photoelastic op• Data kinds: image2d → image2d
• Call: import fullseye as fs; fs.ledger.polariscope_intensity(delta_rad, axis_deg=45.0, setup='plane_dark', polarizer_deg=0.0, intensity=1.0) (to call the implementation directly, import photoelastic; photoelastic.polariscope_intensity(delta_rad, axis_deg=45.0, setup='plane_dark', polarizer_deg=0.0, intensity=1.0); from the registry, opsoptics.get("polariscope_intensity"))
• GPU: yes (mechanical GPU path from the allow-list, CuPy). device="auto" chooses the GPU from the measured size (4,194,304 pixels) up
Closed-form intensity of plane and circular polariscopes in dark and bright field (isochromatics and isoclinics).
intensity is the intensity of the polarised beam leaving the first polariser. With retardance δ and principal (isoclinic) direction θ:
• circular_dark I sin²(δ/2) — isochromatics only (dark at N = 0, 1, 2 …)
• circular_bright I cos²(δ/2) — dark at N = ½, 3/2 …
• plane_dark (crossed, polariser at β) I sin²(2(θ−β)) sin²(δ/2) — isochromatics × isoclinics (dark where θ = β or β+90°)
• plane_bright (parallel) I [1 − sin²(2(θ−β)) sin²(δ/2)]
The default is the crossed plane polariscope (the basic setup, where both the axis and the polariser angle matter); when only δ is given the principal axes are taken at 45 deg to the polariser, where the plane polariscope shows the isochromatics at full contrast (at 0 deg the field is dark everywhere — that is an isoclinic, not "no stress"). These equal the Mueller chain built from optics.mueller_element (the tests compare them). Returns an array of the broadcast shape.
Raises ValueError: an unknown setup, non-finite inputs, a negative intensity, or |δ| beyond 200 fringes (a retardation in nm passed as rad).
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
image2d as input)fraunhofer_pattern · pupil_psf · pupil_blur · psf_to_mtf · encircled_energy · ensquared_energy · energy_radii · mtf_tangential_sagittal
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.