Two-Dimensional Autofocus Technique Based on Spatial Frequency Domain Fragmentation

Existing two-dimensional (2D) autofocus algorithms, exploiting the known structure of 2D phase error, lack the error estimation accuracy in the case of a low signal-to-noise ratio (SNR) due to the non-exhaustive use of the echo signal. In this paper, we propose a novel 2D autofocus algorithm, thoroughly utilizing all the available data and therefore achieving superior estimation performance. Via analytical study, we show that the partial derivative of the 2D error with respect to the azimuth frequency is approximable as a function of single argument, after appropriate change of variable. The established property enables a scheme for the azimuth phase error (APE) measurement, where the polar formatted data are fragmented along the range frequency and then aligned along the azimuth frequency, in order to equalize phase gradients in different fragments. On the one hand, such a scheme avoids the necessity to divide the full-aperture signal into subapertures, while on the other hand, it involves the whole signal support. Improved accuracy of the resulting estimate is achieved through the joint inter-fragment estimation of the APE gradient. The proposed algorithm, based on the mentioned scheme, was validated via computer simulations. The conducted experiments confirmed its preference against the existing techniques. The preference is particularly distinct for low SNR imagery.