wave op• Data kinds: image2d × image2d → image2d
• Call: import fullseye as fs; fs.ledger.pupil_blur(image, pupil, defocus_waves=0.0, wavelength_um=0.55, f_number=5.6, pixel_pitch_um=5.0, oversample=4, opd_waves=None) (to call the implementation directly, import optics; optics.pupil_blur(image, pupil, defocus_waves=0.0, wavelength_um=0.55, f_number=5.6, pixel_pitch_um=5.0, oversample=4, opd_waves=None); from the registry, opsoptics.get("pupil_blur"))
Blur an image with the PSF of a pupil shape at one wavelength band.
The forward imaging model of *one* spectral band: the PSF of
:func:pupil_psf (same pupil / defocus / wavelength / f-number
arguments), binned to the image's pixel pitch so the blur is in the
image's own units, convolved with the image (FFT, reflect-padded borders so
a flat field stays flat and nothing wraps around). Call it once per band
with that band's `defocus_waves (from :func:defocus_from_shift` and a
focal shift versus wavelength) and you have the polychromatic image of a
lens with longitudinal chromatic aberration seen through any pupil — the
ingredient of the "colour from chromatic blur" hypothesis for
single-photoreceptor eyes (Stubbs & Stubbs, *PNAS* 113:8206, 2016).
Returns a float64 `image2d` of the image's shape. Linear: no clipping,
no re-normalisation of the image (the PSF sums to 1, so a constant image
is returned unchanged to rounding).
Ground truth it reproduces (measured, `tests/test_optics.py`): a constant
image is unchanged to 1e-12; a delta image returns the binned PSF itself
(the impulse response, to 1e-12 where the kernel fits); with
`defocus_waves = 0` and a diffraction spot much smaller than the pixel
(`lambda N = 0.8 um` on a 5 um pitch) a sharp edge is unchanged to
within 1 % — the *identity at focus*; the blurred image's total is the
input's total to 1e-9 (flux is conserved by the reflect padding).
Raises `ValueError: everything :func:pupil_psf` raises, plus
*image* not 2-D / smaller than 2x2 / over the size cap / complex / masked
/ non-finite, and a non-finite result (an FFT overflow).
Shift-invariant: one PSF for the whole field. Field-dependent blur
(vignetting, off-axis aberration) is `lensimage.render_through_lens`.
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.
• 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
image2d as input)fraunhofer_pattern · pupil_psf · psf_to_mtf · polarization_demosaic · polarization_demosaic_color · illumination_uniformity · render_through_lens · surface_defect
wave)airy_pattern · angular_spectrum_propagate · fraunhofer_pattern · gaussian_beam · defocus_from_shift · pupil_psf
*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.