Lens group
Traces a whole prescription — one row per surface, with radius, spacing and the glass that follows — as real glass bodies. Cemented and air-spaced groups are the same table, so an achromatic doublet corrects its own colour instead of being told to. Pulse GDD follows the real traced path through each glass.
Open in the canvas →In the real world
A compound lens is specified as an ordered surface table. Each row names one refracting surface by its signed radius, gives the axial distance to the next surface, and names the optical medium after it. The convention is compact because the same rows describe both shape and topology: consecutive glass media form neighbouring elements in a cemented group, while an air medium followed by another glass creates a real air space.
Achromatic doublets exploit that topology by pairing crown and flint glasses whose dispersion and powers oppose one another. Their net focal power remains useful while the first-order F- and C-line focal shift approaches zero. Published optical-glass catalogues therefore specify both the d-line index and the Abbe number used to compare dispersion[1].
In OpticalSetup
Each editable row is radius R · thickness to next · medium after. Radius uses exactly the thick-singlet convention: for the default left-to-right direction, positive R puts the centre of curvature toward local +x, negative R puts it toward −x, and zero is a plane. The last row always exits into air and has no following thickness.
The table is turned into one closed boundary per glass body. Every ray meets the drawn plane or exact circular-arc faces and refracts with the selected glass's wavelength-dependent index. The focal length and back focal distance readouts are a separate paraxial surface-by-surface summary; the tracer never aims rays at them. Longitudinal colour is reported as the difference between the F- and C-line back focal distances, so the supplied singlet and achromat presets can be compared at the same nominal 100 mm focal length.
Cemented and air-spaced groups are not separate element types. Consecutive glass rows make a cemented interface; an air row makes an authored air gap. A cemented interface is realized as two equal-radius faces separated by 0.06 mm of air. That tiny gap is deliberate: the tracer ignores a new hit within 0.05 mm of the previous one, so coincident glass boundaries would silently lose an interaction and send the ray into the wrong medium. The gap, the outlines, the exact trace, and every cardinal readout all use the same realized prescription.
The clear aperture can also change that prescription. If widening it would make two spherical faces cross at the rim, OpticalSetup thickens that body until at least 0.4 mm of edge remains and moves every downstream surface with it. The readouts follow the adjusted geometry rather than continuing to quote the impossible typed shape.
An air row can carry an aperture stop. Its two absorbing segments block light outside the configured clear diameter without adding power; stopping down a fast group therefore reduces its visible spherical caustic by rejecting the marginal rays. “Null F–C colour” varies the chosen row's radius by deterministic bisection, but accepts a solution only when it keeps a finite focal length with the original sign and comparable power. Any first row edit — including the purple on-canvas last-radius control — copies an active preset into a custom table instead of pretending a preset was edited when it was still authoritative.
This is a 2D meridional geometric model with spherical or plane faces. On-axis spherical and visible longitudinal chromatic behavior emerge from the geometry and are meaningful within that scope; off-axis behavior is qualitative. The model does not include skew rays, aspheres, diffraction, quantitative coma or astigmatism, field curvature, coatings, Fresnel reflection, cement index, manufacturing tolerances, or a full optical-design merit function. The 0.06 mm cement gap is a tracer workaround rather than a physical cement model. Catalogue glasses use two-term visible-band Cauchy fits anchored to nd and Abbe number[1], not full Sellmeier curves; deep-UV, infrared, and temporal dispersion claims are outside this element's scope. Per-surface transmission is a configured percentage, not coating physics.