wave op• Data kinds: none → table (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.gaussian_beam(waist_um=100.0, wavelength_um=1.064, distance_mm=0.0, n_medium=1.0) (to call the implementation directly, import optics; optics.gaussian_beam(waist_um=100.0, wavelength_um=1.064, distance_mm=0.0, n_medium=1.0); from the registry, opsoptics.get("gaussian_beam"))
Gaussian-beam propagation: spot size, wavefront curvature and Gouy phase.
The q-parameter solution of the paraxial wave equation, evaluated at *distance_mm* from the waist. With zR = pi*w0^2*n/lambda:
w(z) = w0*sqrt(1 + (z/zR)^2) · R(z) = z*(1 + (zR/z)^2) · psi(z) = arctan(z/zR) (Gouy) · far-field half-divergence theta = lambda/(pi*n*w0).
Returns a dict: radius_um the 1/e^2 field radius w(z) · rayleigh_mm zR · wavefront_radius_mm R(z) · curvature_per_mm 1/R(z) · gouy_deg · divergence_mrad the far-field half angle · waist_um and distance_mm echoed back.
wavefront_radius_mm is inf exactly at the waist, by contract:
the wavefront there is planar and a plane has infinite radius. That is why curvature_per_mm is also returned — it is 0 at the waist and finite everywhere, so downstream arithmetic never has to divide by an infinity. A negative R (before the waist, z < 0) means a converging wavefront.
Ground truth it reproduces exactly (verified at machine precision): at z = zR the spot is sqrt(2)*w0, the wavefront radius is 2*zR (its minimum over all z) and the Gouy phase is exactly 45 degrees; the beam-parameter product w0*theta = lambda/(pi*n) holds for every input.
Raises ValueError: non-positive or non-finite *waist_um*, *wavelength_um*, *n_medium*; non-finite *distance_mm*.
Paraxial and fundamental-mode (TEM00) only: a real multimode beam needs an M^2 factor, which this op deliberately does not fake by accepting one silently.
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
table as input)abcd_matrix · wavefront_stats · sfr_from_edge · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd
wave)airy_pattern · angular_spectrum_propagate · fraunhofer_pattern · fourier_plane_filter · four_f_filter · defocus_from_shift · pupil_psf · pupil_blur
*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.