wave opimage2d → image2dimport fullseye as fs; fs.ledger.fraunhofer_pattern(aperture, wavelength_um=0.55, distance_mm=100.0, pixel_pitch_um=10.0) (実装を直接呼ぶなら import optics; optics.fraunhofer_pattern(aperture, wavelength_um=0.55, distance_mm=100.0, pixel_pitch_um=10.0)、台帳から引くなら opsoptics.get("fraunhofer_pattern"))Far-field (Fraunhofer) diffraction intensity of an aperture.
In the far field the diffracted amplitude is the Fourier transform of the
aperture transmittance, so the intensity is
|FFT{aperture}|^2 (fftshifted, DC at the centre) normalised to a peak of
exactly 1.0.
Returns a float64 image with the same shape as aperture.
The output plane is sampled differently from the input plane — this is
the trap in every FFT diffraction routine. The observation-plane pitch is
lambda*z/(N_pixels*input_pitch); with the defaults
(0.55 um, 100 mm, 10 um) and a 64-pixel aperture that is
0.55*100000/(64*10) = 85.9 um per pixel. The value is not returned as
an image cannot carry it; compute it from the formula when you need
absolute positions.
A RuntimeWarning is emitted when the Fresnel number
N_F = a^2/(lambda*z) (with a the aperture’s support radius) is not
below 1 — i.e. when you are asking for a far-field pattern at a distance
where the near field still dominates. The result is still returned, because
the Fourier relation is exactly what was asked for; the warning says the
physics, not the arithmetic, is out of range.
Ground truth it reproduces (measured): a rectangular slit w pixels wide
in an N-pixel array puts its diffraction zeros exactly on the DFT bins
k*N/w; a 4-pixel-wide slit in a 64-pixel array has exactly 0.0 at
bins +/-16 and +/-32 from DC (the DFT of a boxcar vanishes there to the
last bit, not merely to rounding); the pattern of a centred symmetric
aperture is symmetric to 2.2e-16.
Raises ValueError: aperture is not 2-D / smaller than 2x2 / over
the size cap / complex / masked / non-finite; a negative transmittance
(that is not an aperture); an opaque aperture (everything zero — an
opaque screen diffracts nothing and the normalisation would be 0/0);
non-positive or non-finite wavelength_um / distance_mm /
pixel_pitch_um.
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.pyimage2d を入力に取れる)pupil_psf · pupil_blur · psf_to_mtf · illumination_uniformity · render_through_lens · surface_defect · defocus_blur
wave)airy_pattern · angular_spectrum_propagate · 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.