Misalignment measurement of membrane diffractive telescope segments by means of edge sensors with form closure

The membrane diffractive telescope is an alternative to future 10-meter class space telescopes due to its possible lower cost of manufacturing and launching. To actively control the misalignment, the edge sensor network is utilized to measure the relative in-plane motions as well as out-of-plane motions of neighboring segments. The measurement is vulnerable to noise and malfunction of sensors. We first model the segment kinematics, which is used to simulate the propagation of sensor error to the segment configuration error. Monte Carlo simulation results show that the sensor error is considerably accumulated in the configuration error, which follows approximately normal distribution. On the other hand, the ring-arranged segments imply the form closure with redundancy of edge sensors. It is employed to judge whether there are abnormal sensor readings and then to identify the malfunctioning sensors. A better estimation can further be obtained as correction to the abnormal readings. Simulation results show that without sensor error, the algorithm in most cases can identify two malfunctioning in-plane sensors and two malfunctioning out-of-plane sensors. While considering the sensor error, only one malfunctioning in-plane sensor and one malfunctioning out-of-plane sensor can be identified with a sufficiently big ratio of abnormal reading to the normal sensor error.