wave op• 資料種類:image2d → image2d
• 呼叫: 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)(要直接呼叫實作,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);從台帳取用則 opsoptics.get("pupil_psf"))
任意形狀光瞳加離焦的繞射 PSF(總和為 1)。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
*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 的每個運算子都先檢驗輸入再計算(不讓任何東西無聲通過):
• 單位寫進參數名 —— _mm / _um / _deg / _mrad。把 mm 和 µm 弄混不會當掉,而是給出「看似合理卻是錯的答案」,所以用命名來防。這裡絕不從數值大小去猜單位。
• **字串一律 ValueError** —— float('50') 會成功,於是未解析的設定值會被當成長度混進來(實測:thin_lens('50', '200') 曾回傳看似合理的 66.667 mm)。bool 也按 True == 1 的隱式提升拒絕。
• **complex / masked array 一律 ValueError(僅接受實數槽位;拒絕無聲丟棄虛部或剝掉遮罩)。所有輸入中的 NaN/Inf 一律 ValueError**。
• 逐項點名拒絕除零及其近親:焦距 0、曲率半徑 0、折射率 <= 0、全不透明光闌(全為 0,正規化變成 0/0)、總和 <= 0 的 PSF、S0 = 0 的 Stokes 向量、物體位於前焦點(像在無窮遠)。
• 只有兩個運算子會回傳非有限值,而且都寫進了契約:depth_of_field 在超焦距以外回傳 far_mm = inf(這正是超焦距的定義),gaussian_beam 在束腰處回傳 wavefront_radius_mm = inf(平面波前的曲率半徑)。兩者都同時回傳一個有限的夥伴(far_is_infinite / curvature_per_mm)。**除此之外的無聲 NaN/Inf 都在內部檢出並 ValueError** ——「float64 溢位了」和「答案是無窮大」是兩種不同的主張,不能拿後者的臉去交付前者。
• 尺寸上限:生成網格受 optics.MAX_GRID(4096)限制,傳入的場/PSF/光闌受 optics.MAX_FIELD_ELEMENTS(2^24),ABCD 元件序列受 optics.MAX_SYSTEM_ELEMENTS(1024),Zernike 受 MAX_ZERNIKE_TERMS(512)/ MAX_ZERNIKE_ORDER(40)/ MAX_ZERNIKE_BASIS(2^25)。以 fail-closed 堵住「小參數引發巨大內部配置」的路徑(實測:n_max=40 × 4096² 需要 108 GB)。
• 物理上不可能的狀態同樣拒絕:偏振度 > 1 的 Stokes 向量、負穿透率、負強度、n-|m| 為奇數等非法 Zernike 指標。
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• 演算法的正典(作者・年份)與用途見上面的族使用指南。
• optics_imaging — py -3.11 examples/optics_imaging.py
image2d 作為輸入)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 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.