# Factors that make beam divergence worse after refocusing

A beam of light of width $W$ and wavelength $\lambda$ with divergence that is diffraction-limited is refocused with an optical element placed at a distance $D$ from the beam source. Will the refocused beam have worse divergence than the one imposed by diffraction limits? how much worse?

Is there an optical way to improve the beam divergence of the refocused beam? If a 2nd refocusing element, very similar to the 1st one, is placed on front of it, will the divergence get progressively worse? by how much?

Finally, does it matter if the beam is a Gaussian or Fresnel beam?

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