imaging op• Data kinds: none → pairs (an op determined by its arguments alone — it takes no image or data input)
• Call: import optics; optics.mtf_diffraction(f_number=5.6, wavelength_um=0.55, samples=64) (or opsoptics.get("mtf_diffraction"))
The diffraction-limited MTF of a circular pupil (closed form).
`MTF(x) = (2/pi)*(arccos(x) - x*sqrt(1 - x^2)) with x = nu/nu_c` the
frequency normalised to the cutoff `nu_c = 1/(lambda*N)`. This is the
ceiling: no aberration-free lens at this f-number can do better, and a
measured :func:psf_to_mtf curve above it means the measurement is wrong.
Returns a `(samples, 2) float64 pairs` array: column 0 the spatial
frequency in cycles per millimetre from 0 to the cutoff, column 1 the
MTF in [0, 1].
Ground truth it reproduces exactly (machine precision): `MTF(0) = 1`,
`MTF(nu_c) = 0, and at half the cutoff the textbook 0.391`
(`(2/pi)*(pi/3 - sqrt(3)/4) = 0.3910022...`). The cutoff itself at
`lambda = 0.55 um, N = 5.6 is 324.7 cycles/mm` — which is why
stopping a machine-vision lens past f/8 stops buying depth of field and
starts buying blur (compare :func:depth_of_field).
Raises `ValueError`: non-positive or non-finite *f_number* /
*wavelength_um*; *samples* outside `[2, MAX_GRID]`.
Incoherent illumination, circular unobstructed pupil, no aberration, no
defocus, and no detector: the pixel aperture and the sensor's own MTF
multiply on top of this and are not included.
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
pairs as input)—
imaging)*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.