Simulation and experimental study of the OTF based alignment and phasing of segmented mirrors

For a segmented mirror telescope, the desired resolution can only be achieved when all the segments are precisely co-aligned, co-focused and co-phased. The process of minimization of the piston errors is called co-phasing, which is one of the most stringent tasks in handling the segmented mirror telescope. The OTF based phasing technique samples light from the center of the segments, which is re-imaged on the detector plane, forming a fringed PSF. The Fourier transform of the PSF gives the OTF, which carries information about the piston and tip/tilt errors of the segments. The phase part (PTF) of the OTF can be primarily utilized to extract segment tip-tilt and piston errors lesser than ±λ/4, whereas, the magnitude part (MTF) can provide piston measurements up to a few hundreds of micron. To study the OTF technique in detail, we have developed a Python-based simulation code, that can generate realistic PSF images for the OTF based phasing system under practical conditions. It takes into consideration all the external effects, such as the stellar magnitude and spectral type, atmospheric turbulence and extinction, losses due to optics, and various noises. The OTF is also affected by the segment tip/tilt errors, and hence we have studied the effects of cross-talk between piston and tip/tilt errors on the measurements. In addition to these simulations, we have also conducted laboratory experiments so that the simulation results can be validated. In this paper, we present the results of our extensive simulations as well as experimentation.