typed op• データ種: cimage → cimage
• 呼び出し: fullseye.apply(img, "tb_angular_spectrum_propagate", a=0.5, b=0.5) (2-D は 1 画像 + 2 スカラつまみ a,b∈[0,1] のモデル)
*図は合成の入力 128×128 で実際に走らせた出力。左が入力、右が出力。点群は上から見た散布(明るさ = z)、1-D 列は折れ線、体積は z 方向の最大値投影、動画は中央フレーム、複素画像は振幅、絵にならない返り値は値そのもの。*
つまみ a を振る(0.1 / 0.5 / 0.9、もう一方は既定):
▸ tb_angular_spectrum_propagate: knob a sweep (docs site)
つまみ b を振る(0.1 / 0.5 / 0.9、もう一方は既定):
▸ tb_angular_spectrum_propagate: knob b sweep (docs site)
段階(前置きの op → この op。左から順):
▸ tb_angular_spectrum_propagate: stages (docs site)
別の画像でも(合成シーン / 写真 / 硬貨。上段が入力、下段がその出力。つまみは既定):
▸ tb_angular_spectrum_propagate: other inputs (docs site)
複素場の厳密なスカラー自由空間伝搬（角スペクトル法）。
> 以下の詳細説明は原文のままです —— 要約と見出しは訳出済み。
`U(z) = IFFT{ FFT{U(0)} * exp(i*2*pi*z*sqrt(1/lambda^2 - fx^2 - fy^2)) }`
in the `exp(-i*omega*t)` convention, so a positive *distance_um*
propagates forward. Components beyond the propagating cone
(`fx^2 + fy^2 > 1/lambda^2`) are attenuated by
`exp(-2*pi*|z|*sqrt(fx^2 + fy^2 - 1/lambda^2))`, which is the physical
evanescent decay — not zeroed, so `distance_um = 0` is an *exact*
identity and the transfer function is continuous through it.
Unlike Fresnel propagation this makes no paraxial approximation: it is the
exact solution of the Helmholtz equation for a band-limited field, valid
from a fraction of a wavelength outward.
Returns a complex128 array with the same shape as *field*.
Ground truth it reproduces (measured): `distance_um = 0` returns the field
bit-identically (it short-circuits the transform pair); propagating `+z`
then `-z` returns the original to a relative L2 error of 4.3e-16 to
5.3e-16 for a band-limited field (measured on three: 64x64 random at
+/-50 um, a 64x64 Gaussian at +/-250 um, a 128x128 random at +/-500 um);
total power is conserved to between 0 and 3.5e-16 relative on the same
three. A field *with*
evanescent content does not round-trip — those components are gone by
construction, in both directions, because that is what physically happens.
*field* is a field in the space domain, not a spectrum: do not hand it
the fftshifted output of :func:complexops.cx_fft. Real input is promoted
to complex, which loses nothing.
Aliasing: the discrete transfer function is periodic, so a field that
diffracts past the array edge wraps around. The practical guard is the
usual one — pad the field so the propagated support stays inside, and keep
`pixel_pitch_um below lambda/(2*NA)`. No warning can detect this
reliably from the array alone, so none is invented.
Raises `ValueError`: *field* is not 2-D, smaller than 2x2, larger than
:data:MAX_FIELD_ELEMENTS, masked, or non-finite; non-positive or
non-finite *wavelength_um* / *pixel_pitch_um*; non-finite *distance_um*.
Typed bridge of the optics op `angular_spectrum_propagate into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. a drives wavelength_um (default 0.55) and b drives distance_um` (default 100).
• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
下のプログラムは実際に走ることを確かめてある(図と同じ入力)。Studio のヘルプではこのブロックがボタンになり、その場で読み込んで実行できる。
img_to_cimage 0.50 0.50 tb_angular_spectrum_propagate 0.50 0.50
▸ Load this pipeline · Load & run
次の例は元の台帳 op angular_spectrum_propagate を呼ぶもの。この橋渡し op は同じ実装を fn(v, a, b) 規約に合わせただけなので、挙動はそのまま当てはまる(呼び出し形だけ違う)。
• optics_imaging — py -3.11 examples/optics_imaging.py
cimage を入力に取れる)identity · tb_cx_ifft · tb_cx_magnitude · tb_cx_phase · tb_cx_real · tb_cx_imag · tb_cx_log_magnitude · tb_cx_apply_transfer_function
typed)tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal · tb_voxel_grid_downsample
*Provenance: ops.py — 2D operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.