Measurement of alignment parameters in spherical segmented-mirrors using novel algorithm and advanced phase unwrapping method

One of the present trends in telescope design is the use of segmented primary mirrors. One major challenge in the design of this type of mirror is the achievement of proper segment positioning, as they have to be properly aligned to make the system work as one mirror. Aiming at the co-phasing of segmented spherical mirrors, an advanced phase unwrapping algorithm based on branch set algorithm is presented. The Hough transform is used to obtain the edge of each segmented-mirror. Then the individual segments of one interferogram can be processed at one time. A new equation to calculate tilt, tip and piston of segmented spherical mirror is presented. The algorithm is based on the character of oblique spherical mirror which turns around any axis in different position and different angle. Therefore, the method is useful to obtain each segmented spherical mirror's position and orientation. Moreover, an equation used to calculate alignment parameters of the segmented parabolic mirror is presented following the same idea. In the experiment, a mounting device which allows tilt, tip and piston movement of the segmented-mirror is designed. And the phase of the whole system is obtained with a FISBA phase shifting interferometer. The experimental results show that the piston error is less than 10 nm and the tilt/tip error is less than 0.09 sec. The method can be used to calibrate the spherical segmented-mirror system.