Temporal tomography: a new approach to tomographic adaptive optics

Traditional approaches to tomographic reconstruction in AO rely on the use of multiple wavefront sensors (WFSs). The altitude of the turbulence layers is inferred through the commonalities and differences in the wavefronts observed by each WFS. We present progress on a new technique we call "temporal tomography," based on the work behind predictive Fourier control. In the Fourier modal basis individual atmospheric layers have unique characteristic temporal frequencies. This means that temporal filtering of the data from a single WFS (e.g., through digital recursive filtering) enables the extraction of a single layer's contribution to the integrated wavefront. In doing this we can turn a complex multi-conjugate reconstruction into a series of relatively simple single-conjugate reconstructions. Moreover, the necessary parameters can all be extracted from a time series of Fourier modal coefficients, facilitating the use of data-driven techniques (e.g., machine learning). We present the results of end-to-end simulations to demonstrate this approach, as well as tests derived from archival ground layer AO telemetry data obtained by 'Imaka on the University of Hawaii 2.2m telescope.