lensmerit op• 資料種類:table → table
• 呼叫: import fullseye as fs; fs.ledger.optimize_lens_operands(system=None, operands=None, variables=None, iterations: 'int' = 30, fields=None, wavelengths=None, field_weights=None, wavelength_weights=None, damping: 'float' = 0.001, tolerance: 'float' = 1e-07, min_thickness: 'float' = 0.5, max_thickness=None, min_radius: 'float' = 1.0, glass_candidates=None, glass_iterations: 'int' = 12, outer_iterations: 'int' = 3) -> 'dict'(要直接呼叫實作,import lensmerit; lensmerit.optimize_lens_operands(system=None, operands=None, variables=None, iterations: 'int' = 30, fields=None, wavelengths=None, field_weights=None, wavelength_weights=None, damping: 'float' = 0.001, tolerance: 'float' = 1e-07, min_thickness: 'float' = 0.5, max_thickness=None, min_radius: 'float' = 1.0, glass_candidates=None, glass_iterations: 'int' = 12, outer_iterations: 'int' = 3) -> 'dict';從台帳取用則 opsoptics.get("optimize_lens_operands"))
• GPU:無(僅 CPU 參考實作)
用 LM 法最小化運算元表的評價函數,玻璃也可以作為變數(table)。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
The residual vector is the stack of the table's rows (merit_evaluate); *variables* are those of lensopt.optimize_lens ("c<i>" / "R<i>" curvature, "t<i>", "k<i>", "A4_<i>" ...; default every finite radius) plus glass variables "g<i>". The continuous steps are lensopt's: forward-difference Jacobian, (JtJ + lambda diag(JtJ)) delta = -Jt r, a step is kept only if the merit falls (lambda /3, else x4, six tries), stalled after two iterations without an accepted step. *min_thickness*, *max_thickness* and *min_radius* clamp the variables as in optimize_lens (the table's bound rows are what keep edges, centres and gaps in range). A glass variable moves the glass of surface *i* over *glass_candidates* (a list of media: catalogue names, (n_d, V_d) pairs or raytrace.glass dicts; or a dict "g<i>" -> list) by an outer discrete sweep: after the continuous optimisation has converged each candidate is tried once (swapped in, the continuous variables re-optimised for *glass_iterations* iterations) and the best is kept if it lowers the merit; this repeats up to *outer_iterations* times with a full continuous re-optimisation between sweeps. A candidate equal to the glass already there is skipped, so a list holding only the current glass gives exactly the continuous result.
Returns {"system", "table_before", "table_after", "merit_initial", "merit_final", "history", "iterations", "rejected_steps", "converged", "status", "variables", "glass", "dominant_after", "violated_after"}; table_before / table_after are merit_evaluate results, rejected_steps counts the trial steps refused, glass lists each glass variable with its initial / final medium and every candidate's merit.
Example::
r = optimize_lens_operands(lens, ops, ["c0", "c1", "t0", "g0"], glass_candidates=[(1.52, 64.2), (1.62, 36.4)],
fields=m["fields"])
r["merit_initial"], r["merit_final"], r["glass"][0]["final"]
optics 的每個運算子都先檢驗輸入再計算(不讓任何東西無聲通過):
• 單位寫進參數名 —— _mm / _um / _deg / _mrad。把 mm 和 µm 弄混不會當掉,而是給出「看似合理卻是錯的答案」,所以用命名來防。這裡絕不從數值大小去猜單位。
• 字串一律 ValueError —— float('50') 會成功,於是未解析的設定值會被當成長度混進來(實測:thin_lens('50', '200') 曾回傳看似合理的 66.667 mm)。bool 也按 True == 1 的隱式提升拒絕。
• complex / masked array 一律 ValueError(僅接受實數槽位;拒絕無聲丟棄虛部或剝掉遮罩)。所有輸入中的 NaN/Inf 一律 ValueError。
• 逐項點名拒絕除零及其近親:焦距 0、曲率半徑 0、折射率 <= 0、全不透明光闌(全為 0,正規化變成 0/0)、總和 <= 0 的 PSF、S0 = 0 的 Stokes 向量、物體位於前焦點(像在無窮遠)。
• 只有兩個運算子會回傳非有限值,而且都寫進了契約:depth_of_field 在超焦距以外回傳 far_mm = inf(這正是超焦距的定義),gaussian_beam 在束腰處回傳 wavefront_radius_mm = inf(平面波前的曲率半徑)。兩者都同時回傳一個有限的夥伴(far_is_infinite / curvature_per_mm)。除此之外的無聲 NaN/Inf 都在內部檢出並 ValueError ——「float64 溢位了」和「答案是無窮大」是兩種不同的主張,不能拿後者的臉去交付前者。
• 尺寸上限:生成網格受 optics.MAX_GRID(4096)限制,傳入的場/PSF/光闌受 optics.MAX_FIELD_ELEMENTS(2^24),ABCD 元件序列受 optics.MAX_SYSTEM_ELEMENTS(1024),Zernike 受 MAX_ZERNIKE_TERMS(512)/ MAX_ZERNIKE_ORDER(40)/ MAX_ZERNIKE_BASIS(2^25)。以 fail-closed 堵住「小參數引發巨大內部配置」的路徑(實測:n_max=40 × 4096² 需要 108 GB)。
• 物理上不可能的狀態同樣拒絕:偏振度 > 1 的 Stokes 向量、負穿透率、負強度、n-|m| 為奇數等非法 Zernike 指標。
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• 演算法的正典(作者、年份)與用途見上面的族使用指南。
• optimized_lens_tolerance_sensitivity — py -3.11 examples/optimized_lens_tolerance_sensitivity.py
• poc_lens_merit_operands — py -3.11 examples/poc_lens_merit_operands.py
table 作為輸入)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
lensmerit)merit_operands_list · merit_evaluate · merit_default · merit_boundary_operands · merit_contributions
*Provenance: lensmerit.py — OPTICS 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.