fullseye

lens_system — OPTICS design op

• データ種: なし → table(引数だけで決まる op —— 画像やデータの入力を取らない)
• 呼び出し: import fullseye as fs; fs.ledger.lens_system(surfaces=None, stop=None, object_mm=inf, wavelength_um=0.58756, index_object=1.0, image_mm=None, field=None, aim='paraxial', vignetting=None, image_R=inf, image_k=0.0, afocal=False) (実装を直接呼ぶなら import raytrace; raytrace.lens_system(surfaces=None, stop=None, object_mm=inf, wavelength_um=0.58756, index_object=1.0, image_mm=None, field=None, aim='paraxial', vignetting=None, image_R=inf, image_k=0.0, afocal=False)、台帳から引くなら opsoptics.get("lens_system"))

使い方

Build a validated sequential prescription (the table every other op consumes).

surfaces is a list; each entry is a dict {"R", "t", "n", "k", "ap", "mirror", "decenter", "tilt", "asph"} or a tuple (R, t, n[, k[, ap]]):

• R radius (mm, inf for flat), t thickness to the next surface (mm, the last one is the distance to the image plane when image_mm is not given — use None to place the image at the paraxial focus), n medium after the surface (index, (nd, vd) or :func:glass), k conic (default 0), ap semi-aperture in mm (default None = unlimited), mirror bool, decenter (dx, dy) mm, tilt (ax, ay) degrees about x and y, asph even aspheric coefficients (A4, A6, A8, …) in mm⁻³, mm⁻⁵, … (default none = pure conic), f the focal length (mm, negative = diverging) of an ideal paraxial lens.
• An ideal lens surface ({"f": 50.0, "t": …}) has zero thickness, no shape and no glass (R is flat and n is the medium it sits in; both may be left out). It turns every ray by the thin-lens law exactly, tan θ' = tan θ − h/f per transverse axis (h = the ray height), so a collimated beam crosses the axis at f and a point object images at the Gaussian conjugate with m = −s'/s. Its optical path is the stigmatic one (f − √(h² + f²) for a collimated input, which is the quadratic phase −h²/(2f) at small h; a first surface with a finite object uses that object and its Gaussian image instead), so spot, OPD and PSF analyses of an aberration-free lens read zero aberration. It adds no Seidel terms and no dispersion, takes no mirror / conic / asph, and the non-coaxial raytrace3d does not read it.
• stop: index of the aperture-stop surface (default: the first surface). The stop’s ap is the stop radius. If omitted, the smallest non-null aperture on any surface is used; an error is raised only if none exists.
• object_mm: distance from the first vertex to the object (inf for a collimated object); index_object: index of object space.
• field: default field for the analysis ops — degrees (infinite object) or object height in mm (finite object). Default 0 (on axis).
• aim: how the pupil rays are launched. "paraxial" (the default, and what every earlier version did) aims them at the paraxial entrance pupil, with only the chief ray moved onto the stop centre; in a system with pupil aberration the marginal rays then land outside the stop and are clipped (the stock Cooke triplet loses 48 of 217 rays on axis). "stop" is real-ray aiming: every pupil ray is iterated (Newton, tolerance 1e-11 of the stop radius, ValueError if it does not converge) so that it crosses the stop surface at the requested point, which is what lens-design software reports. See :func:with_aiming.

• vignetting: per-field pupil vignetting factors as design software stores them, a list of {"field", "vdx", "vdy", "vcx", "vcy", "van"} (field in the same unit as field; missing keys are 0). Definition: the format’s user guide (topic “Vignetting Factors”) and knowledge-base article KA-01393. The normalised pupil p is first scaled and shifted, p' = (VDX, VDY) + diag(1 - VCX, 1 - VCY) p, and the result is then rotated by van degrees (counter-clockwise, x' = x cos - y sin): q = R(van) p' — the decentre rotates too. It is applied before the rays are aimed (at the stop with aim="stop", at the paraxial entrance pupil otherwise). A field between two records is interpolated linearly, one outside the listed range takes the nearest record. :func:set_vignetting computes them from the apertures.

• a2 the r^2 term of the sag (mm^-1; the even asphere’s PARM 1) and odd the general power series (B1, B2, ..., B8) added to the sag, z += B1 r + B2 r^2 + ... (an odd asphere; the coefficient of r^i is in mm^(1-i)). Both are left out of the surface dict when zero, so a prescription without them is bit-identical to before.
• solve a declarative rule that sets this surface’s curvature or the thickness after it from the rest of the prescription (marginal / chief ray height or angle, paraxial image, F/#, concentric, aplanatic, pickup); lenssolve.lens_solve_set builds one, lenssolve.lens_apply_solves resolves them (lens_system resolves them once at construction, so the R / t it returns already hold the solved values). A surface with a thickness solve may leave t out.
• image_R, image_k: radius (mm, inf flat) and conic constant of the image surface; rays are intersected with it and spot / OPD are measured on it (the paraxial image is unchanged). Positive R: centre to the right.
• afocal: the image space is collimated (an afocal system: telescope, beam expander). It needs an object at infinity; paraxial_trace then reports angular_magnification and the exit pupil instead of a focal length (efl = bfl = inf), ray_bundle / spot_stats / ray_fan report the exit angle in arcminutes (relative to the chief ray) in place of the image-plane position, and opd_samples references a plane wave. A system flagged afocal whose collimated beam does not leave collimated is refused (ValueError).

Default (no surfaces): a plano-convex BK7 singlet, f ≈ 100 mm, f/4, stop at the first surface — a sensible starting point for the examples and for the no-argument registry call.

Returns a plain dict (JSON-friendly) — pass it to the other functions.

ファミリ共通の入力契約(fail-closed)

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):

• 単位は引数名に埋め込む — _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。
• 文字列は 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。
• complex / masked array は 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。
• 0 除算とその親戚を名指しで拒否: 焦点距離 0・曲率半径 0・屈折率 <= 0・不透明な開口(全 0 なので正規化が 0/0)・総和 <= 0 の PSF・S0 = 0 の Stokes ベクトル・物体が前側焦点にある(像が無限遠)。
• 非有限を返すのは 2 op だけ、しかも契約として明記: 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。
• サイズ上限: 生成格子は 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。

詳しい使い方ガイド

• optics_imaging ファミリ ガイド

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。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。

実行できる例(この op を実際に呼ぶ検証済みサンプル)

• anim3d_lens_aberrations — py -3.11 examples/anim3d_lens_aberrations.py
• lens_calibration_loop_demo — py -3.11 examples/lens_calibration_loop_demo.py
• lens_defect_dataset_demo — py -3.11 examples/lens_defect_dataset_demo.py
• lens_design_demo — py -3.11 examples/lens_design_demo.py
• lens_optimize_demo — py -3.11 examples/lens_optimize_demo.py
• optical_design_metrics — py -3.11 examples/optical_design_metrics.py
• plenoptic_capture_pipeline — py -3.11 examples/plenoptic_capture_pipeline.py
• poc_chromatic_confocal — py -3.11 examples/poc_chromatic_confocal.py
• poc_lens_file_roundtrip — py -3.11 examples/poc_lens_file_roundtrip.py
• poc_lens_global_search — py -3.11 examples/poc_lens_global_search.py
• poc_lens_merit_operands — py -3.11 examples/poc_lens_merit_operands.py
• poc_lens_solves_afocal — py -3.11 examples/poc_lens_solves_afocal.py
• poc_lens_tolerancing — py -3.11 examples/poc_lens_tolerancing.py
• poc_material_optical_library — py -3.11 examples/poc_material_optical_library.py
• poc_noncoaxial_optics — py -3.11 examples/poc_noncoaxial_optics.py
• poc_optics_drawings — py -3.11 examples/poc_optics_drawings.py
• poc_photograph_through_prescription — py -3.11 examples/poc_photograph_through_prescription.py
• poc_plenoptic_camera — py -3.11 examples/poc_plenoptic_camera.py
• poc_tdi_linescan — py -3.11 examples/poc_tdi_linescan.py
• poc_telecentric_metrology — py -3.11 examples/poc_telecentric_metrology.py
• poc_zoom_configurations — py -3.11 examples/poc_zoom_configurations.py

型が繋がる次の op(table を入力に取れる)

abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd

同カテゴリ(design)

thick_lens · glass · example_system · glass_catalog · sellmeier · paraxial_trace · seidel_coefficients · spot_stats

---

Provenance: raytrace.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.

This site is open source. Improve this page.