photoelastic op• 資料種類:polsweep → table
• 呼叫: import fullseye as fs; fs.ledger.photoelastic_phase_estimate(images, analyzers='camera4', min_modulation=0.01, sum_tolerance=0.05)(要直接呼叫實作,import photoelastic; photoelastic.photoelastic_phase_estimate(images, analyzers='camera4', min_modulation=0.01, sum_tolerance=0.05);從台帳取用則 opsoptics.get("photoelastic_phase_estimate"))
• GPU:無(僅 CPU 參考實作)
由偏振影像以閉式反求相位延遲 δ 與主軸 θ → dict。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
Inverse of photoelastic_polarization_images (right-circular illumination). With S0 = ½(I0 + I90 + I45 + I135) (the mean of the two pair sums), S1 = I0 − I90, S2 = I45 − I135:
• camera4 (4 linear analysers): sin δ = √(S1² + S2²)/S0 and δ = arcsin(·) — unique only for δ ∈ [0, π/2] (a quarter wave):
linear analysers alone cannot see the sign of cos δ.
• stokes6 (+ right/left circular): S3 = IR − IL and δ = atan2(√(S1² + S2²), S3) ∈ [0, π].
In both, θ = ½ atan2(−S1, S2) mod 180 deg, in (−90, 90] — the fast axis (for a material with C > 0, σ1 lies at θ + 90°). The pair (δ, θ) and (−δ, θ + 90°) give identical images; the estimate returns the representative with δ ≥ 0. Where the modulation √(S1²+S2²)/S0 (= |sin δ|) is at or below min_modulation (default 0.01, i.e. δ within ~0.01 rad of 0 or π, where 1 % intensity noise already turns the axis by tens of degrees) the axis is undefined: axis_valid is False and axis_deg is 0 there.
One exposure obeys I0 + I90 = I45 + I135 (and = IR + IL). Real frames do so only to the noise and the demosaic interpolation, so the check is per pixel and relative: sum_mismatch = |I45 + I135 − (I0 + I90)| / S0 (for stokes6 the larger of that and |IR + IL − S0| / S0).
images : (K, H, W) array or list of K frames in the order of analyzers.
analyzers : "camera4" (0/45/90/135) or "stokes6" (+ right/left circular).
min_modulation : modulation at or below which the axis is not reported.
sum_tolerance : largest sum_mismatch a pixel may have and stay valid
(relative to S0, default 0.05). Measured basis: with 1 % independent
noise per frame the mismatch stays below it (99th percentile 2.9 %,
maximum 4.6 % over 40 000 pixels), and the bilinear interpolation of
optics.polarization_demosaic leaves ≤ 1.5 % on 95 % of a disc with
nine resolved fringes; pixels above it are aliased fringes, saturated
or moving pixels, or frames from another exposure. Must lie in [0, 1].
Returns delta_rad, axis_deg, axis_valid, valid (sum_mismatch ≤ sum_tolerance; delta_rad is still computed where it is False but is not a measurement there, and axis_valid is False), sum_mismatch, modulation, intensity (S0) and stokes ((4, H, W); S3 = 0 for camera4, which is a limitation, not a measurement).
Raises ValueError: wrong number of frames, non-2-D / non-finite / negative frames, a dark pixel (S0 = 0), sum_tolerance outside [0, 1], or frames whose pair sums disagree by more than sum_tolerance on more than half of the pixels (not one camera exposure, the wrong frame order, or fringes too dense for the sensor).
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。
• photoelastic_roundtrip — py -3.11 examples/photoelastic_roundtrip.py
table 作為輸入)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
photoelastic)brazilian_disc_stress · kirsch_plate_stress · principal_stress · retardation_from_birefringence · photoelastic_retardation · retardation_convert · cubic_photoelastic_birefringence · silicon_piezo_optic_coefficients
*Provenance: photoelastic.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.