Accurate piston error detection unaffected by tip-Tilt error

Astronomical observation wants more distant and fainter object with a better resolution, larger primary mirror telescopes are needed to improve the diffraction limit and increase the collected light energy, but limited by monolithic primary mirror manufacture, testing, transportation and launch. And segmented telescopes can address these. However, segmented telescopes also introduce co-phasing errors. In this paper, we put forward a new method to measure piston error based on analyzing the intensity distribution and Fourier optics principle. This method can detect the piston error with a high accuracy in a larger capture when the residual tip-Tilt error still exists. 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). 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). Then we derive the relationships between the piston error and the MTF′s side-lobe peaks and we found that tip-Tilt error influences the accurate detection of piston error in term of the relationship. Thus, we take the MTF′s side-lobe peaks obtained when only tip-Tilt error exists as the normalized factor, then the influences of tip-Tilt error is removed. Simulation has been done to validate the feasibility of the method. The results state that this method's capture range is the operating light′s coherence length, the accuracy is 10.0nm RMS, preliminary experimental results also proved the assumption.