Estimation of astronomical images from the bispectrum of atmospherically distorted infrared data.

Abstract

The uses of the bispectrum for recovering the images of one-dimensional infrared astronomical speckle data are examined in detail. An analytic model for the bispectral transfer function, the variance, and the covariance of the bispectrum are developed. The models are evaluated by Monte Carlo integration and the results are compared to sample estimates of the same quantities obtained from simulated data. For comparison, the same sample quantities are computed from observed data. The bispectrum is shown to be useful for determining estimates of the object phase. A recursive method which is used to obtain the object phase estimates is introduced. Since the bispectrum provides multiple estimates of each object phase, a number of methods for combining the multiple estimates are developed and compared. Many techniques have been proposed to determine the phase of images which have been atmospherically distorted. Among these techniques are the Knox-Thompson, and the Simple Shift-and-Add algorithms. These methods are compared to the bispectrum via an objective measure which is developed. Optimization techniques are used to great success. A model for the bispectrum of a binary star is developed and fit to the image bispectrum by the Levenberg-Marquardt algorithm for non-linear least squares. The ability of the algorithm to determine binary star parameters from the bispectrum is tested with both simulated and observed data. Since the bispectrum may not always be available, a method is developed which determines binary star parameters from the image Fourier transform. The full set of object phases and moduli are determined by use of the conjugate gradient and conjugate direction algorithms in the last section. Two starting points for each algorithm are employed. The first starting point uses the estimates of the object phases obtained from the recursive bispectrum technique. The second assumes no information is known about the object. The speed of convergence of each algorithm is analyzed and recommendations are made for future use.