imaging op• Data kinds: image2d → table
• Call: import fullseye as fs; fs.ledger.mtf_tangential_sagittal(psf, pixel_pitch_um=1.0, tangential_axis='y') (to call the implementation directly, import optics; optics.mtf_tangential_sagittal(psf, pixel_pitch_um=1.0, tangential_axis='y'); from the registry, opsoptics.get("mtf_tangential_sagittal"))
Tangential and sagittal MTF from the 2-D transform of a point-spread function (table).
The radial average of psf_to_mtf hides astigmatism and coma; a lens designer reads the two meridians separately. For a field point displaced along +y (the convention of raytrace) the tangential (meridional) MTF is the transform along y, the line through the OTF at fx = 0, and the sagittal MTF is the one along x. Each is a slice of |FFT2(PSF)| / |OTF(0)| at the exact grid frequencies k / (n * pitch) up to the Nyquist limit, with no radial binning. (By the projection-slice theorem the y slice is the transform of the line spread function that integrates the PSF across x.) *tangential_axis* = 'x' swaps the roles for a field along x.
Returns {"tangential": (n, 2) pairs, "sagittal": (m, 2) pairs, "nyquist_cpmm", "tangential_axis"} with frequencies in cycles per millimetre and the MTF in [0, 1]. A PSF binned onto detector pixels (psf_from_opd(pixel_pitch_um=...)) carries the pixel aperture in its MTF; a fine-grid PSF does not.
Ground truth it reproduces: the diffraction-limited circular pupil (2/pi)(arccos x - x sqrt(1 - x^2)) on both curves (mtf_diffraction); the two curves are identical for a rotationally symmetric PSF on axis and separate for an astigmatic one (measured in tests/test_optdesign_psf_metrics.py).
Raises ValueError: bad *psf* (see encircled_energy) or *pixel_pitch_um*; *tangential_axis* not 'x' or 'y'.
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.
• optical_design_metrics — py -3.11 examples/optical_design_metrics.py
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
imaging)psf_to_mtf · mtf_diffraction · encircled_energy · ensquared_energy · energy_radii · wavefront_stats · edge_spread · sfr_from_edge
*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.