photoelastic op• Data kinds: none → table (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.kirsch_plate_stress(hole_radius_m=0.005, remote_stress_pa=1000000.0, load_angle_deg=0.0, half_width_m=0.02, size=129, x=None, y=None) (to call the implementation directly, import photoelastic; photoelastic.kirsch_plate_stress(hole_radius_m=0.005, remote_stress_pa=1000000.0, load_angle_deg=0.0, half_width_m=0.02, size=129, x=None, y=None); from the registry, opsoptics.get("kirsch_plate_stress"))
• GPU: none (CPU reference implementation only)
Closed-form σx, σy, τxy and polar components for an infinite plate with a hole under uniaxial tension (Kirsch solution) → dict.
Infinite plate with a circular hole of radius a under a remote uniaxial stress S along the direction load_angle_deg (Kirsch 1898). With θ measured from the load direction::
σrr = S/2 (1 − a²/r²) + S/2 (1 − 4a²/r² + 3a⁴/r⁴) cos 2θ
σθθ = S/2 (1 + a²/r²) − S/2 (1 + 3a⁴/r⁴) cos 2θ
τrθ = −S/2 (1 + 2a²/r² − 3a⁴/r⁴) sin 2θ
Hole edge: σrr = τrθ = 0 and σθθ = S(1 − 2 cos 2θ) — 3S at θ = 90°, −S at θ = 0°. Far away the field tends to the uniform uniaxial stress.
Returns a dict with sxx, syy, txy, srr, stt, trt [Pa] (θ of the polar components is measured from the x axis), x, y, inside (False inside the hole on the grid, stresses 0 there), pixel_m, and stress_concentration = 3.0 (max σθθ/S on the edge).
Raises ValueError: non-finite or non-positive radius / half width, a non-finite stress or angle, a hole that does not fit the grid, only one of x/y, or explicit points inside the hole.
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 · principal_stress · retardation_from_birefringence · photoelastic_retardation · retardation_convert · cubic_photoelastic_birefringence · 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.