Inverse problems for microcavity tilt readout

Inverse problems in physics involve deducing system causes from observed effects, presenting challenges due to potential ill-posedness. Regularization techniques, addressing errors and instability, are vital in solving these problems, often combining analytical and numerical methods.

In this work we want to inversely solve a Schrödinger equation to deduce the potential inside an optical microcavity. We apply this method to read out and stabilize the angular orientation of the two mirrors comprising an optical microcavity.

To do so we observe mode patterns inside the microcavity and utilize key properties of the Schrödinger equation. We introducing and compare different regularization methods for efficacy assessment.