illumination op• Data kinds: table → table
• Call: import fullseye as fs; fs.ledger.solid_angle_boundaries(light, view_na=0.1) (to call the implementation directly, import illumdesign; illumdesign.solid_angle_boundaries(light, view_na=0.1); from the registry, opsoptics.get("solid_angle_boundaries"))
Closed-form slope thresholds of a smooth specular facet (table).
Illumination cone half-angle α, axis tilt ψ (from *light*); observation half-angle β = asin *view_na*. A facet tilted by θ in the plane of the cone tilt moves the mirrored cone axis to d = |2θ − ψ| from the camera axis. Returned:
• flat_brightness — the flat surface (θ = 0), from the cap
intersection: 1 when ψ + β ≤ α, Ω_α/Ω_β when the whole
(narrower) source cone sits inside the pupil, 0 when ψ ≥ α + β;
• invisible_below_deg — max(|α − β| − ψ, 0)/2: every |θ| below it keeps one cap wholly inside the other, so the brightness does not change and such slopes do not show at all. It is 0 only for matched cones (α = β, or a tilt that puts the flat ground on the edge): there every slope dims from the first fraction of a degree;
• dark_beyond_deg — (α + β + ψ)/2, the slope (tilted toward the cone) where the pupil empties; dark_beyond_other_side_deg — (α + β − ψ)/2 for the opposite tilt;
• sensitivity_per_deg — dB/dθ at θ = 0 from the closed form (0 in the fully lit plateau, non-zero when the flat ground sits on the edge, which is what makes the slope sign readable);
• regime — bright_field (the flat ground sees the whole of the narrower cone: ψ ≤ |α − β|), dark_field (flat dark:
ψ ≥ α + β) or edge (in between: the flat ground sits on the
boundary).
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.
• mv_illumination_practice — Lighting in practice — wavelength, polarisation, drive modes, ambient light, safety
• 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.
• poc_illumination_cone_vs_na — py -3.11 examples/poc_illumination_cone_vs_na.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
illumination)light_source · irradiance_map · illumination_uniformity · defect_contrast · lighting_sweep · illumination_design · solid_angle_light · solid_angle_brightness
*Provenance: illumdesign.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.