geometric op• Data kinds: none → table (an op determined by its arguments alone — it takes no image or data input)
• Call: import optics; optics.depth_of_field(focal_mm=50.0, f_number=8.0, subject_mm=2000.0, coc_mm=0.03) (or opsoptics.get("depth_of_field"))
Photographic depth of field: near limit, far limit and hyperfocal distance.
The classical circle-of-confusion model. With `H = f^2/(N*c) + f` the
hyperfocal distance and `s` the focused subject distance:
`near = s*(H - f) / (H + s - 2f) and far = s*(H - f) / (H - s)`.
Returns a dict: `near_mm · far_mm · depth_mm (far - near`) ·
`hyperfocal_mm · far_is_infinite` (a bool, so a caller never has to
test for `inf` by accident).
**`far_mm is inf` at or beyond the hyperfocal distance, by contract,
not by accident** — focus at `H and everything from H/2` to infinity
is acceptably sharp, which is the whole point of the hyperfocal distance.
`depth_mm is then inf too. far_is_infinite` says so explicitly,
and the identity `near(H) == H/2` is exact (verified in the tests).
*coc_mm* is the acceptable circle of confusion in the image plane: the
35 mm convention is 0.03 mm, a machine-vision rule of thumb is 1-2 pixel
pitches. It is a *choice*, not a property of the lens — halve it and the
depth of field halves with it, which is why two depth-of-field calculators
disagree.
Ground truth: `f = 50, N = 8, c = 0.03 gives H = 10466.67 mm`; at
`s = H the near limit is exactly H/2 = 5233.33 mm` and the far limit
is `inf; the near/far limits bracket the subject for every s < H`.
Raises `ValueError`: non-positive or non-finite *focal_mm*,
*f_number*, *subject_mm*, *coc_mm*; `subject_mm <= focal_mm` (an object
inside the front focal length cannot be imaged by this lens — see
:func:thin_lens); a hyperfocal distance that is not greater than the
focal length (a degenerate combination of `N and c`).
Paraxial, thin, and blur-circle based: it ignores diffraction, which for
small apertures becomes the real resolution limit — compare with
:func:mtf_diffraction before trusting an `N = 22` calculation.
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.
• lightfield_depth — py -3.11 examples/lightfield_depth.py
• optics_imaging — py -3.11 examples/optics_imaging.py
table as input)abcd_matrix · wavefront_stats · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd · spot_diagram
geometric)thin_lens · abcd_matrix · abcd_trace · relative_illumination
*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.