  In paraxial approximation, the electromagnetic eigenmodes inside an optical
microresonator can be derived from a Schr\"odinger-type eigenvalue problem. In
this framework, tilting the cavity mirrors effectively introduces a linear
potential to the system. In our work, we apply solution strategies for inverse
problems to precisely determine and control the relative orientation of two
mirrors forming an optical microcavity. Our approach employs the inversion of
the Schr\"odinger equation to reconstruct the effective potential landscape,
and thus mirror tilts, from observed mode patterns. We investigate
regularization techniques to address the ill-posed nature of inverse problems
and to improve the stability of solutions. Our method consistently achieves an
angle resolution of order 100 nanoradians per measurement.
