Alignment of multi-mirror telescopes with computational vector fiducials and reverse optimization

This study presents a computational vector fiducial deflectometry method for aligning multi-mirror telescopes. The method is demonstrated on both a Cassegrain and a three-mirror off-axis system, with experimental validation performed for the Cassegrain case. Computational vector fiducial patterns are customized for each telescope configuration, and misalignments are interpreted using Zernike gradient vector polynomials. Component sensitivities of the degree of freedom are analyzed, and suitable polynomial bases are identified to characterize misalignment. Simulations with arbitrary misalignments confirm that the method is applicable to both the Cassegrain and the three-mirror off-axis systems, improving the wavefront error from PV=27 λ to PV=0.45 λ for the LAF-TMS case. An experimental alignment of the Cassegrain telescope further verifies the feasibility of the approach, yielding a successful result in obtaining wavefront errors with PV=0.84 λ and MS=0.18 λ . These results highlight the feasibility of the vector fiducial deflectometry and reverse optimization as a systematic method for multi-mirror alignment.