imaging op• Data kinds: table → pairs
• Call: import fullseye as fs; fs.ledger.sfr_from_edge(esf, window, *, correction, ends=1.0, apodize='none') (to call the implementation directly, import edgesfr; edgesfr.sfr_from_edge(esf, window, *, correction, ends=1.0, apodize='none'); from the registry, opsoptics.get("sfr_from_edge"))
Derives the SFR (MTF measured from an edge) from the ESF.
*esf* is the return value of edge_spread (a dict) or a 1-D array with 1 px step (treated as oversample = 1). Cut ±*window* px around the edge centre (maximum of the absolute difference), normalize with the means of *ends* px at both ends as the black/white references, take the forward difference to get the LSF, and divide the absolute value of its Fourier transform by DC.
*window* (required, px): half-width to cut out. ★Stray light (the tails) lies outside the window, so the narrower the window, the less of it the SFR shows. *correction* (required): undoing the sinc created by sampling.
"none" — no correction (for an image of a discrete step blurred with a discrete PSF, the forward difference is the discrete LSF itself, and this is correct).
"derivative" — the forward difference of an ESF sampled at points from a continuous edge averages the LSF with a box of width Δ, so divide by sinc(fΔ).
"derivative+bin" — the bin mean of edge_spread (width Δ) is 1 more box, so divide by sinc(fΔ)².
*apodize*: "none" or "hamming" (the LSF window of ISO 12233:2017).
Returns (n, 2) pairs: column 0 = frequency [cyc/px] (perpendicular to the edge), column 1 = SFR. 0 to min(1.0, 0.5/Δ) cyc/px (up to the Nyquist of the bin step Δ, but cut off at 2 times the pixel Nyquist = 1 cyc/px; beyond that the sinc correction blows up).
Raises ValueError: esf empty or NaN / window not positive finite or longer than the ESF / ends ≥ window / correction or apodize not in the list / black and white references equal (no edge).
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.
• measurement_uncertainty — Measurement uncertainty and calibration — what it takes to claim you are measuring
• mv_cameras — Industrial camera makers (sensor mapping, line scan / TDI)
• virtual_machine_vision — Virtual machine vision — enumerating the parameters and an object model
• 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_veiling_glare — py -3.11 examples/poc_veiling_glare.py
pairs as input)imaging)psf_to_mtf · mtf_diffraction · wavefront_stats · edge_spread · mtf50 · veiling_glare_index
*Provenance: edgesfr.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.