A phase model using the Huber norm for estimating point spread function under frozen flow hypothesis

Abstract In astronomical observation and space exploration, the light of an object in the outer space is inevitably distorted by the atmospheric turbulence around the Earth before it reaches the ground-based telescope aperture. The target object so observed is degraded by unknown point spread functions (PSFs). Estimating the PSFs is thus crucial for ground-based astronomy. In order to know the PSFs, we first need to estimate the phase, i.e., the wavefront aberration of incoming light at telescope aperture. In this paper, under the frozen flow hypothesis, we propose a new model for estimating the phase in the case of single- and multi-layered atmospheric turbulence. The new model, which deploys the Huber norm as the regularizer, can be cast as a saddle-point problem and solved efficiently by existing well-developed optimization algorithms. We test a spatially-varying image deblurring problem by using the estimated PSFs, which demonstrates the compelling numerical performance of the new phase model.