wave opなし → image2d(引数だけで決まる op —— 画像やデータの入力を取らない)import fullseye as fs; fs.ledger.airy_pattern(size=64, wavelength_um=0.55, f_number=5.6, pixel_pitch_um=0.5) (実装を直接呼ぶなら import optics; optics.airy_pattern(size=64, wavelength_um=0.55, f_number=5.6, pixel_pitch_um=0.5)、台帳から引くなら opsoptics.get("airy_pattern"))The diffraction-limited PSF of a circular pupil (Airy pattern).
I(r) = [2*J1(v)/v]^2 with v = pi*r/(lambda*N), r the radial
distance in the image plane, N the working f-number. Sampled on a
size x size grid centred between pixels for even size and on a pixel
for odd size. The normalisation is analytic (I(0) = 1 by the
v -> 0 limit), not a division by the sampled maximum: for odd size
the centre pixel is therefore exactly 1.0, and for even size the true
peak falls between pixels so the largest sample is below it (0.9679 at
size = 8 with the defaults, measured). Rescaling to the sampled maximum
instead would quietly change the physics with the parity of the grid.
Returns a (size, size) float64 intensity image.
Ground truth it reproduces (measured, tests/test_optics.py): the first
dark ring sits at the first zero of J1, r = 1.2197*lambda*N — at
lambda = 0.55 um, N = 5.6 that is 3.7567 um, and the sampled
radial minimum lands at 3.760 um on a 0.01 um grid (0.3 of a sample
away, which is the sampling, not an error); the peak is exactly 1.0 at the
centre and the pattern is symmetric to 1e-16.
The encircled energy inside that ring is the textbook 83.8% of the whole
infinite pattern — which a finite grid cannot measure: the Airy tails fall
off only as 1/r^3, so a 25.6 um half-width grid reports 0.857 and a
51.2 um one 0.847 (both measured). The number is quoted here as physics,
not as something this op returns.
The v -> 0 limit is evaluated explicitly as 1.0 rather than left to
0/0: that division is the classic silent-NaN in every hand-rolled Airy
routine, and the centre pixel is exactly where it bites.
Raises ValueError: size outside [2, MAX_GRID]; non-positive or
non-finite wavelength_um, f_number, pixel_pitch_um.
Scalar, aberration-free, unobstructed circular pupil, low NA. A central
obscuration (a mirror telescope) changes the ring structure; high NA needs a
vector treatment. For the measured PSF of a real system use
:func:psf_to_mtf on an image of a point source instead.
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.pypy -3.11 examples/poc_veiling_glare.pyimage2d を入力に取れる)fraunhofer_pattern · pupil_psf · pupil_blur · psf_to_mtf · illumination_uniformity · render_through_lens · surface_defect · defocus_blur
wave)angular_spectrum_propagate · fraunhofer_pattern · gaussian_beam · defocus_from_shift · pupil_psf · pupil_blur
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.