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Focusing and Collimating

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Focusing and Collimating

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As a first example, we look at a common application, the focusing of a laser beam to a small spot. The situation is shown in Figure 1. Here we have a laser beam, with radius y1 and divergence θ1 that is focused by a lens of focal length f. From the figure, we have θ2 = y1/f. The optical invariant then tells us that we must have y2 = θ1f, because the product of radius and divergence angle must be constant.As a numerical example, let’s look at the case of the output from a Newport R-31005 HeNe laser focused to a spot using a KPX043 Plano-Convex Lens. This Hene laser has a beam diameter of 0.63 mm and a divergence of 1.3 mrad. Note that these are beam diameter and full divergence, so in the notation of our figure, y1 = 0.315 mm and θ1 = 0.65 mrad. The KPX043 lens has a focal length of 25.4 mm. Thus, at the focused spot, we have a radius θ1f = 16.5 µm. So, the diameter of the spot will be 33 µm.This is a fundamental limitation on the minimum size of the focused spot in this application. We have already assumed a perfect, aberration-free lens. No improvement of the lens can yield any improvement in the spot size. The only way to make the spot size smaller is to use a lens of shorter focal length or expand the beam.

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