imaging op• 資料種類:image2d → pairs
• 呼叫:import optics; optics.psf_to_mtf(psf, pixel_pitch_um=1.0)(或 opsoptics.get("psf_to_mtf"))
由實測點擴散函數得到徑向平均的 MTF。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
`OTF = FFT{PSF}, MTF = |OTF| / |OTF(0)|`, then averaged over annuli of
constant spatial frequency out to the Nyquist limit `1/(2*pitch)`. This
is the measurement side of resolution: image a point source (or a slit, or
differentiate a knife edge), hand the spot here, and compare the curve with
the diffraction limit from :func:mtf_diffraction.
Returns an `(n, 2) float64 pairs` array: column 0 the spatial
frequency in cycles per millimetre, column 1 the MTF in [0, 1]. One row
per non-empty radial bin (a very anisotropic array can leave a bin empty;
those rows are dropped rather than filled with a NaN).
Ground truth it reproduces (measured): a delta PSF gives MTF == 1 at every
frequency exactly (max deviation 0.0); a Gaussian PSF of sigma pixels
gives the closed form `exp(-2*pi^2*sigma^2*f^2)` — the maximum absolute
deviation over the whole curve is 4.1e-4 at sigma = 2 px on 128x128,
8.3e-4 at sigma = 1.5 px on 64x64 and 2.4e-4 at sigma = 3 px on 256x256
(the residual is the radial average over a square grid, not an error in the
transform). Doubling *pixel_pitch_um* halves every reported frequency and
leaves the MTF column bit-identical.
The PSF is not re-normalised or re-centred: a PSF whose energy is not
centred carries a linear phase, which the modulus discards, so the MTF is
unaffected — but the *phase* transfer function, which is where a
decentred/asymmetric PSF shows up, is deliberately not summarised here.
Raises `ValueError`: *psf* is not 2-D / smaller than 2x2 / over the
size cap / complex / masked / non-finite; a PSF that sums to zero or less
(the DC normalisation would be 0/0 — an all-zero "PSF" is not a PSF);
non-positive or non-finite *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。
• measurement_uncertainty — 計測の不確かさと校正の知識 — 「測れている」を主張するために
• mv_cameras — 産業用カメラメーカー（センサとの紐付け・ラインスキャン / TDI）
• virtual_machine_vision — 仮想マシンビジョン — パラメータの洗い出しとオブジェクト模型
• 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
• poc_veiling_glare — py -3.11 examples/poc_veiling_glare.py
pairs 作為輸入)—
imaging)mtf_diffraction · wavefront_stats
*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.