imaging op• Data kinds: image2d → pairs
• Call: import optics; optics.psf_to_mtf(psf, pixel_pitch_um=1.0) (or opsoptics.get("psf_to_mtf"))
Radially-averaged MTF of a measured point-spread function.
`OTF = FFT{PSF}, MTF = |OTF| / |OTF(0)|`, then averaged over annuli of
constant spatial frequency out to the Nyquist limit `1/(2*pitch)`. This
is the measurement side of resolution: image a point source (or a slit, or
differentiate a knife edge), hand the spot here, and compare the curve with
the diffraction limit from :func:mtf_diffraction.
Returns an `(n, 2) float64 pairs` array: column 0 the spatial
frequency in cycles per millimetre, column 1 the MTF in [0, 1]. One row
per non-empty radial bin (a very anisotropic array can leave a bin empty;
those rows are dropped rather than filled with a NaN).
Ground truth it reproduces (measured): a delta PSF gives MTF == 1 at every
frequency exactly (max deviation 0.0); a Gaussian PSF of sigma pixels
gives the closed form `exp(-2*pi^2*sigma^2*f^2)` — the maximum absolute
deviation over the whole curve is 4.1e-4 at sigma = 2 px on 128x128,
8.3e-4 at sigma = 1.5 px on 64x64 and 2.4e-4 at sigma = 3 px on 256x256
(the residual is the radial average over a square grid, not an error in the
transform). Doubling *pixel_pitch_um* halves every reported frequency and
leaves the MTF column bit-identical.
The PSF is not re-normalised or re-centred: a PSF whose energy is not
centred carries a linear phase, which the modulus discards, so the MTF is
unaffected — but the *phase* transfer function, which is where a
decentred/asymmetric PSF shows up, is deliberately not summarised here.
Raises `ValueError`: *psf* is not 2-D / smaller than 2x2 / over the
size cap / complex / masked / non-finite; a PSF that sums to zero or less
(the DC normalisation would be 0/0 — an all-zero "PSF" is not a PSF);
non-positive or non-finite *pixel_pitch_um*.
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 — 計測の不確かさと校正の知識 — 「測れている」を主張するために
• mv_cameras — 産業用カメラメーカー（センサとの紐付け・ラインスキャン / TDI）
• virtual_machine_vision — 仮想マシンビジョン — パラメータの洗い出しとオブジェクト模型
• 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.
• optics_imaging — py -3.11 examples/optics_imaging.py
• poc_veiling_glare — py -3.11 examples/poc_veiling_glare.py
pairs as input)—
imaging)mtf_diffraction · wavefront_stats
*Provenance: optics.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.