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Beam Expander Calculator

Calculate lens focal lengths, system length, output beam diameter, and divergence for Keplerian and Galilean beam expander configurations.

A beam expander increases beam diameter by a factor M while reducing divergence by 1/M, using a pair of lenses separated by the sum of their focal lengths. Two configurations exist: Keplerian (positive–positive lens pair, real intermediate focus) and Galilean (negative–positive, no intermediate focus, more compact). This calculator determines both lens focal lengths, the physical system length, and the output beam diameter and divergence for a given expansion ratio and input beam. Use this tool when coupling to spatial filters, reducing laser beam divergence for long propagation paths, or increasing beam diameter to fill a large aperture.

Expander Parameters
Input Beam
Optical Design
Input lens f₁
25.0mm
Output lens f₂
125.0mm
System length L
150.0mm
Output Beam
Output diameter d_out
5.00mm
Output divergence θ_out
0.200mrad
Min. output lens aperture
6.0mm

Note: The Keplerian configuration has an internal focal point between the lenses, suitable for spatial filtering with a pinhole. Avoid with high-power pulsed lasers due to air breakdown risk at focus.

Abridged Optics — Beam Expander Calculator v1.0Keplerian: L = f₁+f₂. Galilean: L = f₂−|f₁|. θ_out = θ_in/M.

All information, equations, and calculations have been compiled and verified to the best of our ability. For mission-critical applications, we recommend independent verification of all values. If you find an error, please let us know.