# SAR Image Focus Errors due to Incorrect Geometrical Positioning in Fast Factorized Back-Projection

[Licentiatavhandling]

Synthetic Aperture Radar, SAR, is an aperture synthesis technique to generate an image of the ground from air or space with high resolution. Signal processing is performed in frequency domain with Fourier Transform techniques, or in time domain with Back Projection techniques. The advantage of Back-Projection processing is that any aperture shape can be handled and the processing can be performed in real time. The Fast Factorized Back Projection algorithm, FFBP, is also computationally efficient and comparable to Fast Fourier Transform methods. When the resolution is near wavelength size the FFBP algorithm is dependent on accurate positioning data and topography information to avoid defocusing due to range errors. Other SAR image formation methods can use an autofocus method to relax the demands on the positioning data or to remove residual phase errors after the image formation. However, none of the existing autofocus methods will fit the way FFBP is executed. Thus a new autofocus method which will be integrated with FFBP is needed.

This thesis is focused on the analysis of different range errors that can occur in one merging step in the FFBP processing and how they can be avoided or corrected, topography errors as well as aperture errors. The analysis of aperture geometry errors is built on coordinate transformation matrixes which can be used for every type of geometry error to calculate the corresponding image shift at any location in the image. A few illustrating examples of aperture geometry errors have been analyzed and a method to track the geometry error by measuring the image shift is presented.

It is concluded that defocusing due to topography errors will only arise when the subapertures are not co-linear. The defocusing increases with the angle between the subaperture directions, the subaperture length and the size of the topography error. An expression of the accuracy of topography data needed to preserve the focus for different aperture sizes and subaperture tilts is presented.

Different subaperture geometry errors will differently give rise to image shifts in the resulting image. As long as there is contrast in the scene such that image shifts can be accurately determined, a focusing preserving processing geometry can be found by correlation measurements. The estimated geometry can differ from the true geometry relative to the ground. If this is the case, the image will be distorted but still be focused which means that the estimated image is just another view of the true image. Image distortions can also be detected with correlation measurements between subaperture images but only if one image is distorted differently than the other.

**Nyckelord: **SAR, Back-Projection, Autofocus, range distortions, topography effects

Denna post skapades 2008-05-20. Senast ändrad 2008-06-04.

CPL Pubid: 71084