wave op• 数据种类:image2d → image2d
• 调用: 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)(要直接调用实现,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);从台账取用则 opsoptics.get("pupil_psf"))
任意形状光瞳加离焦的衍射 PSF(总和为 1)。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
*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 的每个算子都先校验输入再计算(不让任何东西无声通过):
• 单位写进参数名 —— _mm / _um / _deg / _mrad。把 mm 和 µm 弄混不会崩溃,而是给出「看着合理却是错的答案」,所以用命名来防。这里绝不从数值大小去猜单位。
• 字符串一律 ValueError —— float('50') 会成功,于是未解析的配置值会被当成长度混进来(实测:thin_lens('50', '200') 曾返回看着合理的 66.667 mm)。bool 也按 True == 1 的隐式提升拒绝。
• complex / masked array 一律 ValueError(仅接受实数槽位;拒绝无声丢弃虚部或剥掉掩码)。所有输入中的 NaN/Inf 一律 ValueError。
• 逐项点名拒绝除零及其近亲:焦距 0、曲率半径 0、折射率 <= 0、全不透明光阑(全为 0,归一化变成 0/0)、总和 <= 0 的 PSF、S0 = 0 的 Stokes 矢量、物体位于前焦点(像在无穷远)。
• 只有两个算子会返回非有限值,而且都写进了契约:depth_of_field 在超焦距以外返回 far_mm = inf(这正是超焦距的定义),gaussian_beam 在束腰处返回 wavefront_radius_mm = inf(平面波前的曲率半径)。两者都同时返回一个有限的搭档(far_is_infinite / curvature_per_mm)。除此之外的无声 NaN/Inf 都在内部检出并 ValueError ——「float64 溢出了」和「答案是无穷大」是两种不同的主张,不能拿后者的脸去交付前者。
• 尺寸上限:生成网格受 optics.MAX_GRID(4096)限制,传入的场/PSF/光阑受 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「小参数引发巨大内部分配」的路径(实测:n_max=40 × 4096² 需要 108 GB)。
• 物理上不可能的状态同样拒绝:偏振度 > 1 的 Stokes 矢量、负透过率、负强度、n-|m| 为奇数等非法 Zernike 指标。
• 示例数据目录(下载 URL / 许可证) —— 2-D 用 skimage.data(BSD/公有领域)加合成图,3-D 给出真实数据源(Stanford/PDS 等)的下载 URL。
• 算子来历与参考文献 —— 该算子族所依据的研究/方法出处。
• 算法的正典(作者、年份)与用途见上面的族使用指南。
• optics_imaging — py -3.11 examples/optics_imaging.py
image2d 作为输入)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 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.