wave op• 資料種類:無 → measurement(僅由參數決定的運算子 —— 不接受影像或資料輸入)
• 呼叫: import fullseye as fs; fs.ledger.defocus_from_shift(shift_um=10.0, wavelength_um=0.55, f_number=5.6)(要直接呼叫實作,import optics; optics.defocus_from_shift(shift_um=10.0, wavelength_um=0.55, f_number=5.6);從台帳取用則 opsoptics.get("defocus_from_shift"))
把軸向焦點偏移換算為離焦波前誤差(光瞳邊緣處的波數)。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
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 :func: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
measurement 作為輸入)—
wave)airy_pattern · angular_spectrum_propagate · fraunhofer_pattern · gaussian_beam · pupil_psf · pupil_blur
*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.