wave op• データ種: image2d → image2d
• 呼び出し: import fullseye as fs; fs.ledger.pupil_psf(pupil, defocus_waves=0.0, wavelength_um=0.55, f_number=5.6, oversample=4, pixel_pitch_um=None, opd_waves=None) (実装を直接呼ぶなら import optics; optics.pupil_psf(pupil, defocus_waves=0.0, wavelength_um=0.55, f_number=5.6, oversample=4, pixel_pitch_um=None, opd_waves=None)、台帳から引くなら opsoptics.get("pupil_psf"))
Diffraction PSF of an arbitrary pupil shape with defocus (sums to 1).
*pupil* is a square (n, n) amplitude transmittance (0 = opaque, 1 = clear; a binary mask is the usual case) drawn on a grid whose full width is the pupil's clear diameter D — so a circle filling the grid is a conventional round stop, a W-shaped band or an off-axis hole inside the grid is just a different mask, and f_number = f / D refers to that full width in every case. The wavefront over the grid is W(rho) = defocus_waves * rho^2 (+ opd_waves) with rho the radius from the grid centre normalised to 1 at the grid half-width (the Seidel defocus W20; defocus_from_shift converts an axial shift to it), and the PSF is the Fraunhofer intensity of the pupil function
PSF = | FFT{ pupil * exp(i 2 pi W) } |^2
on a zero-padded M x M grid, M = n * oversample (rounded up to even), centred on sample M//2 and normalised to unit sum. The image plane sample spacing is
dx = lambda * N * n / M ~= lambda * N / oversample [um]
— with *pixel_pitch_um* the fine PSF is area-integrated onto detector pixels of that pitch (odd (K, K), centred on a pixel, unit sum), which is what an image convolution needs; the pitch must not be finer than dx. Without it the fine PSF is returned and dx is yours to compute from the formula (an image cannot carry it).
Returns a float64 image2d.
Ground truth it reproduces (measured, tests/test_optics.py):
• a circle filling a 64-sample grid, oversample = 16: the first dark ring at 1.2197 lambda N within 0.5 % of the Airy value (three wavelength / f-number pairs), and the same ring at the same *micrometre* radius within 5 % after binning to a pixel pitch of lambda N / 8 (2.1 % measured — the parabolic minimum on a 9.8-pixel ring, not the binning) — so the pitch bookkeeping is right in physical units, not only in samples; the binned spot is centro-symmetric to 1e-17 and correlates with airy_pattern sampled at the same pitch at 0.99999 (0.9999 at lambda N / 4, 0.9997 at lambda N / 3);
• pure defocus of a circular pupil: the on-axis intensity relative to the unaberrated peak is the closed-form [sin(pi W20)/(pi W20)]^2 (0.405 at half a wave, 0 at one wave — the dark centre of the one-wave defocused Airy spot), within 1 %;
• defocus_waves = 0 and a clear circular pupil is the Airy pattern of airy_pattern to the sampling of the disc edge;
• the sign identity: for a real pupil, -W is the complex conjugate of +W, so PSF(-W)(x) = PSF(+W)(-x) exactly. The test pins it on a W-shaped band: the two PSFs are mirror images through the centre to 1e-12, and they are *not* equal to each other (the W pupil is asymmetric, so the direction of defocus is visible in the blur), while for the circle they are equal (a symmetric pupil cannot tell the sign). Rotating the W pupil by 90/180/270 degrees rotates the PSF the same way (checked, so the asymmetry is the pupil's, not the grid's).
Raises ValueError: *pupil* is not 2-D, not square, smaller than 2x2, over the size cap, complex, masked or non-finite; negative transmittance; an all-opaque pupil (nothing to diffract, the normalisation would be 0/0); *opd_waves* not the same shape as *pupil*; non-finite *defocus_waves*; non-positive or non-finite *wavelength_um* / *f_number* / *pixel_pitch_um*; *oversample* outside [1, 64]; an FFT side over MAX_PUPIL_FFT; an aliased phase — more than MAX_WAVES_PER_SAMPLE waves between neighbouring pupil samples (the message says how many samples the grid needs); a pixel pitch finer than the fine sample spacing (raise *oversample*).
Scalar Fraunhofer optics: no polarisation, no high-NA obliquity, no pupil apodisation by the lens itself. The defocus term is the paraxial rho^2 (see defocus_from_shift). A pupil that reaches the grid edge is fine (the zero padding is the field stop); a pupil *larger* than the grid cannot be expressed — widen the grid and lower f_number.
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):
• 単位は引数名に埋め込む — _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。
• 文字列は 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。
• complex / masked array は 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。
• 0 除算とその親戚を名指しで拒否: 焦点距離 0・曲率半径 0・屈折率 <= 0・不透明な開口(全 0 なので正規化が 0/0)・総和 <= 0 の PSF・S0 = 0 の Stokes ベクトル・物体が前側焦点にある(像が無限遠)。
• 非有限を返すのは 2 op だけ、しかも契約として明記: 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。
• サイズ上限: 生成格子は 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。
• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。
• optics_imaging — py -3.11 examples/optics_imaging.py
image2d を入力に取れる)fraunhofer_pattern · pupil_blur · psf_to_mtf · edge_spread · veiling_glare_index · emva_pair_statistics · emva_defect_pixels · polarization_demosaic
wave)airy_pattern · angular_spectrum_propagate · fraunhofer_pattern · fourier_plane_filter · four_f_filter · gaussian_beam · defocus_from_shift · 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.