wave op• 数据种类:无 → measurement(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.defocus_from_shift(shift_um=10.0, wavelength_um=0.55, f_number=5.6)(要直接调用实现,import optics; optics.defocus_from_shift(shift_um=10.0, wavelength_um=0.55, f_number=5.6);从台账取用则 opsoptics.get("defocus_from_shift"))
把轴向焦点偏移换算为离焦波前误差(光瞳边缘处的波数)。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
Moving the detector (or, equivalently, the focus) by shift_um along the axis of an f/N beam adds the quadratic wavefront error W(rho) = W20 * rho^2 with
W20 = shift / (8 * lambda * N^2) [waves]
— the paraxial Seidel defocus term, rho the normalised pupil radius (1 at the edge). This is the number pupil_psf takes as defocus_waves, so the two compose: a longitudinal chromatic aberration (focal shift versus wavelength, e.g. from raytrace.chromatic_shift or a published df/f(lambda)) becomes a per-band defocus_waves here and a per-band PSF there.
Returns a float (a measurement). The sign is the sign of *shift_um*:
positive = the detector sits beyond the focus (the beam has converged and is diverging again). For a symmetric pupil the PSF does not depend on the sign; for an asymmetric one (a slit, a W, an off-axis hole) the sign flips the PSF through the centre — that is exactly the handle a one-photoreceptor eye can read the direction of defocus from.
Ground truth (closed form, tests/test_optics.py): shift = 8 lambda N^2 is exactly one wave; the function is linear in *shift_um* and inverse in *wavelength_um* and in N^2 (checked at two of each). At N = 1.5, lambda = 0.55 um (a cephalopod-scale f/1.5 eye) a 250 um focus shift is 25.3 waves.
Raises ValueError: non-finite *shift_um*; non-positive or non-finite *wavelength_um* / *f_number*.
Paraxial: W20 = shift/(8 N^2) is the small-angle expansion of the exact shift * (1 - cos theta) sag; at f/1.5 (sin theta = 1/3) the exact edge value is 5.7 % below the paraxial one — the number is a *defocus convention*, not a high-NA wavefront.
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
measurement 作为输入)—
wave)airy_pattern · angular_spectrum_propagate · fraunhofer_pattern · fourier_plane_filter · four_f_filter · gaussian_beam · 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.