optimization op• Data kinds: table → table
• Call: import lensopt; lensopt.optimize_lens(system, variables=None, fields=None, wavelengths=None, rings=4, efl_target=None, efl_weight=None, field_weights=None, iterations=30, damping=0.001, tolerance=1e-07, min_thickness=0.5, max_thickness=None, min_radius=1.0, pupil_fill=0.98) (or opsoptics.get("optimize_lens"))
Damped-least-squares (Levenberg–Marquardt) optimisation of a prescription (`table`).
*variables*: surface parameters to move — strings `"R<i>"/"c<i>"`
(curvature; a radius may pass through flat), `"t<i>"` (thickness),
`"k<i>" (conic), "A4_<i>", "A6_<i>"` … (even aspheric
coefficients). Default: every finite radius. *efl_target*: hold the
effective focal length (default: the starting EFL, so a design does not
"improve" by getting longer); pass `0 / False` to leave it free.
Fields / wavelengths / rings / weights as in :func:merit_function.
Each iteration builds the Jacobian by forward differences, solves
`(JᵀJ + λ diag(JᵀJ)) δ = −Jᵀr` and accepts the step only if the merit
falls (then λ /= 3; otherwise λ ×= 4 and retried, up to 6 times); a step
that yields an invalid prescription counts as a failure. Stops when the
relative merit change is below *tolerance* twice in a row (`converged`,
`status="converged"`), when two iterations in a row accept no step or λ
blows past 1e8 (`status="stalled", converged=False`), or after
*iterations* (`status="iterations"`). Thickness is clamped to
`[min_thickness, max_thickness] and |R| >= min_radius` — the start
included, so the returned system always obeys the bounds.
Returns ``{"system": optimised prescription, "merit_initial",
"merit_final", "rms_initial", "rms_final", "efl_initial", "efl_final",
"history": [merit per accepted iteration], "iterations", "converged",
"variables": [{"name", "surface", "initial", "final"}], "rays_lost"}``.
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.
• lens_optimize_demo — py -3.11 examples/lens_optimize_demo.py
table as input)abcd_matrix · wavefront_stats · paraxial_trace · seidel_coefficients · spot_stats · tolerance_analysis · wavefront_from_opd · spot_diagram
optimization)*Provenance: lensopt.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.