Tip-tilt phase measurement of probe using an optimized extended ptychographic iterative engine

Co-focus and co-phase detections are the primary means to achieve the desired resolution in segmented mirror and synthetic aperture telescopes. As a lensless phase retrieval method, extended ptychographic iterative engine (ePIE) has obvious advantages such as high reconstruction accuracy, simple optical path and operation, and shows great application potential in the above field. However, our research results in this work show that current ePIE algorithm cannot measure the phase of illumination probe when it contains a tip-tilt phase. Accurately measuring tip-tilt phase is a foundation and is highly valuable for phase measurement by this algorithm; otherwise, it will result in the failures of all phase measurements. An optimized ePIE algorithm was presented to measure the tip-tilt phase of the probe by optimizing the initial estimate of the tip-tilt phase and limiting the range of reconstructed probe. Its validity was demonstrated by both simulated and experimental results. As examples: in single probe experiments, the relative errors (REs) of the measured phases are 2.06% and 2.40% for the introduced real tilted angles of 0.4991° and 0.9983°, respectively; in a simultaneous double probe experiment, the REs are 1.84% and 1.61% for the above real angles, respectively. The impacts of the initial estimate and the range limitation on measurement result, and noise robustness, were analyzed by simulations. It can measure the tip-tilt phases of multiple probes simultaneously, and also measure the relative piston phase, providing a potential co-focus and co-phase detection method for segmented mirror telescopes, especially for sparse aperture telescopes.