photoelastic op• Data kinds: polsweep → table
• Call: import fullseye as fs; fs.ledger.photoelastic_phase_estimate(images, analyzers='camera4', min_modulation=0.01, sum_tolerance=0.05) (to call the implementation directly, import photoelastic; photoelastic.photoelastic_phase_estimate(images, analyzers='camera4', min_modulation=0.01, sum_tolerance=0.05); from the registry, opsoptics.get("photoelastic_phase_estimate"))
• GPU: none (CPU reference implementation only)
Closed-form inversion of polarisation images to retardation δ and principal axis θ → dict.
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).
Every optics op validates its input before computing (nothing slips through silently):
• Units are baked into the argument name — _mm / _um / _deg / _mrad. Confusing mm with µm does not crash; it yields a plausible-looking wrong answer, so the name prevents it. Nothing here guesses the unit from the magnitude.
• Strings raise ValueError — float('50') succeeds, so an unparsed configuration value would slip through as a length (measured: thin_lens('50', '200') returned a plausible 66.667 mm). bool is refused too, as the implicit promotion True == 1.
• complex / masked arrays raise ValueError (real-valued slots only; silently dropping the imaginary part or peeling off the mask is refused). NaN/Inf raises ValueError on every input. Exception, declared: the u_map of bottle_fit_from_pattern takes pixels that could not be measured as NaN (infinity is still refused).
• Division by zero and its relatives are refused by name: focal length 0, radius of curvature 0, refractive index <= 0, a fully opaque aperture (all zeros, so the normalisation is 0/0), a PSF whose sum is <= 0, a Stokes vector with S0 = 0, and an object sitting at the front focal point (the image is at infinity).
• Only two ops return a non-finite value, and both state it as a contract: depth_of_field returns far_mm = inf beyond the hyperfocal distance (that is what the hyperfocal distance means), and gaussian_beam returns wavefront_radius_mm = inf at the waist (the radius of curvature of a plane wavefront). Both also return a finite companion (far_is_infinite / curvature_per_mm). Any other silent NaN/Inf is detected internally and raises ValueError — "float64 overflowed" and "the answer is infinite" are different claims, so the first is never returned wearing the face of the second. Exception, declared: bottle_background_map returns NaN in u_mm for pixels whose ray is unusable (total internal reflection and the like), together with a valid mask and the counts.
• Size caps: generated grids are capped by optics.MAX_GRID (4096); supplied fields/PSFs/apertures by optics.MAX_FIELD_ELEMENTS (2^24); ABCD element chains by optics.MAX_SYSTEM_ELEMENTS (1024); Zernike by MAX_ZERNIKE_TERMS (512) / MAX_ZERNIKE_ORDER (40) / MAX_ZERNIKE_BASIS (2^25). This closes, fail-closed, the paths where a small argument triggers a huge internal allocation (measured: n_max=40 × 4096² needs 108 GB).
• Physically impossible states are refused too: a Stokes vector with degree of polarisation > 1, negative transmittance, negative intensity, and invalid Zernike indices such as n-|m| odd.
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• photoelastic_roundtrip — py -3.11 examples/photoelastic_roundtrip.py
• poc_photoelasticity — py -3.11 examples/poc_photoelasticity.py
table as input)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 operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.