Optical lens design, modernized

Local optimization is damped least squares. Above it sit multistart, global search and basin hopping for when the design has to leave the basin it started in. Alongside those are tools that alter the structure of the lens: splitting an element in two, searching for a useful aspheric surface, and synthesis by saddle-point construction, which grows a design by inserting elements at the saddle points of the merit function. Every variable takes its own minimum and maximum, so an optimizer explores shapes you could actually build.

Damped least squares adds one damping value to every variable’s diagonal term, and that single number is standing in for something that is not single — each variable’s own curvature. In a real lens those curvatures differ by orders of magnitude, so whatever value steadies a strongly nonlinear surface curvature will throttle a nearly linear airspace. The usual symptom is a run that crawls, or reports convergence while still some way from the minimum.

As an alternative, LensHH-LT offers PSD II and PSD III — the pseudo-second-derivative methods of D. C. Dilworth, which estimate each variable’s curvature directly and put that on the diagonal instead of a shared damping constant. The estimate costs almost nothing, since it comes from comparing derivatives already computed on two successive iterations. Damped least squares remains the default; PSD is a setting you select per run, in the GUI, the CLI or over MCP. The user guide works through what each one does and when it helps.

The PSD methods are D. C. Dilworth’s. LensHH-LT implements them from his published work: “Pseudo-second-derivative matrix and its application to automatic lens design,” Appl. Opt. 17(21), 3372–3375 (1978); “Improved convergence with the pseudo-second-derivative (PSD) optimization method,” Proc. SPIE 399, 159 (1983); and Lens Design, appendix B.3, which introduces PSD III.

Import and export run in both directions for Zemax (.zmx), CODE V (.seq), OSLO (.len), OpTaliX (.otx) and Optiland (.json). A file brings its surfaces, thicknesses, materials, conics and even-order aspheric terms with it, along with the wavelengths, fields and aperture the original design was specified at — so a design opens as the lens its author drew, not as a shape you have to rebuild and re-check.

Glass names are the part that usually breaks in translation, because every program spells them differently: the catalogs’ N-BK7 and H-ZF52 are NBK7 and HZF52 in CODE V, and a name no catalog claims leaves a surface with no material at all. Names are resolved against your loaded catalogs on the way in and written in each format’s own spelling on the way out, so a lens survives the round trip with its glasses intact. Where a material genuinely cannot be resolved, LensHH-LT says so rather than quietly treating the surface as air.

Windows 10 and 11 get an installer that bundles the .NET 8 runtime, so there is no prerequisite to chase down. Linux ships as a portable AppImage that runs on Ubuntu, Fedora and Arch without being installed. macOS 12 and later runs as a signed app bundle on Apple Silicon — M1 or later; Intel Macs are not supported.

GPU acceleration is available on Windows and Linux, where merit-function evaluation can run on an NVIDIA card. macOS is CPU-only, since there is no CUDA on that platform. Everything else is identical across the three, and a .lhlt file written on one opens unchanged on the others.

Ten catalogs ship with the program, covering SCHOTT, OHARA, CDGM, HOYA, SUMITA, Corning and LightPath — 1,515 glasses in all, model glasses for working from patent data included. Glass substitution searches those catalogs during optimization, per surface, so a design can be steered toward the glasses you can actually buy rather than toward an index and Abbe number nobody melts.

The stock-lens catalog holds 7,623 real parts from Edmund Optics, Thorlabs and Ross Optical. You can search it by focal length, diameter and type, drop a catalog part straight into a design, or ask which stock lenses come closest to an element you have just designed — which is the difference between a design you can order this week and one that needs custom glass.