wave op• 資料種類:image2d × image2d → image2d
• 呼叫: import fullseye as fs; fs.ledger.pupil_blur(image, pupil, defocus_waves=0.0, wavelength_um=0.55, f_number=5.6, pixel_pitch_um=5.0, oversample=4, opd_waves=None)(要直接呼叫實作,import optics; optics.pupil_blur(image, pupil, defocus_waves=0.0, wavelength_um=0.55, f_number=5.6, pixel_pitch_um=5.0, oversample=4, opd_waves=None);從台帳取用則 opsoptics.get("pupil_blur"))
用某一波長帶的光瞳形狀 PSF 模糊影像。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
The forward imaging model of *one* spectral band: the PSF of
:func:pupil_psf (same pupil / defocus / wavelength / f-number
arguments), binned to the image's pixel pitch so the blur is in the
image's own units, convolved with the image (FFT, reflect-padded borders so
a flat field stays flat and nothing wraps around). Call it once per band
with that band's `defocus_waves (from :func:defocus_from_shift` and a
focal shift versus wavelength) and you have the polychromatic image of a
lens with longitudinal chromatic aberration seen through any pupil — the
ingredient of the "colour from chromatic blur" hypothesis for
single-photoreceptor eyes (Stubbs & Stubbs, *PNAS* 113:8206, 2016).
Returns a float64 `image2d` of the image's shape. Linear: no clipping,
no re-normalisation of the image (the PSF sums to 1, so a constant image
is returned unchanged to rounding).
Ground truth it reproduces (measured, `tests/test_optics.py`): a constant
image is unchanged to 1e-12; a delta image returns the binned PSF itself
(the impulse response, to 1e-12 where the kernel fits); with
`defocus_waves = 0` and a diffraction spot much smaller than the pixel
(`lambda N = 0.8 um` on a 5 um pitch) a sharp edge is unchanged to
within 1 % — the *identity at focus*; the blurred image's total is the
input's total to 1e-9 (flux is conserved by the reflect padding).
Raises `ValueError: everything :func:pupil_psf` raises, plus
*image* not 2-D / smaller than 2x2 / over the size cap / complex / masked
/ non-finite, and a non-finite result (an FFT overflow).
Shift-invariant: one PSF for the whole field. Field-dependent blur
(vignetting, off-axis aberration) is `lensimage.render_through_lens`.
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)fraunhofer_pattern · pupil_psf · psf_to_mtf · polarization_demosaic · polarization_demosaic_color · illumination_uniformity · render_through_lens · surface_defect
wave)airy_pattern · angular_spectrum_propagate · fraunhofer_pattern · gaussian_beam · defocus_from_shift · pupil_psf
*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.