hdr 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.hdr_dynamic_range(exposures, eta=0.6, K=0.1, sigma_d_e=8.0, dark_offset_dn=4.0, bits=8, full_well_e=None, n_frames=400, n_levels=97, decades=None, seed=0) (to call the implementation directly, import hdrfusion; hdrfusion.hdr_dynamic_range(exposures, eta=0.6, K=0.1, sigma_d_e=8.0, dark_offset_dn=4.0, bits=8, full_well_e=None, n_frames=400, n_levels=97, decades=None, seed=0); from the registry, opsoptics.get("hdr_dynamic_range"))
• GPU: none (CPU reference implementation only)
Measured dynamic range of an HDR capture (EMVA 1288 definition) with its closed form (table).
> The detailed description below is the original text — the summary and the headings are translated.
シミュで実測: 放射輝度の等比の階段(n_levels 段、各段 n_frames 画素 = 繰り返し)を hdr_exposure_series_simulate(線形、γ = 1)で露出の列に撮り、hdr_merge(weight="linear"、真の線形の逆応答)で合成し、段ごとに SNR = 平均 / 標準偏差。
• L_min: SNR が 1 を切る放射輝度(EMVA 1288 の絶対感度しきい値の HDR 版)。
• L_sat: 最短の露出の出力の分散が最大になる放射輝度(EMVA の飽和の定義)を、粗い階段で見つけた最大の段のまわりを細かい階段で測り直して決める。
• dr = L_sat / L_min、dr_db = 20 log10、dr_bits = log2。
閉形式(並べて返す): 低い側は全露出の和の SNR = 1 —— sensorchar.emva_sensitivity_threshold に σ_d → √P σ_d、K → K/√P を入れた μ_p.min を Σ t で割る。高い側は最短の露出が 2^bits − 1(または満杯)に届く放射輝度。露出 1 枚ならそのまま sensorchar.emva_dynamic_range。
Measured in simulation (EMVA 1288 definitions: SNR = 1 and the maximum of the variance), with the closed form side by side. The closed-form saturation is the maximum of the variance of a clipped Gaussian min(N(μ, σ²(μ)), c) with σ² = K²(σ_d² + μ_e) + 1/12 (exact censored- normal moments); L_clip_closed_form is the plain clip point of the mean, about 5 % higher (measured). ★Full-well clipping is approximated as a DN clip at offset + K·full_well.
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.
• 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_robertson · camera_response_linear · hdr_merge · exposure_fusion_mertens · hdr_exposure_series_simulate · hdr_radiance_error
*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.