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Question for the optics savvy in regard to beam expansion to reduce divergence.

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I'm finding it difficult to find cheap AR coated lenses of the correct focal length for use with beam expansion. However, I have an idea, when using a PCX lens which is too small for the size of the spot hitting it, at its focal length, wouldn't the lens produce the reduced divergence of the spot size it is collimating, even if part of the beam were cut off due to the lens being too small?

To exaggerate the situation, what if I put a 2 inch diameter lens in front of a 6 inch spot, wouldn't that 2 inch lens produce the same divergence of a 6 inch expanded beam, except most of the light is cut off? I'm thinking this might be a way to produce a low divergence beam using a relatively small lens diameter and if the power is high enough, such as from a multimode diode, the trade-off might be advantageous, if not in terms of power delivered at an extreme distance, in terms of reduced size?

Any one know the answer to this? This isn't something I'm finding talked about anywhere yet. Perhaps because it is a hair brained idea and won't work?

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