wave op• Data kinds: image2d → image2d
• Call: import optics; optics.fraunhofer_pattern(aperture, wavelength_um=0.55, distance_mm=100.0, pixel_pitch_um=10.0) (or opsoptics.get("fraunhofer_pattern"))
Far-field (Fraunhofer) diffraction intensity of an aperture.
In the far field the diffracted amplitude is the Fourier transform of the
aperture transmittance, so the intensity is
`|FFT{aperture}|^2` (fftshifted, DC at the centre) normalised to a peak of
exactly 1.0.
Returns a float64 image with the same shape as *aperture*.
The output plane is sampled differently from the input plane — this is
the trap in every FFT diffraction routine. The observation-plane pitch is
`lambda*z/(N_pixels*input_pitch)`; with the defaults
(`0.55 um, 100 mm, 10 um`) and a 64-pixel aperture that is
`0.55*100000/(64*10) = 85.9 um` per pixel. The value is not returned as
an image cannot carry it; compute it from the formula when you need
absolute positions.
A `RuntimeWarning` is emitted when the Fresnel number
`N_F = a^2/(lambda*z) (with a` the aperture's support radius) is not
below 1 — i.e. when you are asking for a far-field pattern at a distance
where the near field still dominates. The result is still returned, because
the Fourier relation is exactly what was asked for; the warning says the
*physics*, not the arithmetic, is out of range.
Ground truth it reproduces (measured): a rectangular slit `w` pixels wide
in an `N`-pixel array puts its diffraction zeros exactly on the DFT bins
`k*N/w`; a 4-pixel-wide slit in a 64-pixel array has exactly 0.0 at
bins +/-16 and +/-32 from DC (the DFT of a boxcar vanishes there to the
last bit, not merely to rounding); the pattern of a centred symmetric
aperture is symmetric to 2.2e-16.
Raises `ValueError`: *aperture* is not 2-D / smaller than 2x2 / over
the size cap / complex / masked / non-finite; a negative transmittance
(that is not an aperture); an opaque aperture (everything zero — an
opaque screen diffracts nothing and the normalisation would be 0/0);
non-positive or non-finite *wavelength_um* / *distance_mm* /
*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.
• 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)psf_to_mtf · illumination_uniformity · render_through_lens · surface_defect · defocus_blur
wave)airy_pattern · angular_spectrum_propagate · gaussian_beam
*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.