Some methods for reducing propagation-induced phase errors in coherent imaging systems I Formalism

The random phase errors induced in an electromagnetic wave propagating through turbulence in the troposphere and/or the ionosphere can degrade the performance of a coherent imaging system such as a synthetic-aperture radar. Several methods for removing or reducing these phase errors are described. Some of these methods, such as cubic-spline approximations with map drift and a deterministic technique based on a Legendre-series expansion of the phase error, are not new but are included for comparison. At least three techniques are (to our knowledge) new; a binary multiplexing scheme, a method using the Wigner–Ville distribution, and an optimal estimator based on the covariance matrix of the Legendre-series expansion coefficients. The method based on the Wigner–Ville distribution promises to be the most effective in reducing the deleterious effects of the phase errors on image quality.