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My questions has two parts:

First of all let's assume I have a gaussian beam and I send it through a telecentric f-$\theta$-lens (e.g. http://specialoptics.com/products/scanning_confocal.html) with no tilt, just a long the optical axis , is it justified to assume a propagation of the gaussian beam as it would be with an equivalent thin lens?

Second part: If so actually scan (tilt) the beam, how can I relate things like beam divergence, waist etc. to the incoming beam, if I assume that I do not clip it at the entrance pupil of the f-theta-lens.

My questions arise , because I a) do not really know which parts are included in an f-theta lens and b) if there is a method analogue to transfer matrices to propagate tilted gaussian beams.

Many Thanks

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So long as your lens diameter at every plane of interest (stops) is larger than, e.g., the $1/e^4$ diameter, you'll maintain a nice gaussian beam shape. -- at least, assuming a nondiverging source beam.

Beyond that, I fear you'll want to get hold of Zemax or equivalent to see exactly what happens to your beam shape.

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