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.brazilian_disc_stress(radius_m=0.025, thickness_m=0.006, load_n=500.0, size=129, x=None, y=None) (to call the implementation directly, import photoelastic; photoelastic.brazilian_disc_stress(radius_m=0.025, thickness_m=0.006, load_n=500.0, size=129, x=None, y=None); from the registry, opsoptics.get("brazilian_disc_stress"))
• GPU: none (CPU reference implementation only)
Closed-form plane stress σx, σy, τxy of a diametrically compressed disc (Brazilian disc) → dict.
Diametrically compressed disc, point loads load_n [N] at (0, ±R) acting along the y axis, plane stress (Hondros / Frocht)::
r1² = x² + (R−y)², r2² = x² + (R+y)², k = 2P/(π t)
σx = −k [ x²(R−y)/r1⁴ + x²(R+y)/r2⁴ − 1/(2R) ]
σy = −k [ (R−y)³/r1⁴ + (R+y)³/r2⁴ − 1/(2R) ]
τxy = k [ x(R−y)²/r1⁴ − x(R+y)²/r2⁴ ]
Stresses are in Pa (tension positive). At the centre σx = 2P/(πDt) and σy = −6P/(πDt). The free rim carries no traction except at the two load points, where the point-load solution is singular.
radius_m, thickness_m : disc radius and thickness [m].
load_n : the compressive load P [N] (positive = compression).
size : grid size (odd puts the centre on a pixel) when x/y are not given.
x, y : optional evaluation points [m] (arrays that broadcast). Points
outside the disc or exactly on a load point are refused.
dict with sxx, syy, txy [Pa], x, y [m], inside (bool; on the grid, the rim pixel ring and the pixels next to the load points are False and their stresses are 0 — the point-load singularity is not a measurement), pixel_m (grid spacing, or 0 for explicit points).
Raises ValueError: non-finite or non-positive radius / thickness / load, a thickness that looks like millimetres, only one of x/y, points outside the disc or on a load point.
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)kirsch_plate_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.