wave op• Data kinds: cimage × cimage → cimage
• Call: import fullseye as fs; fs.ledger.four_f_filter(field, transfer, invert=True) (to call the implementation directly, import optics; optics.four_f_filter(field, transfer, invert=True); from the registry, opsoptics.get("four_f_filter"))
> This operator's description has not been translated yet. The original text follows as it is.
4f 光学プロセッサ: 2 枚のレンズとフーリエ面のフィルタを通した出力。
入力面 → レンズ 1 → フーリエ面(`transfer` を掛ける)→ レンズ 2 →
出力面。スカラ回折の理想 4f 系では出力は
`out(x, y) = (u * h)(-x, -y)`
—— 畳み込みに座標反転が付く。2 枚のレンズがそれぞれ*前向きの*フーリエ
変換を行い、`F{F{u}}(x) = u(-x)` だからである。「フーリエ面で掛けるだけ」
の計算と実物の 4f 系はここが違うので、反転は既定でする。
離散でもこの反転は厳密で、添字の写像 `n -> (-n) mod N` になる
(`np.roll(a[::-1], 1)`)。反転そのものは添字の入れ替えなので誤差を持たない
—— 残る誤差は FFT の往復が乗せる 1e-16 台だけである(`transfer` を 1 に
した実測で最大絶対差 3.4e-16)。
*invert* を `False` にすると反転を省く(フィルタ後の場を入力座標のまま
見たいとき。物理の 4f 系ではないので、既定にはしない)。
真値(この op が再現するもの):
• `identity` フィルタ → 入力の 180 度回転に一致(実測 3.4e-16)。
• `block` フィルタ → 厳密にゼロ。
• `derivative_x` order=n → *n* 階の空間微分。ガウシアン(w=8, 64x64)で
1 階 5.8e-08 / 2 階 5.4e-08 の相対誤差 —— 1e-16 にならないのは
ガウシアンが厳密に帯域制限されていないから(打ち切りの分)。
• 線形性 `4f(a*u1 + b*u2) = a*4f(u1) + b*4f(u2)`。
• 合成 `4f(4f(u, H1), H2) = 4f(u, H1*H2)`(反転を 2 回かけた分だけずれる
ので、合成を試すときは *invert* を `False` にする)。
• `|H| = 1` のフィルタは総パワーを保つ(Parseval)。
Raises `ValueError`: *field* / *transfer* が 2-D でない、形が違う、
2x2 未満、:data:MAX_FIELD_ELEMENTS 超、非有限、マスク付き。
Every optics op validates its input before computing (nothing slips through silently):
• Units are baked into the argument name — _mm / _um / _deg / _mrad. Confusing mm with µm does not crash; it yields a plausible-looking wrong answer, so the name prevents it. Nothing here guesses the unit from the magnitude.
• **Strings raise ValueError** — float('50') succeeds, so an unparsed configuration value would slip through as a length (measured: thin_lens('50', '200') returned a plausible 66.667 mm). bool is refused too, as the implicit promotion True == 1.
• **complex / masked arrays raise ValueError (real-valued slots only; silently dropping the imaginary part or peeling off the mask is refused). NaN/Inf raises ValueError on every input.**
• Division by zero and its relatives are refused by name: focal length 0, radius of curvature 0, refractive index <= 0, a fully opaque aperture (all zeros, so the normalisation is 0/0), a PSF whose sum is <= 0, a Stokes vector with S0 = 0, and an object sitting at the front focal point (the image is at infinity).
• Only two ops return a non-finite value, and both state it as a contract: depth_of_field returns far_mm = inf beyond the hyperfocal distance (that is what the hyperfocal distance means), and gaussian_beam returns wavefront_radius_mm = inf at the waist (the radius of curvature of a plane wavefront). Both also return a finite companion (far_is_infinite / curvature_per_mm). **Any other silent NaN/Inf is detected internally and raises ValueError** — "float64 overflowed" and "the answer is infinite" are different claims, so the first is never returned wearing the face of the second.
• Size caps: generated grids are capped by optics.MAX_GRID (4096); supplied fields/PSFs/apertures by optics.MAX_FIELD_ELEMENTS (2^24); ABCD element chains by optics.MAX_SYSTEM_ELEMENTS (1024); Zernike by MAX_ZERNIKE_TERMS (512) / MAX_ZERNIKE_ORDER (40) / MAX_ZERNIKE_BASIS (2^25). This closes, fail-closed, the paths where a small argument triggers a huge internal allocation (measured: n_max=40 × 4096² needs 108 GB).
• Physically impossible states are refused too: a Stokes vector with degree of polarisation > 1, negative transmittance, negative intensity, and invalid Zernike indices such as n-|m| odd.
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• optics_four_f_processor — py -3.11 examples/optics_four_f_processor.py
cimage as input)angular_spectrum_propagate · jones_apply
wave)airy_pattern · angular_spectrum_propagate · fraunhofer_pattern · fourier_plane_filter · gaussian_beam · defocus_from_shift · pupil_psf · pupil_blur
*Provenance: optics.py — OPTICS operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.