wave op• 数据种类:image2d → image2d
• 调用:import optics; optics.fraunhofer_pattern(aperture, wavelength_um=0.55, distance_mm=100.0, pixel_pitch_um=10.0)(或 opsoptics.get("fraunhofer_pattern"))
开口的远场(Fraunhofer)衍射强度。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
In the far field the diffracted amplitude is the Fourier transform of the
aperture transmittance, so the intensity is
`|FFT{aperture}|^2` (fftshifted, DC at the centre) normalised to a peak of
exactly 1.0.
Returns a float64 image with the same shape as *aperture*.
The output plane is sampled differently from the input plane — this is
the trap in every FFT diffraction routine. The observation-plane pitch is
`lambda*z/(N_pixels*input_pitch)`; with the defaults
(`0.55 um, 100 mm, 10 um`) and a 64-pixel aperture that is
`0.55*100000/(64*10) = 85.9 um` per pixel. The value is not returned as
an image cannot carry it; compute it from the formula when you need
absolute positions.
A `RuntimeWarning` is emitted when the Fresnel number
`N_F = a^2/(lambda*z) (with a` the aperture's support radius) is not
below 1 — i.e. when you are asking for a far-field pattern at a distance
where the near field still dominates. The result is still returned, because
the Fourier relation is exactly what was asked for; the warning says the
*physics*, not the arithmetic, is out of range.
Ground truth it reproduces (measured): a rectangular slit `w` pixels wide
in an `N`-pixel array puts its diffraction zeros exactly on the DFT bins
`k*N/w`; a 4-pixel-wide slit in a 64-pixel array has exactly 0.0 at
bins +/-16 and +/-32 from DC (the DFT of a boxcar vanishes there to the
last bit, not merely to rounding); the pattern of a centred symmetric
aperture is symmetric to 2.2e-16.
Raises `ValueError`: *aperture* is not 2-D / smaller than 2x2 / over
the size cap / complex / masked / non-finite; a negative transmittance
(that is not an aperture); an opaque aperture (everything zero — an
opaque screen diffracts nothing and the normalisation would be 0/0);
non-positive or non-finite *wavelength_um* / *distance_mm* /
*pixel_pitch_um*.
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)psf_to_mtf · illumination_uniformity · render_through_lens · surface_defect · defocus_blur
wave)airy_pattern · angular_spectrum_propagate · gaussian_beam
*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.