Telescope Alignment From Sparsely Sampled Wavefront Measurements Over Pupil Subapertures

Alignment of two-element telescopes is a classic problem. During recent integration and test of the Space Interferometry Mission s (SIM s) Astrometric Beam Combiner (ABC), the innovators were faced with aligning two such telescope subsystems in the presence of a further complication: only two small subapertures in each telescope s pupil were accessible for measuring the wavefront with a Fizeau interferometer. This meant that the familiar aberrations that might be interpreted to infer system misalignments could be viewed only over small sub-regions of the pupil, making them hard to recognize. Further, there was no contiguous surface of the pupil connecting these two subapertures, so relative phase piston information was lost; the underlying full-aperture aberrations therefore had an additional degree of ambiguity. The solution presented here is to recognize that, in the absence of phase piston, the Zygo measurements primarily provide phase tilt in the subaperture windows of interest. Because these windows are small and situated far from the center of the (inaccessible) unobscured full aperture, any aberrations that are higher-order than tilt will be extremely high-order on the full aperture, and so not necessary or helpful to the alignment. Knowledge of the telescope s optical prescription allows straightforward evaluation of sensitivities (subap mode strength per unit full-aperture aberration), and these can be used in a predictive matrix approach to move with assurance to an aligned state. The technique is novel in every operational way compared to the standard approach of alignment based on full-aperture aberrations or searching for best rms wavefront. This approach is closely grounded in the observable quantities most appropriate to the problem. It is also more intuitive than inverting full phase maps (or subaperture Zernike spectra) with a ray-tracing program, which must certainly work in principle, but in practice met with limited success. Even if such classical alignment techniques became practical, the techniques reported here form a reassuringly transparent and intuitive check on the course of the alignment with very little computational effort.