Circularize an Elliptical Laser Beam
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Using a Pair of Cylindrical Lenses
It is easiest to think of this method as a telescope for one axis only.
InputD/OutputD=fl1/fl2 when the lenses are at fl1+fl2 distance apart.
If your laser beam is 2mm wide and 7mm tall and you want to get as close to round as you can.
You will align a cylindrical lens so the cylinder is on the wide axis. This will spread the beam. The second lens acts to re-collimate the beam.
It is easy to obtain cylindrical lenses in 25mm focal length increments from places like Edmund Industrial Optics. If you were to choose 25 mm and 75 mm you would be close at 1/3.
Placing these lenses at 100mm apart your beam would be re-collimated at 6mm x 7mm which is closer to cylindrical.
The laser beam does not care about the orientation of the lenses but the laser does, there are two ways to minimize the reflection back to the laser. One is to place the flat side of the lenses towards the laser and mis-align the lens so the back reflection misses the laser. The other is to place the convex surfaces towards the laser so the back reflection gets spread into a larger area. Which method you choose has to do with how close the lenses are to the laser.
Using a Pair of Anamorphic Prisms
This drawing shows an anamorphic prism pair expanding a single axis of a laser beam. It is also posible to reduce a single axis as well. Note: only one side of each prism needs to be AR coated if the laser beam is P-Polarized as the other is close to Brewster's Angle.
The two dis-advantages of this system is that the beam is displaced and it will only work on one axis if it is not AR coated on all faces.