hdr op• Data kinds: images → table
• Call: import fullseye as fs; fs.ledger.camera_response_robertson(images, exposures, levels=256, max_iter=30, tol=1e-06, max_pixels=200000) (to call the implementation directly, import hdrfusion; hdrfusion.camera_response_robertson(images, exposures, levels=256, max_iter=30, tol=1e-06, max_pixels=200000); from the registry, opsoptics.get("camera_response_robertson"))
• GPU: none (CPU reference implementation only)
Inverse camera response by Robertson, Borman & Stevenson's alternating estimate (table).
> The detailed description below is the original text — the summary and the headings are translated.
E_i = Σ_j w(Z_ij) t_j I(Z_ij) / Σ_j w(Z_ij) t_j²(放射輝度)と I(m) = mean{ t_j E_i : Z_ij = m }(逆応答)を交互に、I((L−1)/2) = 1 で正規化して相対変化が tol を切るまで。重みはガウス exp(−4 (z − c)²/c²) で、両端の段(0 と L−1 = 真っ黒と飽和)は 0(放射輝度の式が w t² で重むので、端に残る小さな重みでも飽和した長い露出が支配する —— 実測)。画素は max_pixels 個まで等間隔に間引く(決定的)。観測の無い段は隣の段から線形補間。
Returns the same table as camera_response_debevec (method="robertson", with iterations and converged). ★max_iter=30 follows OpenCV's CalibrateRobertson default. With noisy data the fixed point is biased near both ends (censored pixels just below saturation / just above the dark offset): measured on a 5-exposure EMVA series, the ln error at level 240 grows from −0.03 (20 iterations) to −0.25 (500) while mid levels stay within 0.02 — more iterations is not better. Debevec's smoothness prior does not drift this way. The scale is fixed by I(mid) = 1 (g(mid) = 0).
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.
• poc_hdr_glossy_metal_inspection — py -3.11 examples/poc_hdr_glossy_metal_inspection.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
hdr)camera_response_debevec · camera_response_linear · hdr_merge · exposure_fusion_mertens · hdr_exposure_series_simulate · hdr_radiance_error · hdr_dynamic_range
*Provenance: hdrfusion.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.