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Laser Beam Expander Calculator
Calculate the output beam diameter and divergence reduction produced by a laser beam expander of a given magnification.
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mrad
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What a beam expander does
A laser beam expander increases the diameter of a collimated laser beam while proportionally reducing its angular divergence, which is useful for long-range applications, tighter focusing, and reducing beam spread.
The formula
Output beam diameter Dout = Din × M, where M is the expander’s magnification. Because etendue (the product of beam size and divergence) is conserved in an ideal optical system, output divergence θout = θin / M — expanding the beam by M times reduces divergence by the same factor.
This is the standard ideal (lossless, aberration-free) beam expander relationship used for first-pass optical system design.
Last reviewed August 2026