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; :func: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 :func: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
:func: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 :data:MAX_PUPIL_FFT; an aliased phase — more than
:data: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 :func: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 · polarization_demosaic · polarization_demosaic_color · illumination_uniformity · render_through_lens · surface_defect
wave)airy_pattern · angular_spectrum_propagate · fraunhofer_pattern · 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.