fullseye
tb_angular_spectrum_propagate — 2D 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):
つまみ b を振る(0.1 / 0.5 / 0.9、もう一方は既定):
段階(前置きの op → この op。左から順):
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):
使い方
Exact scalar free-space propagation of a complex field (angular spectrum).
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).
参考(サンプルデータ・文献)
- 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。
Studio で試す
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
実行できる例(この op を実際に呼ぶ検証済みサンプル)
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 - poc_grating_interferometry —
py -3.11 examples/poc_grating_interferometry.py
型が繋がる次の op(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
同カテゴリ(typed)
tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_project_points · tb_render_point_depth · tb_points_render · tb_statistical_outlier_removal · tb_radius_outlier_removal
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.