Design Galilean and Keplerian beam expanders. Calculate output beam size, divergence reduction, lens focal lengths, and Rayleigh range improvement.
A beam expander is an optical system that increases the diameter of a laser beam while proportionally reducing its divergence. This is one of the most common operations in laser optics, used whenever a laser needs to propagate over long distances with minimal spread, focus to a smaller spot, or fill a larger optical element. The two classic designs — Galilean and Keplerian — each offer distinct advantages.
A Galilean beam expander uses a diverging lens followed by a converging lens, separated by the difference of their focal lengths. It is compact and avoids an intermediate focal point, making it preferred for high-power lasers. A Keplerian expander uses two converging lenses separated by the sum of their focal lengths, creating an intermediate focus that can be used for spatial filtering but poses a risk for high-power beams.
This calculator computes the output beam size for any magnification, the resulting divergence reduction, Rayleigh range improvement, and (when focal lengths are provided) the total system length and lens specifications. The magnification comparison table helps you choose the optimal expansion ratio for your application.
Use this calculator when you need to choose an expansion ratio that actually improves propagation or focusing instead of just making the beam look bigger.
It is useful for laser benches, machine vision, alignment tools, and long-range optical systems where divergence, lens spacing, and beam diameter all need to be balanced together.
Output beam radius: w_out = M × w_in. Output divergence: θ_out = θ_in / M. Lens relation: f₂ = M × f₁. Galilean length: L = f₂ − f₁. Keplerian length: L = f₁ + f₂.
Result: 5 mm output radius, 0.0403 mrad divergence
A 5× Galilean expander increases a 1 mm radius beam to 5 mm while reducing divergence from 0.201 mrad to 0.040 mrad — a 5× improvement.
Beam expanders are usually chosen from the system requirement backward: target spot size, allowable divergence, and available clear aperture. Once you know how much collimation improvement you need, the magnification and lens spacing become much easier to choose.
Do not optimize only for magnification. A larger beam can clip on small optics, overload mounts, or create alignment sensitivity that is worse than the original divergence problem. In Keplerian systems, also account for the intermediate focus because that is where contamination and optical damage tend to show up first. Mechanical clearances and optic coatings still need to be checked after the geometric design looks acceptable.
Galilean is preferred for high-power lasers (no intermediate focus) and is more compact. Keplerian allows spatial filtering at the intermediate focus and inverts the beam.
No. It redistributes the same power over a larger area, reducing intensity (W/cm²). This is useful for staying below damage thresholds of downstream optics.
The product of beam size and divergence is conserved (beam parameter product). Increasing the size necessarily decreases the divergence by the same factor.
It depends on your application. For long-range propagation: maximize M. For focusing: match the expanded beam to the focusing lens diameter. Typical values: 3×–20×.
Yes. Running a beam expander backwards reduces beam size and increases divergence. This is sometimes used to couple laser beams into optical fibers.
The Rayleigh range scales as M² (beam size squared), so a 5× expander increases it by 25×. This dramatically extends the collimated propagation distance.