geometric op• Data kinds: none → table (an op determined by its arguments alone — it takes no image or data input)
• Call: import optics; optics.thin_lens(focal_mm=50.0, object_mm=200.0) (or opsoptics.get("thin_lens"))
Gaussian thin-lens imaging: where the image lands and how big it is.
Solves `1/f = 1/s_o + 1/s_i` in the real-is-positive convention:
*object_mm* (`s_o`) is the lens-to-object distance and must be positive;
the returned `image_mm (s_i`) is positive for a real image on the far
side of the lens and negative for a virtual image on the object side
(which is what a diverging lens, `focal_mm < 0`, always produces).
Returns a dict: `image_mm · magnification m = -s_i/s_o`
(*negative = inverted*, the normal case for a real image; `|m| < 1` is a
demagnified, i.e. machine-vision, geometry) · `object_mm` and
`focal_mm` echoed back so a table of results is self-describing ·
`working_distance_mm = s_o + s_i` for a real image, the
object-to-sensor span a machine builder actually has to fit.
Ground truth it reproduces exactly (verified in `tests/test_optics.py`):
`f = 50, s_o = 200 gives s_i = 200/3 = 66.6667 and m = -1/3`; at
`s_o = 2f the image is at 2f with m = -1` (the 1:1 conjugate);
the reciprocal identity `1/f - 1/s_o - 1/s_i` is 0 to machine precision
over the whole tested range.
Raises `ValueError: focal_mm == 0` (not a lens), non-positive or
non-finite *object_mm*, and — explicitly, instead of returning `inf` —
`object_mm == focal_mm`, where the object sits at the front focal point
and images at infinity (a collimator, not an imaging conjugate).
Paraxial and thin: no aberration, no principal-plane separation. HALCON has
no equivalent (its camera model starts after the lens, at the projection).
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)abcd_matrix · abcd_trace · depth_of_field · 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.