Laser Beam Expander Calculator

Written by Great Medico

Updated September 25, 2026 •2 min read

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A laser beam expander result can look precise while still being wrong if one unit or convention is off. Optical calculations are unforgiving of unit and sign mistakes because wavelength, angle, focal length, and refractive index can change a result quickly. This page keeps the calculation focused so the number is easy to trace back to the values you entered.

What this calculator does

The Laser Beam Expander Calculator turns Image lens’ focal length (fᵢ), Objective lens’ focal length (fₒ), Input diameter (Dᵢ) into the page’s magnifying power using the specific relationship described below. Supporting values appear only where this calculator derives them, which makes the headline easier to audit against the same model.

How to use it

Start with the fields that drive this result: Image lens’ focal length (fᵢ), Objective lens’ focal length (fₒ), Input diameter (Dᵢ), Input divergence (Θᵢ), Distance from the expander (L). Use the unit menu beside each quantity instead of converting by eye; the page normalizes supported units before calculating. Then change one value at a time and watch whether the headline and supporting values move as the formula predicts.

How the calculation works

The current beam-expander model uses magnifying power MP = |fₒ/fᵢ|. Output diameter is Dₒ = MP·Dᵢ and output divergence is Θₒ = Θᵢ/MP. It also estimates beam diameter after distance L as Dₗ = Dₒ + L·tan(2Θₒ). The page separately shows magnification as 1/MP.

Example

Using the default example on the page (Image lens’ focal length (fᵢ) = 25 m; Objective lens’ focal length (fₒ) = 150 m; Input diameter (Dᵢ) = 2 m; Input divergence (Θᵢ) = 0.4 mrad), the calculator returns magnifying power of 6 ×. A modest change to one driving input should move the answer in the direction predicted by the equation, which is a useful unit check.

How to interpret the result

Read the magnifying power as the optical quantity defined by this page, not as a general rating of image or beam quality. Keep the displayed unit attached, and compare cases only after checking that angles, distances, wavelengths, and refractive indices use the same convention.

Limitations and notes

Real optical systems can add aberration, alignment error, finite bandwidth, diffraction, scattering, detector response, and component tolerances beyond the ideal relationship shown here. For this page, verify Image lens’ focal length (fᵢ), Objective lens’ focal length (fₒ) first; a wrong unit or convention there can outweigh any benefit from extra decimal precision. Critical design or acceptance work should still be checked against the applicable standard and measured data.