Image plane wavefront sensing and Kalman filtering for automated alignment of off-axis aspherics.

Abstract

Automated alignment can significantly increase optical system precision and flexibility, and reduce time and labor costs in system setup and maintenance. We present an automated alignment technique on a double off-axis parabolic mirror system, which poses challenging alignment problems due to the mirrors' high sensitivity to aberrations, rotational asymmetry, and non-orthogonality in stage adjustments. In our methodology, we use focal plane wavefront sensing to eliminate the non-common path error, increase optical throughput, and reduce cost and system complexity. We incorporate model-based optimal estimation and control to better handle the nonlinearity, model uncertainty, and noise. Using either an iterated extended Kalman filter or a square-root unscented Kalman filter as the optimal nonlinear misalignment state estimator, we are able to consistently reduce the linear misalignment from around 1mm to <5µm and the angular misalignment from around 500 to <6a r c s e c in simulation, achieving a final wavefront error of <5∗10-5 waves in the field of view when tested at wavelength 635nm. We discover a multi-state coupling effect, which implies that different misalignment states have compensating effects on system measurements, thus interfering with the estimator's observation of misalignment state changes. We further investigate the coupling's effects on alignment quality through observability analysis.