wave op• 資料種類:image2d → image2d
• 呼叫:import optics; optics.fraunhofer_pattern(aperture, wavelength_um=0.55, distance_mm=100.0, pixel_pitch_um=10.0)(或 opsoptics.get("fraunhofer_pattern"))
開口的遠場(Fraunhofer)繞射強度。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
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)psf_to_mtf · illumination_uniformity · render_through_lens · surface_defect · defocus_blur
wave)airy_pattern · angular_spectrum_propagate · gaussian_beam
*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.