Tomographic alignment algorithm for an extremely large three-mirror telescope: invisible modes

We analyze the optical effects due to distortions of a three-mirror telescope that is sufficiently large that all three mirrors must be actively controlled. Numerical experiments on telescopes with both monolithic and segmented primary mirrors reveal the existence of telescope misalignment configurations (modes) that are invisible to a fixed focal station wavefront sensor, even for highly redundant multidirectional tomographic measurement schemes. We describe these modes and give a theoretical explanation for them.