watervision op• 資料種類:無 → table(僅由參數決定的運算子 —— 不接受影像或資料輸入)
• 呼叫: import fullseye as fs; fs.ledger.bottle_fit_from_pattern(u_map, x_mm, pixel_pitch_um, camera_distance_mm, background_distance_mm, known=None, free_background=False, rows_per_section=None, restarts=3) -> 'dict'(要直接呼叫實作,import watervision; watervision.bottle_fit_from_pattern(u_map, x_mm, pixel_pitch_um, camera_distance_mm, background_distance_mm, known=None, free_background=False, rows_per_section=None, restarts=3) -> 'dict';從台帳取用則 opsoptics.get("bottle_fit_from_pattern"))
• GPU:無(僅 CPU 參考實作)
從背景圖案的畸變反推瓶子 -> 字典(半徑、壁厚、折射率、液面,以及各量能確定到什麼程度)。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
u_map (rows, cols) is the background coordinate (mm) each pixel looks at (the u_mm of bottle_background_map, or a phase-shifting measurement of it; NaN where unusable); x_mm the column positions in the plane of the axis, pixel_pitch_um the pitch, the camera and the pattern are camera_distance_mm and background_distance_mm from the axis (known from the set-up). The fill line is found first, from the jump of the map between rows (the liquid and the air bend the pattern differently): rows above it are the empty section, rows below the filled one (level_mm as in fill_level_from_image: (rows below the boundary) * pitch). Each section is reduced to one profile (the median over its rows, rows_per_section of them if given, the two rows next to the boundary left out) and a closed-form model of concentric circles, written without the tracer (an angle and an impact parameter per ray), is fitted by Levenberg-Marquardt over radius_mm, wall_mm, n_glass and n_liquid (the filled section; a bottle with no fill line is one section whose core index is fitted). known is a dict of values held fixed ("radius_mm", "wall_mm", "n_glass", "n_liquid"); free_background=True also fits the distance of the pattern. The start is a scan of the radius from the silhouette (where the map leaves the straight line) with restarts (1 to 3) different index starts; the table reports how far the starts that reach the same cost disagree (start_spread).
The table has radius_mm, wall_mm, n_glass, n_liquid, background_distance_mm, free (the fitted names), sigma (1 sigma of each free name from the Gauss-Newton covariance with the residual scatter as the noise, None if not free), corr (correlation matrix of the free names) with corr_names, cond (condition number of the Jacobian with unit-length
columns: a large value means some combination of the parameters is hardly seen), singular_values, weak_direction (the combination with the smallest singular value, one number per free name) and weak_rel_sigma (the 1 sigma relative change along it), residual_rms_mm, n_columns and columns_rejected (resolved pixels the model calls blocked), converged, iterations, level_found / level_mm / level_row / level_jump_mm (False and None when the rows do not
jump: an empty or a full bottle has no fill line to read; level_mm is then None), fill_state ("partial" or "uniform"). poorly_determined lists the fitted names whose 1 sigma exceeds 1 % of the value or that sit on a bound, and separated is True only when the fit converged and that list is empty. This is a rule of thumb for the error of the noise, not a guarantee: the 1 % was chosen after measuring (at 25 % the flag called 15-20 % of the wrong wall estimates, and 73-76 % of the trials with n_glass off by more than 0.02, separated; at 1 % none of 535 wrong trials in two disjoint seed sets), the covariance assumes the model is exact, and a model error such as an off-centre inner wall changes the estimates without changing the residual, the sigma or this flag. n_liquid is None when no row of the map is left in the filled section. Quantities that barely move the pattern (a thin wall against the glass index when the edge pixels are lost, the pattern distance against the liquid index) come back there, with a large sigma and cond; they are not separated, and the table says so rather than giving a number without it. The model assumes concentric circles with a uniform wall, a horizontal 2-D section, an ideal pinhole, a flat background, exactly known distances and pitch, no dispersion and a flat liquid surface; the maps of bottle_background_map obey the same assumptions, so a test on them proves consistency, not that a real bottle is recovered. A map with fewer than 12 usable columns, a wrong shape, an unknown known name or a camera not beyond one diameter are refused.
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。但已宣告的缺測除外:bottle_fit_from_pattern 的 u_map 以 NaN 接收未能測得的像素(∞ 仍被拒絕)。
• 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。但已宣告的缺測除外:bottle_background_map 對光線不可用的像素(全反射等)在 u_mm 中回傳 NaN,並同時回傳 valid 遮罩和數量。
• 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。
• poc_bottle_pattern_inverse — py -3.11 examples/poc_bottle_pattern_inverse.py
table 作為輸入)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
watervision)caustic_irradiance · bottle_image · fill_level_from_image · bottle_background_map · wet_surface_appearance · wet_dry_inspection_pair · underwater_inspection_image · caustic_floor_segmentation
*Provenance: watervision.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.