(実測: thin_lens('50', '200') がもっともらしい 66.667 mm を返していた)。bool も True == 1 の暗黙昇格として拒否。ValueError(実数枠のみ。虚部の無言切り捨て・マスク剥がしを拒否)。NaN/Inf は全入力で ValueError。depth_of_field の過焦点距離以遠の far_mm = inf(それが過焦点距離の定義)と gaussian_beam のウエストでの wavefront_radius_mm = inf(平面波面の曲率半径)。どちらも有限の相棒(far_is_infinite / curvature_per_mm)を併せて返す。それ以外の無言 NaN/Inf は内部で検出して ValueError —「float64 が溢れた」と「答えが無限大」は別の主張なので、後者の顔で前者を返さない。optics.MAX_GRID(4096)、供給された場/PSF/開口は optics.MAX_FIELD_ELEMENTS(2^24)、ABCD 素子列は optics.MAX_SYSTEM_ELEMENTS(1024)、Zernike は MAX_ZERNIKE_TERMS(512)/ MAX_ZERNIKE_ORDER(40)/ MAX_ZERNIKE_BASIS(2^25)。小さな引数から巨大な内部確保が起きる経路(実測: n_max=40 × 4096² で 108 GB)を fail-closed で塞ぐ。| 物理的に不可能な状態も拒否: 偏光度 > 1 の Stokes ベクトル、負の透過率、負の強度、n- | m | が奇数などの不正な Zernike 添字。 |
py -3.11 examples/optics_imaging.pytable を入力に取れる)abcd_matrix · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd · spot_diagram · ray_fan
imaging)Provenance: optics.py — OPTICS operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.