photoelastic op• Data kinds: image2d × image2d × image2d → table
• Call: import fullseye as fs; fs.ledger.cubic_photoelastic_birefringence(sxx, syy, txy, pi11_minus_pi12, pi44, refractive_index, crystal_angle_deg=0.0) (to call the implementation directly, import photoelastic; photoelastic.cubic_photoelastic_birefringence(sxx, syy, txy, pi11_minus_pi12, pi44, refractive_index, crystal_angle_deg=0.0); from the registry, opsoptics.get("cubic_photoelastic_birefringence"))
• GPU: none (CPU reference implementation only)
Stress birefringence Δn and slow axis of a cubic crystal on a {100} plane (e.g. a Si wafer) → dict.
Light travels along the [100] normal of a {100} plate. crystal_angle_deg φ is the angle between the [010] direction and the x axis (Stoehr et al. 2020, Eq. 19). The 4th-order piezo-optic tensor of the cubic crystal is rotated, π'_ijkl = R_im R_jn R_ko R_lp π_mnop, the impermeability change is ΔB_ij = π'_ijkl σ_kl and the in-plane birefringence is Δn = (n³/2)(ΔB_II − ΔB_I) — which reproduces Eq. (26) of that paper::
Δn = (n³/4) √( 2((π11−π12)² + π44²)(4τ² + (σx−σy)²)
+ 2((π11−π12)² − π44²)[((σx−σy)² − 4τ²) cos 4φ
+ 4τ(σx−σy) sin 4φ] )
With π44 = π11 − π12 the material is photoelastically isotropic and Δn = (n³/2)|π11 − π12|(σ1 − σ2). In the sign of photoelastic_retardation (n_σ1 − n_σ2 = C(σ1 − σ2); a change of impermeability ΔB changes the index by −(n³/2)ΔB) that is C = −n³(π11−π12)/2, returned as isotropic_coefficient: π11 − π12 > 0 makes σ1 the fast axis, and the value can be passed to photoelastic_retardation as it is.
Coefficients are in Pa⁻¹ (silicon_piezo_optic_coefficients). Returns delta_n (≥ 0), slow_axis_deg (direction of the larger refractive index, (−90, 90]; 0 where Δn = 0 to 1e-12 of that pixel's own stress scale — the fast axis that optics.mueller_element and photoelastic_polarization_images take is slow_axis_deg + 90), effective_coefficient (|Δn|/(σ1−σ2) ≥ 0 [Pa⁻¹], 0 where σ1 = σ2), isotropic_coefficient (signed, as above) and isotropic (σ1 = σ2).
Raises ValueError: non-finite / empty / non-broadcasting stresses, |π| outside [1e-15, 1e-9] Pa⁻¹ (a table value in ×10⁻⁷ MPa⁻¹ or in MPa⁻¹ passed as Pa⁻¹), or a refractive index outside [1, 10].
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.
• 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.
• 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
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 · silicon_piezo_optic_coefficients · polariscope_intensity
*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.