Multi-tip/tilt errors simultaneous detection for segmented telescopes based on coherent diffraction

Astronomical observation requires more distant and fainter object with a better resolution, so that the larger primary mirror telescope is needed to ensure the better resolution and light energy collection. However, the diameter of monolithic primary mirror is limited due to the manufacturing and logistics limitations. The segmented primary mirror is taken as an alternative solution to break the limitation. The segmented primary mirror must be co-phased to accomplish a diffraction-limited imaging. In this paper, we put forward a new method to measure the tip/tilt errors between the segments in whole aperture simultaneously based on analyzing the intensity distribution and Fourier optics principle. We set a mask with sparse multi-sub-pupils configuration on the segments′ conjugate plane. A point source is taken as the object of the segmented telescope, the pattern focused on the CCD is recorded as the point spread function (PSF). Then, the Fourier transform is performed for the PSF and we can obtain the optical transfer function (OTF) which is composed of the modulation and phase transfer functions (MTF and PTF). Tip/tilt errors can be extracted from the PTF side-lobes. Simulation and preliminary experiments have been done to validate the feasibility of the method. The accuracy of the method is 6.344×10^-16λ(λ=632.8nm) RMS when the tip/tilt error is less than 0.4λ, and when the tip/tilt error is in the range of [0.4λ,2.4λ], the accuracy is 8.55×10^-15λ RMS. We also analyze the disturbance factor of the method in the simulation, including the piston error, the noise of the signal processing system, the surface shape error of the segments, etc. Furthermore, a preliminary experiment is built up to verify the 3 segmented system. This method has a higher detection efficiency and a lower hardware requirement which only needs a mask with sparse sub-aperture configuration.