Comparison of methods for the reduction of reconstructed layers in atmospheric tomography

For the new generation of extremely large telescopes (ELTs), the computational effort for adaptive optics (AO) systems is demanding even for fast reconstruction algorithms. In wide-field AO, atmospheric tomography, i.e., the reconstruction of turbulent atmospheric layers from wavefront sensor data in several directions of view, is the crucial step for an overall reconstruction. Along with the number of deformable mirrors, wavefront sensors and their resolution, as well as the guide star separation, the number of reconstruction layers contributes significantly to the numerical effort. To reduce the computational cost, a sparse reconstruction profile which still yields good reconstruction quality is needed. In this paper, we analyze existing methods and present new approaches to determine optimal layer heights and turbulence weights for the tomographic reconstruction. Two classes of methods are discussed. On the one hand, we have compression methods that downsample a given input profile to fewer layers. Among other methods, a new compression method based on discrete optimization of collecting atmospheric layers to subgroups and the compression by means of conserving turbulence moments is presented. On the other hand, we take a look at a joint optimization of tomographic reconstruction and reconstruction profile during atmospheric tomography, which is independent of any a priori information on the underlying input profile. We analyze and study the qualitative performance of these methods for different input profiles and varying fields of view in an ELT-sized multi-object AO setting on the European Southern Observatory end-to-end simulation tool OCTOPUS.