DEVION OPTICS DESIGN TOOLS

Zoom Lens Calculators.

Two paraxial calculators for a mechanically compensated 4-group zoom. Explore the endpoints or trace the full motion curve.

A first-order (paraxial) starting-point calculator for a mechanically compensated 4-group zoom: it turns a handful of target specifications into an initial guess for each group's focal length and spacing at the two ends of the zoom range, ready to be dropped into a lens design program for real optimization.

Optical layout & workflow

Paraxial (thin-lens) layout. Outward arrowheads mark a positive (converging) group, inward arrowheads a negative (diverging) group. G2 (variator) shifts the focal length; G3 (compensator) tracks it to hold focus.

How this works — the letters below match the ones in the paraxial diagram above.

Enter the six starting specifications on the left of each field (each one is tagged with its letter, F, D, B, z, F₁, Z).
Click Calculate to get the focal length of every group (G1–G4) and the spacing between them, shown at the long (telephoto) end of the zoom.
The tool also derives the short (wide) end configuration: moving the variator by z shortens the G1–G2 airspace and lengthens the G2–G3 airspace by the same amount. Both configurations are drawn as separate diagrams below.
Check the results: if a focal length looks unreasonably large or small, or if any distance between groups comes out negative in either configuration, that combination of inputs isn't physically sensible as a starting point.
In that case, adjust the initial values (try a different F₁, D, or z) and recalculate — this is a first-order estimate meant to be iterated, not a final design.

01 / INPUT PARAMETERS

Starting specifications

Enter your target specifications below.

F Longer (telephoto) focal length

Focal length at the long end of the zoom range.

D First-group-to-last-group distance

Mechanical distance from G1 to G4.

B Back focal length

Distance from G4 to the image plane.

z Variator travel distance

How far G2 physically moves across the zoom range.

F₁ Focal length of the first group

Starting guess for G1's focal length.

Z Zoom ratio

Long focal length ÷ short focal length.

02 / DESIGN OUTPUT

Results

Enter the parameters above and click Calculate to see the group focal lengths and spacings here.

Runs the full motion-curve solve for a mechanically compensated 4-group (PNPN) continuous zoom across the whole variator travel: it re-derives the same starting-point groups as the Dual FOV calculator, self-consistently solves for the variator travel that reproduces your long focal length exactly, then sweeps the compensator (G4) cam curve between the short and long ends.

Calculation workflow

How this works

Enter the same six base specifications (F, D, B, z, F₁, Z) plus a step size for how finely to sample the variator's travel.
Click Calculate. The tool solves for the exact variator travel needed to hit your long focal length, then sweeps group 4's position across the full zoom range.
You'll get each group's focal length, a table of the compensator (cam) motion at every sampled point, and a "Cam Curves" plot of how far the variator (G2) and compensator (G4) sit from group 1 as the objective focal length changes.
If any airspace comes out negative, a warning appears — group 4 would have to sit behind another group, which isn't buildable. This is a first-order estimate: iterate on F₁, D, z, or the zoom ratio and recalculate until the warning clears.