geometric optable → matriximport fullseye as fs; fs.ledger.abcd_matrix(elements) (実装を直接呼ぶなら import optics; optics.abcd_matrix(elements)、台帳から引くなら opsoptics.get("abcd_matrix"))Compose a paraxial system into one 2x2 ray-transfer (ABCD) matrix.
elements is a sequence of (kind, *params) in the order light meets
them (the matrix product is formed right-to-left accordingly, so the list
reads like the optical layout, not like the algebra):
("free", d_mm) free-space / homogeneous medium of length d >= 0 ·
("lens", f_mm) thin lens of focal length f != 0 (negative =
diverging) · ("mirror", r_mm) curved mirror of radius r in the
unfolded system (power -2/r) · ("interface", n1, n2) flat refracting
surface · ("curved", n1, n2, r_mm) curved refracting surface.
Returns a (2, 2) float64 matrix acting on the ray state
[y_mm, theta_rad] — feed it to :func:abcd_trace, which handles the
milliradian conversion at the API boundary.
Ground truth it reproduces exactly: a single free-space section is
[[1, d], [0, 1]]; det(M) = n_in / n_out, hence exactly 1 for any
system that starts and ends in the same medium (checked to ~1e-16 in the
tests, and the cheapest correctness self-check you have); two thin lenses
separated by d compose to the classical combined power
1/f = 1/f1 + 1/f2 - d/(f1*f2); a lens sandwiched between two
free-space sections of length f gives the [[0, f], [-1/f, 0]]
Fourier-transform geometry.
Raises ValueError: an empty system, more than
:data:MAX_SYSTEM_ELEMENTS elements, an element that is not a sequence, an
unknown kind, the wrong parameter count for a kind, a negative free-space
distance (reverse the list instead of running light backwards), a zero
focal length or radius, a non-positive refractive index, or any non-finite
parameter.
HALCON: no equivalent (its optics stop at the pinhole camera model).
optics の全 op は入力を検証してから計算する(黙って通さない):
_mm / _um / _deg / _mrad。mm と µm の取り違えは crash ではなく「もっともらしく間違った答え」なので、名前で防ぐ。大きさから単位を推測する処理は一切しない。ValueError — float('50') は成功してしまうため、未パースの設定値が長さとして通り抜ける(実測: thin_lens('50', '200') がもっともらしい 66.667 mm を返していた)。bool も True == 1 の暗黙昇格として拒否。ValueError(実数枠のみ。虚部の無言切り捨て・マスク剥がしを拒否)。NaN/Inf は全入力で ValueError。depth_of_field の過焦点距離以遠の far_mm = inf(それが過焦点距離の定義)と gaussian_beam のウエストでの wavefront_radius_mm = inf(平面波面の曲率半径)。どちらも有限の相棒(far_is_infinite / curvature_per_mm)を併せて返す。それ以外の無言 NaN/Inf は内部で検出して ValueError —「float64 が溢れた」と「答えが無限大」は別の主張なので、後者の顔で前者を返さない。optics.MAX_GRID(4096)、供給された場/PSF/開口は optics.MAX_FIELD_ELEMENTS(2^24)、ABCD 素子列は optics.MAX_SYSTEM_ELEMENTS(1024)、Zernike は MAX_ZERNIKE_TERMS(512)/ MAX_ZERNIKE_ORDER(40)/ MAX_ZERNIKE_BASIS(2^25)。小さな引数から巨大な内部確保が起きる経路(実測: n_max=40 × 4096² で 108 GB)を fail-closed で塞ぐ。| 物理的に不可能な状態も拒否: 偏光度 > 1 の Stokes ベクトル、負の透過率、負の強度、n- | m | が奇数などの不正な Zernike 添字。 |
py -3.11 examples/optics_imaging.pymatrix を入力に取れる)geometric)thin_lens · abcd_trace · depth_of_field · relative_illumination
Provenance: optics.py — OPTICS 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.