O Mirror, Where Art Thou?

Abstract

Wavefront sensing reveals that a telescope is misaligned, but not which mirror moved or by how much; inferring the mirror positions themselves turns alignment into a direct correction. We describe a simulation framework for inferring telescope mirror misalignment from multi-field Point Spread Function (PSF) measurements projected onto Circular-Bessel and Zernike basis vectors. Two case studies are presented: a Hubble Space Telescope model with five secondary-mirror degrees of freedom and a three-mirror anastigmat with ten primary and secondary mirror degrees of freedom. In both cases, field-dependent multivariate Gaussian likelihoods are explored with nested sampling and refined with differential evolution. Recovered states are validated with residual PSF images and optical path difference (OPD) measurements. In the Hubble benchmark, differential evolution recovers injected misalignments to less than 0.01 microns and reduces on-axis OPD error from 2.3 waves to 3 x 10E-8 waves. In the TMA study, the posterior shows broad marginals and correlated parameter pairs that suggest partial degeneracies at higher dimension; differential evolution recovers the truth alignment state less precisely than in the Hubble benchmark (less than 17 microns) and reduces on-axis OPD error from 8.24 waves to 2 x 10E-3 waves. This generalizable algorithm enables direct sensing of the state of an optical system and automated alignment.