wave op• Data kinds: none → measurement (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.defocus_from_shift(shift_um=10.0, wavelength_um=0.55, f_number=5.6) (to call the implementation directly, import optics; optics.defocus_from_shift(shift_um=10.0, wavelength_um=0.55, f_number=5.6); from the registry, opsoptics.get("defocus_from_shift"))
Defocus wavefront error (waves at the pupil edge) of an axial focus shift.
Moving the detector (or, equivalently, the focus) by `shift_um` along the
axis of an `f/N` beam adds the quadratic wavefront error
`W(rho) = W20 * rho^2` with
`W20 = shift / (8 * lambda * N^2)` [waves]
— the paraxial Seidel defocus term, `rho` the normalised pupil radius
(1 at the edge). This is the number :func:pupil_psf takes as
`defocus_waves`, so the two compose: a longitudinal chromatic aberration
(focal shift versus wavelength, e.g. from `raytrace.chromatic_shift` or a
published `df/f(lambda)) becomes a per-band defocus_waves` here and a
per-band PSF there.
Returns a float (a `measurement`). The sign is the sign of *shift_um*:
positive = the detector sits beyond the focus (the beam has converged
and is diverging again). For a symmetric pupil the PSF does not depend on
the sign; for an asymmetric one (a slit, a W, an off-axis hole) the sign
flips the PSF through the centre — that is exactly the handle a
one-photoreceptor eye can read the direction of defocus from.
Ground truth (closed form, `tests/test_optics.py): shift = 8 lambda N^2`
is exactly one wave; the function is linear in *shift_um* and inverse in
*wavelength_um* and in `N^2 (checked at two of each). At N = 1.5`,
`lambda = 0.55 um (a cephalopod-scale f/1.5` eye) a 250 um focus shift
is 25.3 waves.
Raises `ValueError`: non-finite *shift_um*; non-positive or non-finite
*wavelength_um* / *f_number*.
Paraxial: `W20 = shift/(8 N^2)` is the small-angle expansion of the exact
`shift * (1 - cos theta) sag; at f/1.5 (sin theta = 1/3`) the exact
edge value is 5.7 % below the paraxial one — the number is a *defocus
convention*, not a high-NA wavefront.
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
measurement as input)—
wave)airy_pattern · angular_spectrum_propagate · fraunhofer_pattern · gaussian_beam · 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.