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Astronomical telescopes with increasingly large apertures are required to upgrade the limit of diffraction and collect the light efficiently for the purpose of observing fainter and more remote objects with higher angular resolution. However, it is universally believed that traditional techniques of manufacturing, polishing and measuring large glass mirrors will soon face some practical challenges. Therefore, 10-m class or larger ground-based telescopes will need to employ arrays of several smaller segments to assemble into a large primary mirror. For a telescope with segmented mirrors, the piston errors between segments must be adjusted to nearly zero according to the requirements in order to be integrated into a single optical surface, which is known as co-phasing. One of the current co-phasing techniques, which has been successfully applied to Keck telescopes, employs an integration of edge sensors to detect the mirror shapes in real time with an optical phasing sensor to offer zero references for these sensors regularly. Another technique is demonstrated by use of a pyramid wavefront sensor (PWFS) to align and co-phase segmented mirrors in an active control close-loop with a single measurement. The co-phased best flat positions of segments are used as the zero references in order to measure the interaction matrix between the PWFS and the segmented mirrors. So it must be addressed that how the zero co-phasing reference is calibrated with high precision in a large capture range on the issues of co-phasing segmented mirrors. The current methods either lack accuracies, or just measure piston errors correctly in a small range. In order to solve the problem, a zero co-phasing reference calibration method based on dispersed interferogram is proposed. Specifically, the idea of the method is to define an appropriate cost function which is used to evaluate the piston errors between segments. Then it will be easy to determine the zero co-phasing reference position while all the cost function values are calculated based on the dispersed interferogram data with different piston errors inside the capture range. The proposed cost function is defined as the sum of the ratios of the second peak to the third peak of each of the columns of the two-dimensional dispersed interferogram, whose intensity distribution is along the dispersion direction. The precision and dynamic range of the method are analyzed theoretically and studied by simulations. Furthermore, the optical experiment is set up to demonstrate the efficacy of the method. In the experiment a scanning procedure is applied to one mirror and the dispersed interferograms between two mirrors with different piston errors are obtained. And then, the cost functions of these dispersed interferograms are computed through which the zero co-phasing reference position is located. The experimental results prove that the zero co-phasing reference between two mirrors can be calibrated within an accuracy of about 10 nm by making use of the proposed method. In addition, the novel method solves the problem of 2 ambiguity. Besides its sub-millimeter level wide capture range, this new co-phasing detecting method provides a helpful reference for relevant studies.

For the Fizeau optical interferometric telescope system, the co-phasing detection of piston errors between sub-apertures plays an important role in realizing the high resolution of system. In this paper, the relationship between piston error and the main peak displacement of monochromatic interferogram of two sub-aperture system is analyzed based on physical principles, then the piston error detecting method is developed and clarified based on their linear relationship in the range of one wavelength. Furthermore, an innovative co-phasing detecting method based on grating dispersed interferogram with bandwidth light source is proposed, and its feasibility, detecting precision and dynamic range are analyzed in theory and studied in simulation. The results prove that with this method, the piston error between the two sub-apertures of the system can be soundly detected and its measuring error is less than 20 nm while the piston error is not more than 50 μm. In addition, the novel method solves the problems of 2π ambiguity and direction determination that might exist within some other detecting methods. Besides its millimeter level dynamic range, this new co-phasing detecting method provides a new way and an effective reference for in-depth research of co-phasing detecting techniques.