wave op• 数据种类:无 → image2d(仅由参数决定的算子 —— 不接受图像或数据输入)
• 调用: import fullseye as fs; fs.ledger.airy_pattern(size=64, wavelength_um=0.55, f_number=5.6, pixel_pitch_um=0.5)(要直接调用实现,import optics; optics.airy_pattern(size=64, wavelength_um=0.55, f_number=5.6, pixel_pitch_um=0.5);从台账取用则 opsoptics.get("airy_pattern"))
圆形光瞳的衍射极限 PSF(艾里图样)。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
I(r) = [2*J1(v)/v]^2 with v = pi*r/(lambda*N), r the radial distance in the image plane, N the working f-number. Sampled on a size x size grid centred between pixels for even *size* and on a pixel for odd *size*. The normalisation is analytic (I(0) = 1 by the v -> 0 limit), not a division by the sampled maximum: for odd *size* the centre pixel is therefore exactly 1.0, and for even *size* the true peak falls between pixels so the largest *sample* is below it (0.9679 at size = 8 with the defaults, measured). Rescaling to the sampled maximum instead would quietly change the physics with the parity of the grid.
Returns a (size, size) float64 intensity image.
Ground truth it reproduces (measured, tests/test_optics.py): the first dark ring sits at the first zero of J1, r = 1.2197*lambda*N — at lambda = 0.55 um, N = 5.6 that is 3.7567 um, and the sampled radial minimum lands at 3.760 um on a 0.01 um grid (0.3 of a sample away, which is the sampling, not an error); the peak is exactly 1.0 at the centre and the pattern is symmetric to 1e-16.
The encircled energy inside that ring is the textbook 83.8% of the *whole infinite* pattern — which a finite grid cannot measure: the Airy tails fall off only as 1/r^3, so a 25.6 um half-width grid reports 0.857 and a 51.2 um one 0.847 (both measured). The number is quoted here as physics, not as something this op returns.
The v -> 0 limit is evaluated explicitly as 1.0 rather than left to 0/0: that division is the classic silent-NaN in every hand-rolled Airy routine, and the centre pixel is exactly where it bites.
Raises ValueError: *size* outside [2, MAX_GRID]; non-positive or non-finite *wavelength_um*, *f_number*, *pixel_pitch_um*.
Scalar, aberration-free, unobstructed circular pupil, low NA. A central obscuration (a mirror telescope) changes the ring structure; high NA needs a vector treatment. For the *measured* PSF of a real system use psf_to_mtf on an image of a point source instead.
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
• poc_veiling_glare — py -3.11 examples/poc_veiling_glare.py
image2d 作为输入)fraunhofer_pattern · pupil_psf · pupil_blur · psf_to_mtf · edge_spread · veiling_glare_index · emva_pair_statistics · emva_defect_pixels
wave)angular_spectrum_propagate · fraunhofer_pattern · fourier_plane_filter · four_f_filter · gaussian_beam · defocus_from_shift · pupil_psf · 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.