Automatic Optical Alignment Using Projective Geometry
Aligning and maintaining complex optical beam paths is a central challenge across experimental science, because it is a high-dimensional task with strong cross-coupling between controls, often in systems with limited physical access. We present an automated hardware-software framework that resolves this alignment challenge using low-cost, retro-fittable motorized mounts driven by projective-geometry models and a photodiode-fed optimizer. A compact forward model describes the beam path to paraxial order with only the physical mirror angles left free, so it can be rapidly ($\sim$ms) numerically inverted to return the required mirror angles for a desired beam trajectory. A photodiode-fed optimizer then fine-tunes this geometric starting point, and converged mirror settings are tabulated for retrieval in milliseconds and actuation in seconds. We experimentally demonstrate the performance of this approach on a retro-reflected lattice atom-transport system, yielding improvements in both speed and precision over manual alignment. This framework reduces the manual effort required to align complex beam paths, enables programmable optical control in experiments with limited physical access, and enhances the scalability of complex optical architectures.