An Analytic Expression for the Phase Noise of the Goldstein–Werner Filter.

Interferogram filtering for noise reduction is a key to many radar interferometric applications. Repeat pass radar interferometry often uses data with less than ideal correlation levels resulting from either long spatial or temporal baselines or changes between observations leading to high levels of temporal correlation. To maximize the utility of such pairs filtering the interferogram to get maximal noise reduction is often needed. One technique that has proved quite useful in the geophysical community is power spectral or Goldstein–Werner filtering of the interferogram whereby a power-weighted version of the Fourier transform is used to enhance fringe visibility. Although this paper defining the filter briefly touched upon the spatial resolution and noise reduction induced by the filter, it did not provide a useful formula for predicting the phase noise after filtering. This paper derives a formula for the phase noise obtained from power spectral filtering albeit under the restriction of several simplifying assumptions to make the problem analytically tractable. In particular, it is assumed that the interferometric phase is locally well approximated by a linear phase ramp with nonlinear phase perturbations small in a spectral energy sense compared to the linear term. [ABSTRACT FROM AUTHOR]