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I am trying to estimate the output angles for the following optical setup.

[Only for Risley Prism]

According to this source here (first orientation setup), the output beam is parallel to the optical axis, if the incoming beam is also parallel. But how do I get a parallel beam at the output for the arbitrary incident angles? The rotation of one prism compared to the other will deviate the ray from the optical axis. Should I rotate the prisms(both) in the opposite direction to compensate for the deviation? Is there a general mathematical model for arbitrary angles?

PS: I want to manipulate the rotation of the Risley prism so that I get a normal incident beam at the beamsplitter.

My setup

Rima
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