LOTTTTUCE: Layer Oriented Tip-Tilt Turbulence Tomography using Covariance and Elevation

LOTTTTUCE is based upon the fact that turbulence at the pupil produces correlated tip-tilt motion over the entire field (averaging the tip-tilt across the widest field possible gives the strength of the turbulence at the telescope), while the on-axis (any axis) image motion measures the integrated tip-tilt over the line of sight (single stars provide the variance of the tip-tilt, which allows to infer the integrated seeing). Between these two extremes, the amount of correlation across a given field size is the integral of the turbulence from the ground to the altitude where the tip-tilt decorrelates over the meta-pupil. Differentiating the altitude- integrated tip-tilt with respect to altitude generates an estimate of tip-tilt (hence turbulence, assuming Kolmogorov properties) at each altitude. Alternately, the 3D Fourier transform of a data cube containing the time evolution of the tip (or tilt) across the field allows to determine the amount of energy for "field" frequencies (in other words, the integrated seeing across each same size patches) and the temporal spectrum of each of these features. Differentiating the spectrum with respect to spatial frequency would provide the amount of energy, as well as speed and direction, of each layer. The LOTTTTUCE method is a novel method of measuring the vertical turbulence profile that uses wide field tip-tilt information such as that provided by Pan-STARRS. However, the method also has limitations due to tip-tilt decorrelation as a function of meta-pupil overlap, finite outer scale, and non-Kolmogorov power spectrum.